final book
TRANSCRIPT
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Kuwait University College of Engineering and Petroleum Department of Industrial Engineering IE 496: Industrial Engineering Design Fall 2008
Leader: Hamid Al-Yousufi
Vice Leader: Alaa’ Aboelfotoh
Abrar Hajiya
Aisha Al-Roomi
Amal Al-Fouzan
Basel Nijem
Elaf Ashkanani
Farah Al-Doussery
Maryam Al-Qatami
Moneera Al-Fayyad
Moudi Al-Abassi
Nouf Al-Fraih
Shaikha Al-Dabbous
Shaima'a Dehrab
Sherifa Al-Fulaij
Zahra'a Amir
Supervised by: Prof. Mehmet Savsar
. Eng. Bedour Al-Saleh
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Acknowledgements
As I look at this book, finally printed and looking professional, I cannot help but remember all the pain
and misery that went into putting it all together.
I would like to thank and congratulate all my team members for their excellent contributions to
this project and a special thank you to Basel Nijem, who put up with my obsession of having
everything as perfect as possible. His tireless work in formatting this report made it a reality.
However, before writing this book became a remote reality, we had to navigate the many
presentations and deadlines set by our supervisor. None of this would have been possible without the
amazing dedication of our priceless vice leader, Ala’a Aboelfotoh. For all your hard work, and having
to put up with my insanity throughout the semester, thank you.
Gratitude is also due to the IMSE faculty at KU, who guided us when we were lost, and kept
making ever harder demands for the quality of our work.
The staff at the National Canned Food Production and Trading Company deserves the utmost
appreciation. They provided us with the data we needed whenever they could, and were friendly and
courteous to us during our visits.
To the families and friends of each and every member, a heartfelt thank you. Their love and
support (and teasing) kept us going when we were down.
Finally, I will not use the cliché that we hope you get as much pleasure from reading this book
as we got from writing it, because it was a nightmare to write.
Hamid Al-Yousufi
On behalf of myself and my group, I would like to thank our dear staff for their assistance in making
this design project a successful and pleasant one.
We are particularly grateful to the great management and staff at the National Canned Food
Production and Trading Company for all their assistance in providing us with the material required,
and taking time off their work to help us.
The coordination of all teams and the preparation of this report would not have been
successful without the endless efforts of our leader Hamid Al Yousufi. A special thanks goes to Basel
Nijem for his assistance in the editing and formatting of this report.
Finally, I would like to thank all members for their hard work and congratulate them on their
success. None of this would have been possible without the support of our families and friends to
whom we owe much.
Alaa Aboelfotoh
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Table of Contents
Introduction
1.1 Company Background ..................................................................................... 12
Products ............................................................................................................................14
1.2 General Problem Description .......................................................................... 15
Quality Control
2.1 Introduction ...................................................................................................... 18
Problem Description ............................................................................................................19
Objectives ..........................................................................................................................20
Solution Approach ..............................................................................................................20
2.2 Analysis of the As-Is System .......................................................................... 21
The Can Making Line ...........................................................................................................21
The Can Filling Line .............................................................................................................27
Local Lab ............................................................................................................................33
Central Lab .........................................................................................................................35
The As-Is Raw Material Sampling Plans ..............................................................................39
Quality Control Documentation ........................................................................................57
2.4 New Quality Control Documentation .............................................................. 73
2.5 New Sampling Plans ........................................................................................ 79
2.6 Proposed Double Sampling Plans For Beans ................................................ 88
2.7 Proposed New Single Sampling Plan for Tin Sheets .................................. 116
2.8 Proposed Double Sampling Plans For Tin Sheets ...................................... 123
2. 9 Conclusion ..................................................................................................... 151
Cost Analysis
3.1 Introduction .................................................................................................... 154
3.1.1 Problem Description .................................................................................................. 155
3.1.2 Objectives ................................................................................................................ 156
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3.1.3 Solution Approach .................................................................................................... 156
3.2 Analysis of As-Is System: ............................................................................. 157
3.2.1 System .................................................................................................................... 157
1. Suppliers .................................................................................................................. 158
2. Customers ................................................................................................................ 161
3. Missions and Goals of The National Canned Food Company ............................................ 161
4. Resources ................................................................................................................. 161
5. Output ...................................................................................................................... 163
6. Outcome ................................................................................................................... 163
7. Performance Measures .............................................................................................. 163
8. Decisions The National Canned Food Company Should Consider .................................... 163
3.2.2 Productivity Indices ................................................................................................... 164
1. Direct Cost ................................................................................................................... 164
Direct Labor Costs ......................................................................................................... 165
Direct Material Cost ....................................................................................................... 166
Equipment Direct Cost ................................................................................................... 177
2. Indirect Costs ................................................................................................................ 183
3. Overheads .................................................................................................................... 185
Technical Overheads ...................................................................................................... 185
Company Overheads ...................................................................................................... 186
Marketing Overheads .................................................................................................... 186
5. Variable Cost................................................................................................................. 188
6. Fixed Costs ................................................................................................................... 190
7. Total Cost ..................................................................................................................... 190
8. Total Revenue: .............................................................................................................. 191
9. Total Profit ................................................................................................................... 192
10. Productivity Analysis Results ......................................................................................... 195
11. Break Even Point ......................................................................................................... 195
4. New System ...................................................................................................... 198
A. Overfilling: ................................................................................................................... 198
B. Transportation Costs ..................................................................................................... 200
5. Conclusion ........................................................................................................ 212
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Production Line Analysis and System Maintenance
4.1 Introduction .................................................................................................... 216
Problem Statement ........................................................................................................... 218
Objectives ........................................................................................................................ 218
Solution Approach ............................................................................................................ 218
4.2 Part List ........................................................................................................... 219
4.3 Bill of Materials (BOM) ................................................................................... 220
4.4 Component Part Drawing .............................................................................. 221
4.5 Process Description ....................................................................................... 223
4.6 Process Flow on the Factory Layout ............................................................ 226
4.7 Operation Process Chart ............................................................................... 227
4.8 Route sheets ................................................................................................... 229
4.9 Data Collection and Fitting ............................................................................ 232
4.10 Maintenance Types ...................................................................................... 234
Corrective Maintenance (CM) ............................................................................................. 234
Preventive Maintenance (PM) ............................................................................................ 235
4.11 Maintenance Plan ......................................................................................... 236
Current Maintenance Plan ................................................................................................. 237
Proposed Maintenance Plans ............................................................................................. 239
Alternative 1 ................................................................................................................. 239
Alternative 2 ................................................................................................................. 241
Alternative 3: ................................................................................................................ 244
4.12 The Reliability of the Lines .......................................................................... 247
4.13 Results .......................................................................................................... 251
Can Making Line ............................................................................................................... 251
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Can Filling Line .................................................................................................................. 252
4.14 Availability of the Machines ........................................................................ 254
Inherent Availability (Ai): ................................................................................................ 254
Achieved Availability (Aa) ................................................................................................ 255
Operational Availability (Ao) ............................................................................................ 255
4.15 Spare Parts ................................................................................................... 257
4.16 System Simulation ....................................................................................... 260
Problem Formulation ........................................................................................................ 262
System entities .............................................................................................................. 262
Material handling system ............................................................................................... 263
Current Problems in the Layout ....................................................................................... 264
Work Schedule .............................................................................................................. 264
Scrap Estimate .............................................................................................................. 265
Policies ......................................................................................................................... 265
Simplification Assumptions ............................................................................................. 266
Coding the Arena Model of the As-Is System ........................................................................ 267
Explanation of the As-is Model of the Can Making Line ...................................................... 268
Can Filling line .................................................................................................................. 269
Explanation of the As-is Model of the Can Filling Line ........................................................ 271
Verification and Validation ................................................................................................. 273
Can Making Line ............................................................................................................ 273
4.17 Analysis of Daily Production Runs and Improvement .............................. 281
Can Making Line ............................................................................................................ 281
Can Filling Line .............................................................................................................. 287
4.18 Summary of the Proposed Alternatives ..................................................... 296
4.18 Conclusion .................................................................................................... 297
Inventory Management and Production Planning
5.1 Introduction .................................................................................................... 300
Problem description ......................................................................................................... 301
Solution approach ............................................................................................................. 302
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Methodology .................................................................................................................... 302
5.2 Analysis .......................................................................................................... 302
1- Demand forecasting ...................................................................................................... 303
2- Holt’s method ........................................................................................................... 304
Five Year Forecasts ............................................................................................................ 385
Economic Order Quantity (EOQ) for Production Planning ...................................................... 399
Economic Production Quantity (EPQ) for Production Planning ............................................... 405
Service Level .................................................................................................................... 412
5.3 Conclusion ...................................................................................................... 418
Supply Chain Management
6.1 Introduction .................................................................................................... 420
Warehouses' Locations .................................................................................................. 424
Distribution Network ....................................................................................................... 425
Current Average Demand and Costs .................................................................................... 428
Problem Statement ........................................................................................................... 429
Solution Approach ............................................................................................................ 430
6.2 Analysis and Studies ..................................................................................... 430
Study 1: Establishing a New Factory .............................................................................. 432
Study 2: Using New Trucks ............................................................................................ 437
Justifications for Study 1 and Study 2 ............................................................................. 442
Study 3: Increasing Capacity of Existing Factory ............................................................ 445
Study 4: Demand Increase ............................................................................................. 450
6.3 Conclusion ...................................................................................................... 455
Safety and Human Factors
7.1 Introduction .................................................................................................... 458
Problem Description .......................................................................................................... 459
Objectives ........................................................................................................................ 460
Solution Approach ............................................................................................................ 460
7.2 Safety and Human Factors ............................................................................ 461
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7.3 Hazard Categories .......................................................................................... 463
7.4 Worker interaction with machine and material ............................................ 465
7.5 Data Collection and Findings ........................................................................ 466
7.6 Quick-win Improvements ............................................................................... 473
7.7 Long-term Improvement ................................................................................ 474
7.6 Management Control ...................................................................................... 487
7.7 Conclusion ...................................................................................................... 491
Facilities Planning
8.1 Introduction .................................................................................................... 494
Problem Statment ............................................................................................................. 495
Objectives ........................................................................................................................ 496
Solution Approach ............................................................................................................ 496
8.2 Current Layout................................................................................................ 497
Departments ................................................................................................................... 497
Blue Print of Factory ....................................................................................................... 505
As-Is Layout ................................................................................................................... 506
8.3 Material Handling ........................................................................................... 512
8.4 Method 1: Relationship Diagramming (RDM) Method ................................. 520
8.5 Method 2: CRAFT ........................................................................................... 535
8.6 Comparison of Method 1 and Method 2: Massaged Layouts ..................... 538
8.7 Proposed Layout ............................................................................................ 545
8.8 Savings in Cost .............................................................................................. 546
8.9 Conclusion ...................................................................................................... 548
General Conclusion ............................................................................................. 550
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1. Introduction
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1.1 Company Background
The National Canned Food Production and Trading Co. was founded in 1985
as Kuwait’s only producer of canned and processed food, under the DANIAH brand
name and other local private labels, with a capital of 2,000,000 KD. Today it employs
over 100 people. It is a subsidiary of Mezzan Holding Co.
Figure 1.1: Mother company and subsidaries.
The company’s objectives are to produce high quality canned food with a minimum
number of defects on time to achieve customer and employee satisfaction.
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Products
The company produces three main products:
1. Aqua Gulf water.
2. Vinegar.
3. Canned Food (220g, 400g, 450g)
The Foul Medammes: Foul Medammes American Variety, Foul
Medammes with chili, Broad Beans, and Peeled Foul with chili.
Chickpeas: Chickpeas, Giant Garbanzo, with and without chili sauce.
Hommus Tahineh: Hommus Tahineh and Hommus Tahineh with garlic.
Peas: Green Peas, Mixed Vegetables, and Peas & Carrots.
Mushroom: Whole Mushrooms, Mushroom Pieces and Stems.
Olives: Black and Green Olives.
Corn: Whole Kernel Sweet Corn as well as new products such as Baby
Corn, and Corn Cream.
Sausages: Frankfurter Sausages, Cocktail Sausages and Beef Sausages.
Beans: Baked Beans in tomato sauce, Black Eye Beans, White Beans,
Red Kidney Bean, Red Kidney Beans with chili sauce, Butter Beans.
Figure 1.2: Products offered.
In this study, the production of the 400g cans was focused on since it comprises the
bulk of production. In addition, the company produces its own cans. The factory has
a separate line for Vinegar with which it produces White, Brown and Apple Vinegar.
The factory also trades in Premium Sauces, including Tomato Ketchup, Chili Sauce,
Hot Sauce, Extra Hot sauce, and Tomato Paste.
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1.2 General Problem Description
After thoroughly examining the factory and its operations, numerous, diverse
problems were identified. Table 1.1 provides a summary of the problems found. The
problems were categorized into an area of study within the Industrial Engineering
discipline and teams were formed to study and eradicate each of these problems.
Table 1 .1: Summary of the problems identified.
Names Area of Study General Problem Description
Hamid Al-Yousufi
Shaima’a Dehrab Quality Control
• Inadequate raw material sampling plans. • Poor quality documentation.
• Overfilling of cans during production.
Abrar Hajiya Human Factors and Safety • Unsafe working conditions.
Nouf AL Fraih
Amal AL Fouzan
Shaikha Al Dabbous
Cost Analysis • High overfilling and transportation costs.
Aisha Al-Roumi
Elaf Ashkanani
Moudi Al-Abassi
Zahra’a Amir
Simulation and Maintenance • Frequent machine failure. • Poor maintenance plans.
Farah Al-Douseri
Maryam Al-Qatami
Moneera Al-Fayyad
Sherifa Al-Fulaij
Production Planning and Inventory Control
• Company cannot meet the demand on time. • No specialized inventory plans in place.
• Lead time is relatively long for final product.
Alaa Aboelfotoh
Basel Nijem Supply Chain
• Company at risk of being unable to satisfy demand even with overtime production
hours.
Alaa Aboelfotoh
Basel Nijem
Nouf Al Fraih
Facilities Planning • Machines are too crammed, pathways are
obstructed, inventory spread throughout the factory and a lot of wasted space.
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2. Quality Control
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2.1 Introduction
When dealing with the food industry, there are many quality targets that need
to be met. These include such things as bacteria count, weight accuracy, etc.
The adequacy of the quality control system in place to achieve these targets
was considered, by studying each test separately and determining whether action is
needed to ensure the targets are being met. If a test returned a lot of negative
values, attention was focused on it, to try and eliminate its cause by conducting a
root cause analysis. The products being produced were also assessed to determine
whether they meet all these targets.
Furthermore, the raw material sampling plans in place were evaluated by
using such measures as the probability of acceptance, the average outgoing quality,
and the average total inspection. If any of the plans were found to be inadequate,
new, superior plans were developed.
Problem Description
After studying the current system in depth, three distinct problems were
identified. First of all, the cans are being consistently over filled. This is a source of
waste that will cause the company to lose money unnecessarily.
Secondly, the quality management system in place is inadequate as the
documentation is very poor and thus requires an immediate overhaul. In addition,
there seems to be lack of vigilance in applying quality control, and a disregard for its
importance. This could be due to the fact that the company is not aware of the costs
involved in poor quality.
Last but not least, some of the raw materials sampling plans in place require some
modifications in order for them to adequately discriminate between lots of suitable
and those of unsuitable quality.
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Objectives
The quality control documentation system shall be studied and optimized.
It shall be ensured that all the products adhere to all the specifications
required. If not, the problems causing a failure to meet these specifications
shall be identified and corrected.
New Sampling plans shall be developed that strike a balance between their
different properties, such as the probability of acceptance and the costs
involved.
Solution Approach
In order to rectify the problems discussed previously, and to achieve the
objectives set out, a root cause analysis was carried out to eliminate the over filling
problem, as well as to bring the cost of overfilling to the attention of the company to
educate the company as to the importance of proper quality control,. Furthermore,
new quality documentation was developed to maintain a high level of quality control
in the future. Finally, statistically reliable raw material sampling plans were proposed.
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2.2 Analysis of the As-Is System
The Can Making Line
The company produces its own cans. In this section, the can making line
processes, as well as the quality control procedures implemented for each, is
discussed.
1. Move a sheet metal box from storage to working area.
Note: Sheet metal boxes are stored nearby.
2. Open box manually.
3. Transport sheets to cutting machine manually.
4. Sheet is cut according to required size.
5. Ready sheets are transported to electrical welding machine manually.
Note: Feed rate: 160 sheets per minute.
6. Can is electrically welded.
Note: Copper used to strengthen current.
7. Welded can is transported to lacquering machine by conveyor belt.
8. Varnish is applied to welded section of the can.
9. Can is transported to the oven by belt.
10. Oven heats up glue to allow it to set properly.
11. Random inspection carried out on cans exiting the oven.
12. Can is transported to flanging machine.
13. Can is flanged at both ends.
14. Can is transported towards separator.
15. Distance between consecutive cans is set to a specific amount to complement
the speed of the seaming machine.
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16. Can is transported to seaming machine.
17. Lids fed into seaming machine to coincide with the arrival of the can.
Note: Lids are stored and fed manually into the seaming machine.
Note: 123,760 lids per box.
18. Lid is attached to the can using double seaming process.
Note: Cans arrive upside down to get sealed from below.
19. Can is transported to storage area.
Note: Due to the design of the conveyor belt, cans are turned upright during the
transportation to the storage area.
Note: Since the speed throughout the line is constant, the throughput is 160 cans per
minute
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Detailed description of the Can Making Line
Cutting
Process:
Tin sheets are taken from a box similar to the one shown in figure 2.1 which
contains 1200-1500 sheets, depending on the supplier, and manually moved to the
cutting machine shown in figure 2.2. Each sheet is cut into 32 blanks as seen in
figure 2.3, before they are manually arranged into piles on a table next to the welding
machine shown in figure 2.4.
Quality:
At the start of the production run, the cutting machine blades are checked by
producing thirty two blanks (that are used to manufacture the 400g cans) and
examining the edges to determine if they are smooth enough. If not, the blades are
sharpened. This is a qualitative test.
Figure 2.1: A box of tin sheets.
Figure 2.2: The cutting machine.
Figure 2.3: Sheets cut into 32
blanks.
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Welding
Process:
As depicted in figure 2.4, the tin blanks are fed manually into the welding
machine, where they are bent into a cylindrical shape. Electric currents are induced,
and are then strengthened by the presence of thin wires of copper, to weld the two
edges of the metal blank. The copper wires only help generate electricity and are not
part of the can itself.
Quality:
At the start of production, the first four cans are inspected by applying the Pull
Test, in which tension is applied to both sides before the can is checked for any
tearing.
During full production, two cans are taken every two hours and are subjected
to the same test.
Figure 2.4: Blanks being fed into
welding machine.
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Lacquering
Process:
The welded cans are moved using a conveyor belt from the welding machine
to the lacquering area shown in figure 2.5, where a varnish is applied to both the
outside and inside of the can’s welded area.
Quality:
The varnish is checked by applying sixty strokes of MEK (a solution similar to
paint thinner) to it. No rusting should occur.
Figure 2.5: The Lacquering area.
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Seaming
Process:
After cans are flanged on both sides, the cans are separated an even
distance and enter the seaming machine, where the bottom of the can is sealed
using double seaming. As can be seen in figures 2.6 and 2.7, the lids are stored
adjacent to the line. Double seaming is used to ensure that no microscopic bacteria
can invade its contents.
Quality:
After the seaming process, 8 cans are taken every hour, and the following
tests are carried out:
4 cans are manually inspected. If more than 35% of the cover hook consists
of wrinkles, the can is scrapped.
4 cans undergo the leak test, which is shown in figure 2.8, where the cans are
submerged in water and pressurized at 1.5-2 bar. The tank is then inspected
for the presence of bubbles, which would suggest that leakages are occurring.
Figure 1.6: Lids stored adjacent to the
seaming machine.
Figure 2.7: Lids coincide with the
arrival of the cans.
Figure 2.8: The leak test.
Figure 2.6: Lids stored next to the
seaming machine.
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The Can Filling Line
During the can filling process, the following variables/attributes are checked:
Dry weight
Net weight
Brine temperature
Application of labels
Soaking
Process:
The first step in the can filling line is soaking the beans in water in one to five
of the three ton tanks, depending on the demand, shown in figure 2.9. The beans are
usually left to soak for eight to fourteen hours, depending on the variety. This is
usually done during the night.
Quality:
A 100g sample is taken to check that soaking is correctly carried out. The
weight should double after soaking.
Figure 2.9: Soaking tank.
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Filling
Process:
Solid food goes through the reel washer, a hollow cylindrical pipe with
showers to wash the food. Next, the food is dropped into a bucket elevator which
takes it to the blancher. In the blancher, the food is boiled for about ten minutes to
remove any gases or enzymes, and then goes through a de-stoning process in
which foreign objects are removed. After de-stoning, the food is carried to a hopper,
a funnel-like tank, through bucket elevators. This helps regulate the flow of the food
to the next step. To guarantee good quality, a final manual inspection is done after
the de-stoning process. One layer of the food passes through workers on a
conveyor. The workers check for any defects, such as darkly colored or mashed
pieces, or tiny pieces of wood. After this, the food is again taken to another hopper
using bucket elevators. At this point, the can making line and the can filling lines
meet. The empty cans are washed, filled with food in the solid filling machine shown
in figure 2.12, and then filled with brine (salted water solution) by the liquid filling
machine.
Quality:
As shown in figures 2.10 and 2.12, cans are checked at the start of production
and the filling machine is calibrated accordingly until the nominal value is met. Once
the line is operating properly, 10 cans are checked every 30 minutes. If any errors
occur, the machine is calibrated again.
Figure 2.12: The solid filling
machine.
Figure 2.10: Dry
weight being
checked.
Figure 2.11: The dry
weight meets the nominal
value.
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Seaming
Process:
Figure 2.13 shows cans going through the seaming machine where the top is
seamed using double seaming.
Quality:
Before the seaming process, a built-in thermostat checks the temperature of
the brine. The temperature should not fall below 75 ˚C.
After the seaming process, 8 cans are taken every hour, and the following tests are
carried out:
4 cans are manually inspected. If more than 35% of the cover hook consists
of wrinkles, the can is scrapped.
4 cans undergo the leak test, where the cans are submerged in water and
pressurized at 1.5-2 bar. The tank is then inspected for the presence of
bubbles, which would suggest that leakages are occurring.
Figure 2.13: Cans going through the
seaming machine.
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Coding
Process:
The production date and time are stamped onto the cans. Figure 2.5 shows some
cans that have been stamped. The ink used cannot be erased.
Quality:
Since faulty coding would be extremely expensive; before production, one can of
each product to be produced during the day is coded to make sure that the codes
are correctly applied.
Figure 2.14: Coded cans.
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Cooking
Process:
The cans are cooked for between 10 and 70 minutes depending on the type
of product.
Quality:
Following the cooking in the retort area shown in figures 2.15 and 2.16, 2
cans from each cycle are taken and are qualitatively checked for the following
attributes:
Color
Taste
Texture
Appearance
Figure 2.15: The ovens in the retort area. Figure 2.16: Monitors to control
the cooking process.
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Labeling
Process:
Labels are applied to the cans depending on the product and the brand as
shown in figures 2.17 and 2.18
Quality:
All cans going through the labeling machine are inspected to ensure that the
labels are correctly applied. If labels are incorrectly applied, they are cut off and the
can is re-labeled.
Finally, after labeling, eight cans are sent to the municipality for health related
checks. A further four cans are retained as a sample to check against future
complaints.
Figure 2.17: Labels being inspected. Figure 2.18: A stack of labels.
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Local Lab
All the tests carried out in the local lab shall now be discussed. They are split
into chemical and physical tests.
Chemical Tests
Acidity Test
10 ml of brine is measured using a measuring cylinder and is diluted by using
100 ml of distilled water. Then the mixture is deposited in a conical flask before three
drops of Phenolphthalein is added. Finally, NOH soda drops are added until the
mixture changes color to purple as shown in figure 3.0, indicating that it has become
neutral.
PH Test
The PH meter shown in figure 2.20 is inserted into a bottle containing the
brine and its PH is indicated on the display. A PH of 7 indicates its neutral, below 7 is
acidic and above 7 is basic.
Figure 2.19: The mixture
turns purple when neutral.
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Brix Test
A few drops of brine are deposited on the brix meter shown in figure 2.21, and
is then examined visually as in figure 2.21 and 2.22, to determine how much solid
precipitation of minerals is present.
Physical Tests
Weight Checks
The net and drained weights are measured as can be seen in figures 2.24,
2.25 and 2.26. The net weight should not be below 400g but should not exceed
430g.
Figure 2.21: The brix meter.
Figure 2.22: Using the brix
meeting to test the brix
content.
Figure 2.23: The display of the
brix.
Figure 2.24: Equipment for
measuring the net and drained
weights.
Figure 2.25: Measuring the
drained weight.
Figure 2.26: Measuring the net
weight.
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Central Lab
Receiving the Samples
Samples are received in the central lab and stored in the area shown in figure
2.27. They are transported in the coolers shown in figure 2.28 to avoid defrosting
during the tri. When the sample is to be tested, it is divided into parts and some of it
is stored in a refrigerator for retesting in case there is a problem with the findings of
the initial test. The refrigerator shown in figure 2.29 is used to store media to be used
in the microbiology tests.
Figure 2.27: The entrance
to the sample sotrage area.
Figure 2.28: The coolers
carrying the samples.
0
Figure 2.29: Refrigerator
storing the test media.
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Media Preparation
As can be seen in figure 2.30, the media are bought in powder form and are
stored until needed. Figure 2.31 shows the instructions on the container to help
prepare the medium using some certain solutions, some of which are shown in figure
2.32. The medium is then heated before it is inserted in the machine in figure 3.33,
called the autoclave. Finally, the medium is placed in a Petri-dish and stored until it is
needed as shown in figure 2.34.
Figure 2.30: The powder
media stored.
Figure 2.33: The autoclave
Figure 2.31: Instructions for
preparing the media.
Figure 2.34: The petri dishes
Figure 2.32: Liquid
solutions used in
preparing the media.
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Figure 2.35: The buffer
solution.
Microbiology Tests
A 10g sample is diluted using 100ml of the buffer solution shown in figure
4.35, and it is then placed in the incubator shown in figure 4.36 for 2 hours at 37°C,
after which it is poured in a sterilizing cup and placed in a sterilizer for between 15
and 20 minutes at 80°C, as shown in figure 2.37.
The tests in figure 2.38 count for:
Total Bacteria
Anaerobic
Salmonella
Yeast and Mold
All of them should be nil.
Figure 2.36: The incubator.
Figure 2.37: The sterilizer.
Figure 2.38: Tests counting for
bacteria presence.
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Canned Food
Once the sample is received (note: the number of cans in the sample varies
according to the production scheduled for that day), one of the cans is taken as a
fresh sample and immediately undergoes weight, PH, and brix tests. The rest of the
sample is split into 2 groups of equal size. One is stored at 55°C, whilst the other is
stored at 37°C as shown in figure 2.39, and kept for 5 days before they undergo the
same tests as the fresh sample.
Note: The central lab carries out all the tests in the local lab, in addition to the
microbiology tests discussed.
Figure 2.39: Samples kept at 55°C for 5 days.
Figure CL.17
Page | 39
The As-Is Raw Material Sampling Plans
The current sampling plans used to test the quality of the incoming raw
materials are evaluated in this section. The probability of acceptance, the average
outgoing quality and the average total inspection were calculated for each plan. Note
that most raw materials do not undergo acceptance sampling since the municipality
already checks all food materials coming into Kuwait and in the case of such
materials as glue, the company has an excellent relationship with its suppliers and is
therefore confident enough to accept lots without subjecting them to sampling.
The raw materials that do undergo sampling are the beans, the standard lids,
the easy open lids, and the tin sheets. For all raw materials, one sample is taken
before the lot is sentenced. Therefore, they were modeled as single sampling plans
using the following equations:
The terminology is as follows:
N: Lot size.
Pa: The probability of acceptance.
p: Lot percentage defective.
n: The sample size.
C: Number of defective units accepted in a
sample.
d: The number of defective units in the
sample.
Lots consisting of 1% defective items are deemed acceptable. Therefore, the
sampling plans must have a high Pa value at p = 0.01.
Page | 40
Beans Sampling Plan
N = 400
n = 20
c = 0
Table 2.1: Summary of the beans sampling plan.
Beans
p Pa AOQ ATI
0.01 0.8179 0.78% 89
0.02 0.6676 1.27% 146
0.03 0.5438 1.55% 193
0.04 0.4420 1.68% 232
0.05 0.3585 1.70% 264
0.06 0.2901 1.65% 290
0.07 0.2342 1.56% 311
0.08 0.1887 1.43% 328
0.09 0.1516 1.30% 342
0.10 0.1216 1.15% 354
Page | 41
Table 2.2: Probability of acceptance for different values of p for beans sampling plan.
p Pa
0.01 0.8179
0.02 0.6676
0.03 0.5438
0.04 0.4420
0.05 0.3585
0.06 0.2901
0.07 0.2342
0.08 0.1887
0.09 0.1516
0.10 0.1216
0.00
0.20
0.40
0.60
0.80
1.00
0.00 0.02 0.04 0.06 0.08 0.10
Pa
Lot fraction defective, p
Probablity of Acceptance for the As-Is Beans Sampling Plan
Figure 2.40: Probability of acceptance for the beans sampling plan.
Page | 42
Table 2.3: AOQ for different values of p for beans sampling plan.
p AOQ
0.01 0.78%
0.02 1.27%
0.03 1.55%
0.04 1.68%
0.05 1.70%
0.06 1.65%
0.07 1.56%
0.08 1.43%
0.09 1.30%
0.10 1.15%
0.00%
0.20%
0.40%
0.60%
0.80%
1.00%
1.20%
1.40%
1.60%
1.80%
0.00 0.02 0.04 0.06 0.08 0.10
AO
Q
Lot fraction defective, p
AOQ for the As-Is Beans Sampling Plan
Figure 2.41: AOQ for the beans sampling plan.
Page | 43
Table 2.4: ATI for different values of p for beans sampling plan.
p ATI
0.01 89
0.02 146
0.03 193
0.04 232
0.05 264
0.06 290
0.07 311
0.08 328
0.09 342
0.10 354
0
50
100
150
200
250
300
350
400
0.00 0.02 0.04 0.06 0.08 0.10
AT
I
Lot fraction defective, p
ATI for the As-Is Beans Sampling Plan
Figure 2.42: ATI for the beans sampling plan.
Page | 44
As can be seen in figure 2.42 the probability of acceptance is low even at low values
of p. At a p = 0.01, Pa is only 81.79%. A new sampling plan for this raw material is
needed.
Standard Lids Sampling Plan
N = 4,000,000
n = 50
c = 2
Table 2.5: Summary of the standard lids sampling plan.
Standard Lids
p Pa AOQ ATI
0.01 0.9862 0.99% 55,318
0.02 0.9216 1.84% 313,757
0.03 0.8108 2.43% 756,848
0.04 0.6767 2.71% 1,293,178
0.05 0.5405 2.70% 1,837,895
0.06 0.4162 2.50% 2,335,035
0.07 0.3108 2.18% 2,756,861
0.08 0.2260 1.81% 3,096,114
0.09 0.1605 1.44% 3,357,846
0.10 0.1117 1.12% 3,553,091
Page | 45
Table 2.6: Probability of acceptance for different values of p for standard lids sampling plan.
p Pa
0.01 0.9862
0.02 0.9216
0.03 0.8108
0.04 0.6767
0.05 0.5405
0.06 0.4162
0.07 0.3108
0.08 0.2260
0.09 0.1605
0.10 0.1117
0.00
0.20
0.40
0.60
0.80
1.00
0.00 0.02 0.04 0.06 0.08 0.10
Pa
Lot fraction defective, p
Probablity of Acceptance for the As-Is Standard Lids Sampling Plan
Figure 2.43: Probability of acceptance for the standard lids sampling plan.
Page | 46
Table 2.7: AOQ for different values of p for standard lids sampling plan.
p AOQ
0.01 0.99%
0.02 1.84%
0.03 2.43%
0.04 2.71%
0.05 2.70%
0.06 2.50%
0.07 2.18%
0.08 1.81%
0.09 1.44%
0.10 1.12%
0.00%
0.50%
1.00%
1.50%
2.00%
2.50%
3.00%
0.00 0.02 0.04 0.06 0.08 0.10
AO
Q
Lot fraction defective, p
AOQ for the As-Is Standard Lids Sampling Plan
Figure 2.44 AOQ for the standard lids sampling plan.
Page | 47
Table 2.8: ATI for different values of p for standard lids sampling plan
p ATI
0.01 55,318
0.02 313,757
0.03 756,848
0.04 1,293,178
0.05 1,837,895
0.06 2,335,035
0.07 2,756,861
0.08 3,096,114
0.09 3,357,846
0.10 3,553,091
0
500,000
1,000,000
1,500,000
2,000,000
2,500,000
3,000,000
3,500,000
4,000,000
0.00 0.02 0.04 0.06 0.08 0.10
AT
I
Lot fraction defective, p
ATI for the Standard Lids Sampling Plan
Figure 2.45: ATI for the standard lids sampling plan.
Page | 48
Figure 2.45 shows that the probability of acceptance is as high as 98.6% at p = 0.01
and falls quickly as p increases. This is a very effective sampling plan.
Easy Open Lids Sampling Plan
N = 1,400,000
n = 50
c = 2
Table 2.9: Summary of the easy open lids sampling plan.
Easy Open Lids
p Pa AOQ ATI
0.01 0.9862 0.99% 19,946
0.02 0.9216 1.84% 112,982
0.03 0.8108 2.43% 272,491
0.04 0.6767 2.71% 465,566
0.05 0.5405 2.70% 661,659
0.06 0.4162 2.50% 840,626
0.07 0.3108 2.18% 992,480
0.08 0.2260 1.81% 1,114,608
0.09 0.1605 1.44% 1,208,830
0.10 0.1117 1.12% 1,279,116
Page | 49
Table 2.10: Probability of acceptance for different values of p for easy open lids sampling plan.
p Pa
0.01 0.9862
0.02 0.9216
0.03 0.8108
0.04 0.6767
0.05 0.5405
0.06 0.4162
0.07 0.3108
0.08 0.2260
0.09 0.1605
0.10 0.1117
0.00
0.20
0.40
0.60
0.80
1.00
0.00 0.02 0.04 0.06 0.08 0.10
Pa
Lot fraction defective, p
Probablity of Acceptance for the As-Is Easy Open Lids Sampling Plan
Figure 2.46: Probability of acceptance for the easy open lids sampling plan.
Page | 50
Table 2.11: AOQ for different values of p for easy open lids sampling plan.
p AOQ
0.01 0.99%
0.02 1.84%
0.03 2.43%
0.04 2.71%
0.05 2.70%
0.06 2.50%
0.07 2.18%
0.08 1.81%
0.09 1.44%
0.10 1.12%
0.00%
0.50%
1.00%
1.50%
2.00%
2.50%
3.00%
0.00 0.02 0.04 0.06 0.08 0.10
AO
Q
Lot fraction defective, p
AOQ for the As-Is Easy Open Lids Sampling Plan
Figure 2.47: AOQ for the easy open lids sampling plan.
Page | 51
Table 2.12: ATI for different values of p for easy open lids sampling plan.
p ATI
0.01 19,946
0.02 112,982
0.03 272,491
0.04 465,566
0.05 661,659
0.06 840,626
0.07 992,480
0.08 1,114,608
0.09 1,208,830
0.10 1,279,116
0
200,000
400,000
600,000
800,000
1,000,000
1,200,000
1,400,000
0.00 0.02 0.04 0.06 0.08 0.10
AT
I
Lot fraction defective, p
ATI for the Easy Open Lids Sampling Plan
Figure 2.48: ATI for the easy open lids sampling plan.
Page | 52
Figure 2.48 shows that the probability of acceptance is as high as 98.6% at p = 0.01
and falls quickly as p increases. This is a very effective sampling plan.
Tins Sheets Sampling Plan
N = 420,000
n = 10
c = 0
Tin sheets
p Pa AOQ ATI
0.01 0.9044 0.90% 40,169
0.02 0.8171 1.63% 76,838
0.03 0.7374 2.21% 110,289
0.04 0.6648 2.95% 140,777
0.05 0.5987 2.99% 168,536
0.06 0.5386 2.69% 193,787
0.07 0.4850 2.42% 216,732
0.08 0.4344 2.17% 237,561
0.09 0.3894 1.95% 256,449
0.10 0.3487 1.74% 273,559
Table 2.13: Summary of the tin sheets sampling plan.
Page | 53
Table 2.14: Probability of acceptance for different values of p for tin sheets sampling plan.
p Pa
0.01 0.9044
0.02 0.8171
0.03 0.7374
0.04 0.6648
0.05 0.5987
0.06 0.5386
0.07 0.4850
0.08 0.4344
0.09 0.3894
0.10 0.3487
0.0000
0.2000
0.4000
0.6000
0.8000
1.0000
0.00 0.02 0.04 0.06 0.08 0.10
Pa
Lot fraction defective, p
Probablity of Acceptance for the As-Is Tin Sheets Sampling Plan
Figure 2.49: Probability of acceptance for the tin sheets sampling plan.
Page | 54
Table 2.15: AOQ for different values of p for tin sheets sampling plan.
p AOQ
0.01 0.90%
0.02 1.63%
0.03 2.21%
0.04 2.95%
0.05 2.99%
0.06 2.69%
0.07 2.42%
0.08 2.17%
0.09 1.95%
0.10 1.74%
0.00%
0.50%
1.00%
1.50%
2.00%
2.50%
3.00%
3.50%
0.00 0.02 0.04 0.06 0.08 0.10
AO
Q
Lot fraction defective, p
AOQ for the As-Is Tin Sheets Sampling Plan
Figure 2.50: AOQ for the tin sheets sampling plan.
Page | 55
Table 2.16: ATI for different values of p for tin sheets sampling plan.
p ATI
0.01 40,169
0.02 76,838
0.03 110,289
0.04 140,777
0.05 168,536
0.06 193,787
0.07 216,732
0.08 237,561
0.09 256,449
0.10 273,559
0
50,000
100,000
150,000
200,000
250,000
300,000
0.00 0.02 0.04 0.06 0.08 0.10
AT
I
Lot fraction defective, p
ATI for the As-Is Tin Sheets Sampling Plan
Figure 2.51: ATI for the tin sheets sampling plan.
Page | 56
As can be seen in figure 2.51, the probability of acceptance is low even at low
values of p. At a p = 0.01, Pa is only around 90%. A new sampling plan for this raw
material is needed.
From studying the three different properties for each sampling plan, it was
conclude that the plans for the beans and tin sheets need to be redesigned because
the Pa curves are inadequate. The procedure followed in the design of the new plans
is shown in sections 9 and 10 of the report.
Page | 57
Quality Control Documentation
Having studied the quality control documentation in place, the finished product
quality sheet shown in figure 2.52 was found to be particularly inadequate as it does
not record individual data and wastes a lot of space on tests that always return a
positive result. Thus, it was decided to come up with new designs based on
statistical and economical considerations. The new quality sheets as well as the
properties taken into consideration while designing them are discussed in detail in
section 8.
Figure 2.53 shows the brine quality sheet which does not show the standards
that need to be met for each product. It was therefore recommended that a sheet
with all the standards written be posted in a clearly visible location in the lab.
Finally, after discussions about the central lab results with the quality
personnel, it was noticed that the specifications are not realistic and need to be
changed since many results for the brix and PH fall outside the limits even though
they were of acceptable quality. It is therefore imperative that the specifications are
reset in conjunction with the input of the quality engineers.
Page | 58
Figure 2.52: The as-is finished product quality sheet.
Page | 59 Figure 2,53: The As-Is brine quality sheet.
Page | 60
2.3 Pareto Analysis of Can Defects
After studying quality control data for a whole month’s worth of production,
there was a need to pinpoint the most common types of defects that occurred.
A Pareto chart was used. The Pareto chart is one of the seven basic tools of
quality control, which include the histogram, Pareto chart, check sheet, control chart,
cause-and-effect diagram, flowchart, and scatter diagram. The Pareto chart is a
special type of bar chart where the values being plotted are arranged in descending
order.
A Pareto chart was constructed for the different types of defects in the can
filling process and determined which defects were to be studied in depth. As shown
in figure 7.0, the main problems were the brine temperature and net weight.
0
5
10
15
20
25
30
35
Brine Temprature
Net Weight Filling weight
Vegetable Oil
Seaming Lacquering Coding
Types of Defects
Figure 2.54: Pareto chart for types defects.
Page | 61
Brine Temperature Problem
Upon further inspection, it was found that there was only one incident where
the temperature was below 70°C. After discussing this with the quality engineer, it
was discovered that products with 70°C brine are acceptable. The target of a
minimum temperature of 75°C is set to keep a safety buffer. Therefore, there was no
need to waste resources studying a problem that did not exist.
Net Weight Problem
A root cause analysis was conducted to pinpoint the source of the problem.
Various quality tools, including the why-why diagram, fishbone diagram, and control
charts were used in the analysis. Since production is sporadic, meaning a single
product will not be produced continually but will be produced based on demand and
thus can sometimes be produced on a monthly basis, for example, there were not
enough data points to construct a control chart with a proper sub group size.
Therefore, individual and moving range charts were constructed instead, to study the
performance of the filling system.
The products used for this analysis were the chick peas and green peas since
they account for the bulk of production (almost 40%). Note that the nominal value for
the 400g cans is set at 415g with a tolerance of ±15g.
Page | 62
Why-Why Diagram
Figure 2.55: Why-why diagram for the cause of overfilling.
Page | 63
Figure 2.56: Fish bone diagram for the cause of overfilling.
Fish Bone Diagram
Page | 64
Control Charts
Individual and Moving Range Charts for the Net Weight of Chick Peas
Comments:
Points are randomly scattered.
The process average is too close to upper specification limit.
Points 12-17 indicate lack of vigilance in meeting the target as the weight
keeps increasing.
70% of points within ± 1σ.
96.67% of points within ± 2σ.
The Process is under control.
Overfilling could be due to a problem in the dry filling. Therefore, we decided
to study the filling weight as well.
Figure 2.57: Control chart for the net weight of chick peas.
Page | 65
Table 2.17: Net Weight data of Chick Peas for the month of October.
Net Weight of Chick Peas
430 430
424 426
426 430
430 428
432 430
434 428
430 430
432 430
430 430
425 426
430 428
426 424
430 428
432 430
430
Page | 66
Individual and Moving Range Charts for the Filling Weight of Chick Peas
Comments:
The nominal value for the chick peas filling weight is 205 with a tolerance of
±5g.
The points are randomly scattered.
The process average is close to the upper specification limit.
The only out of control point corresponds to the nominal target!
Runs of points of equal value indicate ability to consistently produce cans at
the same weight.
86.67% within ± 1σ.
Too many points lie outside the 2σ boundaries. The process variation must be
lowered by being more proactive in changing the process average when
deviations from the nominal target occur.
Figure 2.58: Control chart for the filling weight of chick peas.
Page | 67
Table 2.18: Net Weight data of Chick Peas for the month of October.
Filling Weight of Chick Peas
205 210
208 210
208 209
209 209
208 209
209 209
209 207
208 209
209 208
208 209
208 209
208 208
210 208
210 209
210 209
209 209
208
Page | 68
Individual and Moving Range Charts for the Net Weight of Green Peas
Comments:
Points are randomly scattered.
Process average is lower than for the chick peas.
92.3% of points within ± 1σ.
96.2% of points within ± 2σ.
Process is under control.
Figure 2.58: Control chart for the net weight of green peas.
Page | 69
Table 2.19: Net Weight data for Green Peas for the month of October.
Net Weight of Green Peas
420 424
422 420
420 426
426 418
424 420
421 420
426 422
420 420
424 430
421 426
420 420
422 424
420 424
421
Page | 70
Individual and Moving Range Charts for the Filling Weight of Green Peas
Comments:
The nominal value for the green peas filling weight is 187.5 with a tolerance of
±2,5g.
Points are randomly scattered.
The process average is almost exactly equal to the nominal target. This is
consistent with lower net weight than the chick peas where the filling weight
average was close to the upper specification limit.
92.3% of points within ± 1σ.
92.3% of points within ± 2σ.
There is a reasonable amount of variation, with only one out of control point.
Figure 2.59: Control chart for the filling weight of green peas.
Page | 71
Table 2.20: Filling Weight data of Green Peas for the month of October.
Filling Weight of Green Peas
187 187
188 187
188 188
187 188
188 187
188 188
188 188
187 187
187 187
188 185
189 188
187 187
188 187
Page | 72
Conclusion
The runs of equal points dispersed in the control charts, and the center line of
the filling weight chart for green peas, which corresponds to its nominal target,
suggested that the process is indeed capable of producing cans with little variability
in the filling weight. However, there seemed to be a lack of interest in correcting
process shifts when they did occur. It was concluded that this was due to ignorance
of the cost of consistently overfilling the cans. By studying the filling data for the
month of October, the Cost Analysis group estimated that the company wastes
around 68,000 KD annually by overfilling their cans.
Page | 73
2.4 New Quality Control Documentation
Considerations for designing the new sheets
The sporadic nature of production means that some products are only
produced for two hours a month, therefore recording only the averages will not
suffice for the construction of proper control charts.
It was decided that tests shall be carried out every 15 minutes as the rate of
production (140 cans/min) is high, and to collect sufficient data to construct reliable
control charts to monitor system performance. This resulted in eight subgroups per
production run.
The subgroup size had to be set so that a single production run would
produce enough data points to construct individual control charts. However this
couldn’t be done arbitrarily and therefore, statistical analysis was used in to
determine the optimum subgroup size.
There are two tolerance widths for the dry weights of the different products, 5
and 10 grams. The tighter width of 5 grams was used to base the subgroup size on,
so that the quality sheets can be applied for all products. It was qualitatively
determined that a change of one gram can be tolerated before a process mean shift
needs to be recognized quickly as it would be close to the specification limit at that
point.
It was also decided that the product PH should be studied immediately after
the cooking operation rather than wait until the production run is finished and the
samples are sent to the labs. In this way, defects can be detected earlier and thus
cumulative costs of poor quality reduced.
With these considerations in mind, two quality control sheets, one for
the filling weight and one for the finished products, measuring both the net weight
and the PH, were created.
Page | 74
Statistical Analysis
The number of standard deviations, k, was taken to be 1.5 because for the
filling weight, σ = 0.7 i.e. the shift (kσ) is almost equal to 1g. Using this k value, β was
found from the following graph:
Figure 2.60
Different parameters were calculated for subgroup sizes of 5 and 10 suing the
following equations:
Average run length, the average number of subgroups before a shift of kσ is
detected:
Page | 75
Average time to signal, the average time before the shift is detected:
The number of individual cans inspected before the process shift is detected:
Cost Considerations
The combined salary of all quality personnel is 1170 KD per month, which
works out to be 45KD per day. It takes 15 seconds to check each can’s weight, 30
seconds to check the temperature, and 30 seconds for transportation.
There are 10 hours of production per day, and a sample is taken every fifteen
minutes, therefore 40 checks per day.
For a subgroup of 10 cans, it takes 6 minutes to carry out the tests. Therefore,
the total time the personnel are engaged in quality tests is 240 minutes per day. This
will cost: 240/600 * 45 = 18 KD/day.
For a subgroup of 5 cans it takes 3.5 minutes to carry out the tests. Therefore,
the total time the personnel are engaged in quality test is 140 minutes per day. This
will cost: 140/600 * 45 = 10.5 KD/day.
Page | 76
Decision
Table 2.21
The Average Run Length for both subgroup sizes of 5 and 10 is smaller
than 2.
I is smaller for n = 5.
Cost is almost half for n = 5.
Therefore the trade off of a slightly higher average run length is worth it and we shall
consider n = 5 as our sample size.
n = 10 n = 5
β 0.1 0.3
ARL 1.11 1.43
I 11.1 7.15
ATS 16.65 21.45
Cost (KD/day) 18 10.5
Page | 77
Date:__ /__ /__
Production Run 1 - Variant: Can Size(g):
Time #1 Time #2 Time #3 Time #4 Time #5 Time #6 Time #7 Time #8
Can #
1
2
3
4
5
Avg
Production Run 2 - Variant: Can Size(g):
Time #1 Time #2 Time #3 Time #4 Time #5 Time #6 Time #7 Time #8
Can #
1
2
3
4
5
Avg
Production Run 3 - Variant: Can Size(g):
Time #1 Time #2 Time #3 Time #4 Time #5 Time #6 Time #7 Time #8
Can #
1
2
3
4
5
Avg
Figure 2.62: The new finished product quality sheet.
Page | 78
National Canned Food Company - Daniah Q.C Department
Quality Sheet of ( )gm can
Date: Can Production Date:
Variant: Can Type:
Time #1: ………………. Time #2: ………………. Time #3: ……………….
Time #4: ……………….
Brine Temp: Brine Temp: Brine Temp: Brine Temp:
Can # Net Wt PH Net Wt PH Net Wt PH Net Wt PH
1
2
3
4
5
Average
Time #5: ………………. Time #6: ………………. Time #7: ……………….
Time #8: ……………….
Brine Temp: Brine Temp: Brine Temp: Brine Temp:
Can # Net Wt PH Net Wt PH Net Wt PH Net Wt PH
1
2
3
4
5
Average
Other Defects
Time # Can # Type: Time # Can # Type:
Time # Can # Type: Time # Can # Type:
Time # Can # Type: Time # Can # Type:
Time # Can # Type: Time # Can # Type:
Key: SS: Seaming Steam CW: Can Wash C: Code
Page | 79
2.5 New Sampling Plans
Proposed New Single Sampling Plan for Beans
A new single sampling plan for beans was constructed using α and β values.
The probability of acceptance had to be at least 95% for a lot with percent defective
of 1 or less (i.e p is no larger 0.01). An attempt was made to achieved a Pa of 98% at
p = 0.01, whilst making the Pa curve is sensitive enough to get a Pa no more than 5%
at p = 0.10. α was set at 5%, whilst β was kept at 10%, in the following equations:
Using the relevant nomograph, the plan that came closest to meeting these
constraints was the one with n = 70, and c = 2.
0.00
0.20
0.40
0.60
0.80
1.00
0.00 0.02 0.04 0.06 0.08 0.10
Pa
Lot fraction defective, p
Probablity of Acceptance for the New Beans Single Sampling Plan
Figure 2.63: Probability of acceptance for the new beans single
sampling plan.
Page | 80
Table 2.22: Probability of acceptance for the new beans single sampling plan at different values of p.
p Pa
0.01 0.9667
0.02 0.8350
0.03 0.6492
0.04 0.4656
0.05 0.3137
0.06 0.2013
0.07 0.1241
0.08 0.0740
0.09 0.0428
0.10 0.0242
Page | 81
Table 2.23: AOQ for the new beans single sampling plan at different values of p.
p AOQ
0.01 0.80%
0.02 1.38%
0.03 1.61%
0.04 1.54%
0.05 1.29%
0.06 1.00%
0.07 0.72%
0.08 0.49%
0.09 0.32%
0.10 0.20%
0.00%
0.20%
0.40%
0.60%
0.80%
1.00%
1.20%
1.40%
1.60%
1.80%
0.00 0.02 0.04 0.06 0.08 0.10
AO
Q
Lot fraction defective, p
AOQ for the New Beans Single Sampling Plan
Figure 2.64: AOQ for the new beans single sampling plan.
Page | 82
Table 2.24: ATI for the new beans single sampling plan at different values of p.
p ATI
0.01 81
0.02 124
0.03 186
0.04 246
0.05 296
0.06 334
0.07 359
0.08 376
0.09 386
0.10 392
Figure 2.65 shows that the Probability of acceptance became much more acceptable
with a value of 96.67% at p =0.01 and decreasing very quickly, thereafter.
050
100150200250300350400450
0.00 0.02 0.04 0.06 0.08 0.10
AT
I
Lot fraction defective, p
ATI for the New Beans Single Sampling Plan
Figure 2.65: ATI for the new beans single sampling plan.
Page | 83
Comparison between the New Single Sampling and As-Is Plans For
Beans
To judge whether the new sampling plan is superior to the exising one, the Pa
curve did not siffice to make our decision. It also had to be verified that the cost of
the new plan was lower at most values of p, by using the following equations:
Cost of poor quality = AOQ * cost of producing one unit * total annual production
Cost of inspection = ATI * hourly wage of quality personnel * average time to inspect
one unit of raw material (in hours)
As mentioned in section 8, the hourly wages of the quality personnel is 4.5 KD.
The average time to inspect one bag of beans is 30 minutes.
The average time to inspect one tin sheet is 2 minutes.
Page | 84
Table 2.25: Comparison between the probability of acceptance for the beans as-is and new single
sampling plans at different values of p.
p As-Is
New Single
Sampling
0.01 0.8179 0.9667
0.02 0.6676 0.8350
0.03 0.5438 0.6492
0.04 0.4420 0.4656
0.05 0.3585 0.3137
0.06 0.2901 0.2013
0.07 0.2342 0.1241
0.08 0.1887 0.0740
0.09 0.1516 0.0428
0.10 0.1216 0.0242
0.00
0.20
0.40
0.60
0.80
1.00
0 0.02 0.04 0.06 0.08 0.1
Pa
Lot fraction defective, p
Comparison between the Probability of Acceptance for the Beans As-Is and New Single Sampling Plans
New Single Sampling Plan
As is Plan
Figure 2.66: Comparison between the probability of acceptance for
the beans as-is and the new single sampling plan.
Page | 85
Table 2.26: Comparison between the AOQ for the beans as-is and new single sampling plans at different
values of p.
p As-Is New Single Sampling
0.01 0.78% 0.80%
0.02 1.27% 1.38%
0.03 1.55% 1.61%
0.04 1.68% 1.54%
0.05 1.70% 1.29%
0.06 1.65% 1.00%
0.07 1.56% 0.72%
0.08 1.43% 0.49%
0.09 1.30% 0.32%
0.10 1.15% 0.20%
0.00%
0.20%
0.40%
0.60%
0.80%
1.00%
1.20%
1.40%
1.60%
1.80%
0 0.02 0.04 0.06 0.08 0.1
AO
Q
Lot fraction defective, p
Comparison between the AOQ for the Beans As-Is and New Single Sampling Plans
New Single Sampling Plan
As is Plan
Figure 2.67: Comparison between the AOQ for the beans as-is and the new single sampling plan.
Page | 86
Table 2.27: Comparison between the ATI for the beans as-is and new single sampling plan at different
values of p.
p As-Is New Single Sampling
0.01 89 81
0.02 146 124
0.03 193 186
0.04 232 246
0.05 264 296
0.06 290 334
0.07 311 359
0.08 328 376
0.09 342 386
0.10 354 392
0
100
200
300
400
500
0 0.02 0.04 0.06 0.08 0.1
AT
I
Lot fraction defective, p
Comparison between the ATI for the Beans As-Is and New Single Sampling Plans
New Single Sampling Plan
As is Plan
Figure 2.88: Comparison between the ATI for the beans as-is and the new single sampling plan.
Page | 87
Table 9.28: Comparison between the costs of the beans as-is and new single sampling plan at different
values of p.
p As-Is New Single Sampling
0.01 23595 24194
0.02 38521 41761
0.03 47098 48798
0.04 51093 46811
0.05 51863 39632
0.06 50440 30752
0.07 47600 22386
0.08 43916 15545
0.09 39808 10445
0.1 35571 6889
As is clear from figure 2.89, the cost of the new single sampling plan is lower
for most values of p.
0
10000
20000
30000
40000
50000
60000
0 0.02 0.04 0.06 0.08 0.1
Co
st
Lot fraction defective, p
Comparison between Costs of the Beans As-Is and New Single Sampling Plans
New Single sampling Plan
As-is plan
Figure 2.89: Comparison between the costs of the beans as-is and the new single sampling plan.
Page | 88
2.6 Proposed Double Sampling Plans For Beans
After construtcing the new sampling plan, the possibility of constructing a
superior double sampling plan that will reduce the cost of sampling but still meet the
target of having a Pa no less than 95% when p = 0.01, was also considered. Six
different double sampling plans were tested and the best was chosen based on the
total cost of the plan.
Calculations of the paramters for the double sampling plans were made usin
the following equations:
The parameters for the six plans are summarized as follows:.
Table 9.29: Summary of the parameters of the six proposed beans double sampling plans
Plan 1 Plan 2 Plan 3 Plan 4 Plan 5 Plan 6
n1 10 15 20 25 30 35
n2 30 45 60 75 90 60
c1 0 0 0 0 0 0
c2 2 2 2 2 2 2
Where:
n1: Size of the first sample.
n2: Size of the second sample.
c1: The number of defects tolerated in the first sample without a need for the second
sample.
c2: The number of defects tolerated in both samples, combined, before the lot is
rejected.
Page | 89
Table 2.30: Probability of acceptance for the first proposed beans sampling plan at different values of.
p Pa
0.01 0.9955
0.02 0.9721
0.03 0.9265
0.04 0.8633
0.05 0.7892
0.06 0.7106
0.07 0.6325
0.08 0.5582
0.09 0.4898
0.10 0.4281
0.00
0.20
0.40
0.60
0.80
1.00
0.00 0.02 0.04 0.06 0.08 0.10
Pa
Lot fraction defective, p
Probablity of Acceptance for the First Proposed Beans Sampling Plan
Figure 2.90: Probability of acceptance for the first proposed beans sampling plan.
Page | 90
Table 2.31: AOQ for the first proposed beans sampling plan at different values of p.
p AOQ
0.01 0.96%
0.02 1.87%
0.03 2.67%
0.04 3.31%
0.05 3.78%
0.06 4.08%
0.07 4.24%
0.08 4.28%
0.09 4.23%
0.10 4.11%
0.00%
0.50%
1.00%
1.50%
2.00%
2.50%
3.00%
3.50%
4.00%
4.50%
0.00 0.02 0.04 0.06 0.08 0.10
AO
Q
Lot fraction defective, p
AOQ for the First Proposed Beans Sampling Plan
Figure 2.91: AOQ for the first proposed beans sampling plan.
Page | 91
Table 2.32: ATI for the first proposed beans sampling plan at different values of p.
p ATI
0.01 14
0.02 26
0.03 44
0.04 69
0.05 98
0.06 128
0.07 158
0.08 186
0.09 212
0.10 235
0
50
100
150
200
250
0.00 0.02 0.04 0.06 0.08 0.10
AT
I
Lot fraction defective, p
ATI for the First Proposed Beans Sampling Plan
Figure 2.92: ATI for the first proposed beans sampling
plan.
Page | 92
Table 2.33: Probability of acceptance for the 2nd proposed beans sampling plan at different values of p.
p Pa
0.01 0.9865
0.02 0.9263
0.03 0.8278
0.04 0.7130
0.05 0.5992
0.06 0.4963
0.07 0.4080
0.08 0.3347
0.09 0.2748
0.10 0.2262
0.00
0.20
0.40
0.60
0.80
1.00
0.00 0.02 0.04 0.06 0.08 0.10
Pa
Lot fraction defective, p
Probability of Acceptance for the Second Proposed Beans Sampling Plan
Figure 2.93: Probability of acceptance for the second proposed beans sampling plan.
Page | 93
Table 2.34: AOQ for the second proposed beans sampling plan at different values of p
p AOQ
0.01 0.94%
0.02 1.74%
0.03 2.32%
0.04 2.67%
0.05 2.81%
0.06 2.80%
0.07 2.69%
0.08 2.53%
0.09 2.35%
0.10 2.15%
.
0.00%
0.50%
1.00%
1.50%
2.00%
2.50%
3.00%
0.00 0.02 0.04 0.06 0.08 0.10
AO
Q
Lot fraction defective, p
AOQ for the Second Proposed Beans Sampling Plan
Figure 2.94: AOQ for the second proposed beans sampling plan.
Page | 94
Table 2.35: ATI for the second proposed beans sampling plan at different values of p.
p ATI
0.01 26
0.02 52
0.03 90
0.04 133
0.05 175
0.06 213
0.07 246
0.08 273
0.09 296
0.10 314
0
50
100
150
200
250
300
350
0.00 0.02 0.04 0.06 0.08 0.10
AT
I
Lot fraction defective, p
ATI for the Second Proposed Beans Sampling Plan
Figure 2.95: ATI for the second proposed beans sampling plan.
Page | 95
Table 2.36: Probability of acceptance for the third proposed beans sampling plan at different values of p.
p Pa
0.01 0.9718
0.02 0.8637
0.03 0.7142
0.04 0.5659
0.05 0.4395
0.06 0.3393
0.07 0.2625
0.08 0.2042
0.09 0.1599
0.10 0.1258
0.00
0.20
0.40
0.60
0.80
1.00
0.00 0.02 0.04 0.06 0.08 0.10
Pa
Lot fraction defective, p
Probability of Acceptance for the Third Proposed Beans Sampling Plan
Figure 2.96: Probability of acceptance for the third proposed beans sampling plan.
Page | 96
Table 2.37: AOQ for different values of p for the third proposed beans sampling plan.
p AOQ
0.01 0.90%
0.02 1.58%
0.03 1.96%
0.04 2.08%
0.05 2.03%
0.06 1.89%
0.07 1.72%
0.08 1.53%
0.09 1.36%
0.10 1.19%
0.00%
0.50%
1.00%
1.50%
2.00%
2.50%
0.00 0.02 0.04 0.06 0.08 0.10
AO
Q
Lot fraction defective, p
AOQ for the Third Proposed Beans Sampling Plan
Figure 2.97: AOQ for the third proposed beans sampling plan.
Page | 97
Table 2.38: ATI for different values of p for the third proposed beans sampling plan.
p ATI
0.01 40
0.02 84
0.03 139
0.04 192
0.05 238
0.06 274
0.07 302
0.08 323
0.09 340
0.10 352
0
50
100
150
200
250
300
350
400
0.00 0.02 0.04 0.06 0.08 0.10
AT
I
Lot fraction defective, p
ATI for the Third Proposed Beans Sampling Plan
Figure 2.98: ATI for the third proposed beans sampling plan.
Page | 98
Table 2.39: Probability of acceptance for the fourth proposed beans sampling plan at different values of
p.
p Pa
0.01 0.9515
0.02 0.7913
0.03 0.6027
0.04 0.4417
0.05 0.3209
0.06 0.2344
0.07 0.1730
0.08 0.1288
0.09 0.0965
0.10 0.0726
0.00
0.20
0.40
0.60
0.80
1.00
0.00 0.02 0.04 0.06 0.08 0.10
Pa
Lot fraction defective, p
Probablity of Acceptance for the Fourth Proposed Beans Sampling Plan
Figure 2.99: Probability of acceptance for the fourth proposed beans sampling plan
Page | 99
Table 2.40: AOQ for the fourth proposed beans sampling plan at different values of p.
p AOQ
0.01 0.86%
0.02 1.41%
0.03 1.62%
0.04 1.60%
0.05 1.46%
0.06 1.29%
0.07 1.12%
0.08 0.96%
0.09 0.81%
0.10 0.68%
0.00%
0.20%
0.40%
0.60%
0.80%
1.00%
1.20%
1.40%
1.60%
1.80%
0.00 0.02 0.04 0.06 0.08 0.10
AO
Q
Lot fraction defective, p
AOQ for the Fourth Proposed Beans Sampling Plan
Figure 2.100: AOQ for the fourth proposed beans sampling plan.
Page | 100
Table 2.41: ATI for the fourth proposed beans sampling plan at different values of p.
p ATI
0.01 56
0.02 117
0.03 184
0.04 240
0.05 283
0.06 314
0.07 336
0.08 352
0.09 364
0.10 373
0
50
100
150
200
250
300
350
400
0.00 0.02 0.04 0.06 0.08 0.10
AT
I
Lot fraction defective, p
ATI for the Fourth Proposed Beans Sampling Plan
Figure 2.101: ATI for the fourth proposed beans sampling plan.
Page | 101
Table 2.42: Probability of acceptance for the fifth proposed beans sampling plan at different values of p.
p Pa
0.01 0.9262
0.02 0.7153
0.03 0.5025
0.04 0.3438
0.05 0.2364
0.06 0.1650
0.07 0.1167
0.08 0.0832
0.09 0.0595
0.10 0.0425
0.00
0.20
0.40
0.60
0.80
1.00
0.00 0.02 0.04 0.06 0.08 0.10
Pa
Lot fraction defective, p
Probablity of Acceptance for the Fifth Proposed Beans Sampling Plan
Figure 2.102: Probability of acceptance for the fifth proposed beans sampling plan.
Page | 102
Table 2.42: AOQ for the fifth proposed beans sampling plan at different values of p.
p AOQ
0.01 0.81%
0.02 1.25%
0.03 1.33%
0.04 1.23%
0.05 1.07%
0.06 0.90%
0.07 0.75%
0.08 0.61%
0.09 0.49%
0.10 0.39%
0.00%
0.20%
0.40%
0.60%
0.80%
1.00%
1.20%
1.40%
0.00 0.02 0.04 0.06 0.08 0.10
AO
Q
Lot fraction defective, p
AOQ for the Fifth Proposed Beans Sampling Plan
Figure 2.103: AOQ for the fifth proposed beans sampling plan.
Page | 103
Table 2.43: ATI for the fifth proposed beans sampling plan at different values of p.
p ATI
0.01 74
0.02 151
0.03 223
0.04 277
0.05 314
0.06 340
0.07 357
0.08 369
0.09 378
0.10 384
0
50
100
150
200
250
300
350
400
450
0.00 0.02 0.04 0.06 0.08 0.10
AT
I
Lot fraction defective, p
ATI for the Fifth Proposed Beans Sampling Plan
Figure 2.104: ATI for the fifth proposed beans sampling plan.
Page | 104
Table 2.44: Probability of acceptance for the sixth proposed beans sampling plan at different values of p.
p Pa
0.01 0.9506
0.02 0.7794
0.03 0.5696
0.04 0.3876
0.05 0.2533
0.06 0.1624
0.07 0.1035
0.08 0.0662
0.09 0.0426
0.10 0.0277
0.00
0.20
0.40
0.60
0.80
1.00
0.00 0.02 0.04 0.06 0.08 0.10
Pa
Lot fraction defective, p
Probablity of Acceptance for the Sixth Proposed Beans Sampling Plan
Figure 2.105: Probability of acceptance for the sixth proposed beans sampling
plan.
Page | 105
Table 2.44: AOQ for the sixth proposed beans sampling plan at different values of p.
p AOQ
0.01 0.83%
0.02 1.34%
0.03 1.47%
0.04 1.33%
0.05 1.10%
0.06 0.85%
0.07 0.64%
0.08 0.47%
0.09 0.34%
0.10 0.25%
0.00%
0.20%
0.40%
0.60%
0.80%
1.00%
1.20%
1.40%
0.00 0.02 0.04 0.06 0.08 0.10
AO
Q
Lot fraction defective, p
AOQ for the Sixth Proposed Beans Sampling Plan
Figure 2.106: AOQ for the sixth proposed beans sampling plan.
Page | 106
Table 2.45: ATI f for the sixth proposed beans sampling plan at different values of p.
0
50
100
150
200
250
300
350
400
450
0.00 0.02 0.04 0.06 0.08 0.10
AT
I
Lot fraction defective, p
ATI for the Sixth Proposed Beans Sampling Plan
p ATI
0.01 67
0.02 131
0.03 204
0.04 267
0.05 312
0.06 343
0.07 364
0.08 377
0.09 385
0.10 390
Figure 2.107: ATI for the sixth proposed beans sampling plan.
Page | 107
Comparison between the Proposed Double Sampling Plans for Beans
Table 2.46: Comparison between the probability of acceptance for the proposed beans double sampling
plans at different values of p.
p Plan 1 Plan 2 Plan 3 Plan 4 Plan 5 Plan 6
0.01 0.9955 0.9865 0.9718 0.9515 0.9262 0.9506
0.02 0.9721 0.9263 0.8637 0.7913 0.7153 0.7794
0.03 0.9265 0.8278 0.7142 0.6027 0.5025 0.5696
0.04 0.8633 0.7130 0.5659 0.4417 0.3438 0.3876
0.05 0.7892 0.5992 0.4395 0.3209 0.2364 0.2533
0.06 0.7106 0.4963 0.3393 0.2344 0.1650 0.1624
0.07 0.6325 0.4080 0.2625 0.1730 0.1167 0.1035
0.08 0.5582 0.3347 0.2042 0.1288 0.0832 0.0662
0.09 0.4898 0.2748 0.1599 0.0965 0.0595 0.0426
0.10 0.4281 0.2262 0.1258 0.0726 0.0425 0.0277
0.00
0.20
0.40
0.60
0.80
1.00
0.00 0.02 0.04 0.06 0.08 0.10
Pa
Lot fraction defective, p
Comparison between the Probablity of Acceptance for the Proposed Beans Double
Sampling Plans
Plan 1
Plan 2
Plan 3
Plan 4
Plan 5
Plan 6
Figure 2.108: Comparison between the probability of acceptance for
the proposed beans double sampling plans.
Page | 108
Table 2.47 : Comparison between the AOQ for the proposed beans double sampling plans at different
values of p.
p Plan 1 Plan 2 Plan 3 Plan 4 Plan 5 Plan 6
0.01 0.96% 0.94% 0.90% 0.86% 0.81% 0.83%
0.02 1.87% 1.74% 1.58% 1.41% 1.25% 1.34%
0.03 2.67% 2.32% 1.96% 1.62% 1.33% 1.47%
0.04 3.31% 2.67% 2.08% 1.60% 1.23% 1.33%
0.05 3.78% 2.81% 2.03% 1.46% 1.07% 1.10%
0.06 4.08% 2.80% 1.89% 1.29% 0.90% 0.85%
0.07 4.24% 2.69% 1.72% 1.12% 0.75% 0.64%
0.08 4.28% 2.53% 1.53% 0.96% 0.61% 0.47%
0.09 4.23% 2.35% 1.36% 0.81% 0.49% 0.34%
0.10 4.11% 2.15% 1.19% 0.68% 0.39% 0.25%
0.00%
0.50%
1.00%
1.50%
2.00%
2.50%
3.00%
3.50%
4.00%
4.50%
0.00 0.02 0.04 0.06 0.08 0.10
AO
Q
Lot fraction defective, p
Comparison between the AOQ for the Proposed Beans Double Sampling Plans
Plan 1
Plan 2
Plan 3
Plan 4
Plan 5
Plan 6
Figure 2.109: Comparison between the AOQ for the proposed beans double sampling plans.
Page | 109
Table 2.48: Comparison between the ATI for the proposed beans double sampling plans at different
values of p.
p Plan 1 Plan 2 Plan 3 Plan 4 Plan 5 Plan 6
0.01 14 26 40 56 74 67
0.02 26 52 84 117 151 131
0.03 44 90 139 184 223 204
0.04 69 133 192 240 277 267
0.05 98 175 238 283 314 312
0.06 128 213 274 314 340 343
0.07 158 246 302 336 357 364
0.08 186 273 323 352 369 377
0.09 212 296 340 364 378 385
0.10 235 314 352 373 384 390
0
50
100
150
200
250
300
350
400
0.00 0.02 0.04 0.06 0.08 0.10
AT
I
Lot fraction defective, p
Comparison between the ATI for the Proposed Beans Double Sampling Plans
Plan 1
Plan 2
Plan 3
Plan 4
Plan 5
Plan 6
Figure 2.110: Comparison between the ATI for the proposed beans double sampling plans.
Page | 110
Table 2.49: Comparison between costs for the proposed beans double sampling plans at different values
of p.
p Plan 1 Plan 2 Plan 3 Plan 4 Plan 5 Plan 6
0.01 29,051 28,218 27,191 26,003 24,698 25,244
0.02 56,430 52,533 47,826 42,813 37,881 40,750
0.03 80,411 70,196 59,285 49,151 40,427 44,610
0.04 99,730 80,633 62,942 48,574 37,567 40,747
0.05 113,907 84,916 61,557 44,693 32,892 33,696
0.06 123,125 84,717 57,508 39,676 27,982 26,354
0.07 127,985 81,630 52,341 34,537 23,393 20,011
0.08 129,281 76,896 46,898 29,680 19,294 14,993
0.09 127,834 71,365 41,588 25,246 15,730 11,193
0.1 124,397 65,568 36,588 21,281 12,699 8,377
0
20000
40000
60000
80000
100000
120000
140000
0.00 0.02 0.04 0.06 0.08 0.10
Co
st
Lot fraction defective, p
Comparison between the Costs of the Proposed Beans Double Sampling Plans
Plan 1
Plan 2
Plan 3
Plan 4
Plan 5
Plan 6
Figure 2.111: Comparison between the costs of the proposed beans double sampling
plans.
Page | 111
As can be seen from figure 2.111, plans 5 and 6 have the lowest total costs.
Plan 6 was deemed to the best because it also satisfied the constraint of Pa being at
least 95% at p = 0.01.
Comparison between the As-is and Double Sampling Plans For Beans
Table 2.50: Comparison between the probability of acceptance for the beans as- is and double sampling
plans at different values of p.
p As-Is Double Sampling
0.01 0.8179 0.9506
0.02 0.6676 0.7794
0.03 0.5438 0.5696
0.04 0.4420 0.3876
0.05 0.3585 0.2533
0.06 0.2901 0.1624
0.07 0.2342 0.1035
0.08 0.1887 0.0662
0.09 0.1516 0.0426
0.10 0.1216 0.0277
0.000.200.400.600.801.00
0 0.02 0.04 0.06 0.08 0.1
Pa
Lot fraction defective, p
Comparison between the Probability of Acceptance for the Beans As-Is and
Double Sampling Plans
Double sampling plan
As is Plan
Figure 2.112: Comparison between the probability of acceptance for beans as-is and double sampling plans.
Page | 112
Table 2.52: Comparison between the ATI for the beans as- is and double sampling
plans at different
p As-Is
Double
Sampling
0.01 0.78% 0.83%
0.02 1.27% 1.34%
0.03 1.55% 1.47%
0.04 1.68% 1.33%
0.05 1.70% 1.10%
0.06 1.65% 0.85%
0.07 1.56% 0.64%
0.08 1.43% 0.47%
0.09 1.30% 0.34%
0.10 1.15% 0.25%
0.00%
0.20%
0.40%
0.60%
0.80%
1.00%
1.20%
1.40%
1.60%
1.80%
0 0.02 0.04 0.06 0.08 0.1
AO
Q
Lot fraction defective, p
Comparison between the AOQ for the Beans As-Is and Double Sampling Plans
Double sampling plan
As is Plan
Figure 2.113: Comparison between the AOQ for the beans as-is and double sampling
plans.
Page | 113
Table 2.51: Comparison between the AOQ for the beans as- is and double sampling plan at different
values of p.
p As-Is Double Sampling
0.01 89 67
0.02 146 131
0.03 193 204
0.04 232 267
0.05 264 312
0.06 290 343
0.07 311 364
0.08 328 377
0.09 342 385
0.10 354 390
values of p.
0
50
100
150
200
250
300
350
400
450
0 0.02 0.04 0.06 0.08 0.1
AT
I
Lot fraction defective, p
Comparison between the ATI for the Beans As-Is and Double Sampling Plans
Double sampling plan
As is Plan
Figure 2.114: Comparison between the ATI for the beans as-is and double
sampling plans.
Page | 114
Table 2.53: Comparison between the costs of the beans as- is and double sampling plans at different
values of p
p As-Is Double Sampling
0.01 23,595 25,244
0.02 38,521 40,750
0.03 47,098 44,610
0.04 51,093 40,747
0.05 51,863 33,696
0.06 50,440 26,354
0.07 47,600 20,011
0.08 43,916 14,993
0.09 39,808 11,193
0.1 35,571 8,377
.
Figure 2.115 shows that the cost of the double sampling plan is less than that
of the as-is plan. Therefore, the cost of the double sampling was compared with that
of the new single sampling plan the one with minimum cost was chosen.
0
20000
40000
60000
0 0.02 0.04 0.06 0.08 0.1
Co
st
Lot fraction defective, p
Comparison between Costs of the Beans As-Is and Double Sampling
Plans
Double sampling plan
As-is plan
Figure 2.115: Comparison between costs of the beans as-is and double sampling plans.
Page | 115
p Double Sampling New Single Sampling
0.01 25,244 24,194
0.02 40,750 41,761
0.03 44,610 48,798
0.04 40,747 46,811
0,05 33,696 39,632
0.06 26,354 30,752
0.07 20,011 22,386
0.08 14,993 15,545
0.09 11,193 10,445
0.1 8,377 6,889
Table 2.54: Comparison between the costs of the beans new single sampling and double sampling plans
at different values of p.
As figure 2.116 shows, the double sampling plan gives a lower cost for most
values of p. Therefore, the double sampling plan should be implemented.
0
20000
40000
60000
0 0.02 0.04 0.06 0.08 0.1
Co
st
Lot fraction defective, p
Comparison between Costs of the Beans New Single Sampling and Double
Sampling Plans
Double sampling plan
New Single sampling plan
Figure 2.116: Comparison between costs of the beans as-is and double sampling plans.
Page | 116
2.7 Proposed New Single Sampling Plan for Tin Sheets
As with the case of the beans, a new single sampling plan was developed
using the nomograph and setting α to 5% and β to 10%: Therefore, the same plan of
n = 70 and c = 2 was used.
Table 2.55: Probability of acceptance for the new tin sheets single sampling plan at different values of p.
p Pa
0.01 0.9667
0.02 0.8350
0.03 0.6492
0.04 0.4656
0.05 0.3137
0.06 0.2013
0.07 0.1241
0.08 0.0740
0.09 0.0428
0.1 0.0242
0.00
0.20
0.40
0.60
0.80
1.00
0 0.02 0.04 0.06 0.08 0.1
Pa
Lot fraction defective, p
Probablity of Acceptance for the New Tin Sheets Single Sampling Plan
Figure 2.117: Probability of acceptance for the new tin sheets single sampling plan.
Page | 117
Table 2.56: AOQ for the new tin sheets single sampling plan at different values of p.
p AOQ
0.01 0.97%
0.02 1.67%
0.03 1.95%
0.04 1.86%
0.05 1.57%
0.06 1.21%
0.07 0.87%
0.08 0.59%
0.09 0.39%
0.1 0.24%
0.00%
0.50%
1.00%
1.50%
2.00%
2.50%
0 0.02 0.04 0.06 0.08 0.1
AO
Q
Lot fraction defective, p
AOQ for the New Tin Sheets Single Sampling Plan
Figure 2.118: AOQ for the new tin sheets single sampling plan.
Page | 118
Table 2.57: ATI for the new tin sheets single sampling plan at different values of p.
p ATI
0.01 14,073
0.02 69,367
0.03 147,366
0.04 224,498
0.05 288,253
0.06 335,467
0.07 367,887
0.08 388,935
0.09 402,011
0.1 409,846
0
50,000
100,000
150,000
200,000
250,000
300,000
350,000
400,000
450,000
0 0.02 0.04 0.06 0.08 0.1
AT
I
Lot fraction defective, p
ATI for the New Tin Sheets Single Sampling Plan
Figure 2.119: ATI for the new tin sheets single sampling plan.
Page | 119
Comparison between the New Single Sampling and As-Is Plans For
Tin Sheets
Table 2.58: Comparison between the probability of acceptance for the tin sheets as-is and new single
sampling plans at different values of p.
p As-Is
New Single
Sampling
0.01 0.9044 0.9667
0.02 0.8171 0.8350
0.03 0.7374 0.6492
0.04 0.6648 0.4656
0.05 0.5987 0.3137
0.06 0.5386 0.2013
0.07 0.4840 0.1241
0.08 0.4344 0.0740
0.09 0.3894 0.0428
0.10 0.3487 0.0242
0.00
0.20
0.40
0.60
0.80
1.00
0 0.02 0.04 0.06 0.08 0.1
Pa
Lot fraction defective, p
Comparison between the Probability of Acceptance for the Tin Sheets As-Is and New
Single Sampling Plans
New Single Sampling Plan
As is Plan
Figure 2.120: Comparison between the probability of acceptance for the tin sheets as-is and new
single sampling plans.
Page | 120
Table 2.59: Comparison between the AOQ for the tin sheets as-is and new single sampling plans at
different values of p.
p As-Is
New Single
Sampling
0.01 0.90% 0.97%
0.02 1.63% 1.67%
0.03 2.21% 1.95%
0.04 2.95% 1.86%
0.05 2.99% 1.57%
0.06 2.69% 1.21%
0.07 2.42% 0.87%
0.08 2.17% 0.59%
0.09 1.95% 0.39%
0.10 1.74% 0.24%
0.00%
0.50%
1.00%
1.50%
2.00%
2.50%
3.00%
3.50%
0 0.02 0.04 0.06 0.08 0.1
AO
Q
Lot fraction defective, p
Comparison between the AOQ for the Tin Sheets As-Is and New Single Sampling Plans
New Single Sampling Plan
As is Plan
Figure 2.121: Comparison between the AOQ for the tin sheets as-is and new single sampling plans.
Page | 121
Table 2.60: Comparison between the ATI for the tin sheets as-is and new single sampling plans at
different values of p.
p As-Is New Single Sampling
0.01 40,169 14,073
0.02 76,838 69,367
0.03 110,289 147,366
0.04 140,777 224,498
0.05 168,536 288,253
0.06 193,787 335,467
0.07 216,732 367,887
0.08 237,561 388,935
0.09 256,449 402,011
0.1 273,559 409,846
0
50000
100000
150000
200000
250000
300000
350000
400000
450000
0 0.02 0.04 0.06 0.08 0.1
AT
I
Lot fraction defective, p
Comparison between the ATI for the Tin Sheets As-Is and New Single Sampling Plans
New Single Sampling Plan
As is Plan
Figure 2.122: Comparison between the ATI for the tin sheets as-is and new single sampling plans.
Page | 122
Table 2.61: Comparison between the costs of the tin sheets as-is and new single sampling plans at
different values of p.
p As-Is New Single Sampling
0.01 22,063 21,414
0.02 40,184 40,373
0.03 54,871 52,073
0.04 72,691 56,058
0.05 75,699 54,657
0.06 71,261 50,598
0.07 67,228 45,887
0.08 63,567 41,634
0.09 60,247 38,271
0.1 57,240 35,831
As figure 2.123 shows, the new single sampling plan has a much better Pa
curve, with a value of 96.67% at p=.01 and much higher sensitivity to an increase in
p. The total cost of the new plan is also smaller.
0
50000
100000
00.020.040.060.080.1To
tal c
ost
Lot fraction defetive, p
Comparison between Costs of the Tin Sheets As-Is and New
Single Sampling Plan
New Single sampling Plan
As-is plan
Figure 2.123: Comparison between the costs of the tin sheets as-is and new single sampling plan.
Page | 123
2.8 Proposed Double Sampling Plans For Tin Sheets
Once again, six different double sampling plans were tested with the best plan
chosen based on its total cost. The following table summarizes the paramters of the
six proposed plans:
Table 2.62: Summary of the parameters of the six proposed tin sheets double sampling plans
Plan 1 Plan 2 Plan 3 Plan 4 Plan 5 Plan 6
n1 5 10 10 15 20 35
n2 50 100 150 150 150 55
c1 0 0 0 0 0 0
c2 2 2 2 2 2 2
.
Page | 124
Table 2.63: Probability of acceptance for the first proposed tin sheets sampling plan at different values of
p.
p Pa
0.01 0.9953
0.02 0.9732
0.03 0.9343
0.04 0.8852
0.05 0.8323
0.06 0.7798
0.07 0.7299
0.08 0.6836
0.09 0.6410
0.10 0.6019
0.00
0.20
0.40
0.60
0.80
1.00
0.00 0.02 0.04 0.06 0.08 0.10
Pa
Lot fraction defective, p
Probablity of Acceptance for the First Proposed Tin Sheets Sampling Plan
Figure 2.124: Probability of acceptance for the first proposed tin sheets sampling plan.
Page | 125
Table 2.64: AOQ for the first proposed tin sheets sampling plan at different values of p.
p AOQ
0.01 1.00%
0.02 1.95%
0.03 2.80%
0.04 3.54%
0.05 4.16%
0.06 4.68%
0.07 5.11%
0.08 5.47%
0.09 5.77%
0.10 6.02%
0.00%
0.50%
1.00%
1.50%
2.00%
2.50%
3.00%
3.50%
4.00%
0.00 0.02 0.04 0.06 0.08 0.10
AO
Q
Lot fraction defective, p
AOQ for the First Proposed Tin Sheets Sampling Plan
Figure 2.125: AOQ for the first proposed tin sheets sampling plan.
Page | 126
Table 2.65: Probability of acceptance for the first proposed tin sheets sampling plan at different values of
p.
p ATI
0.01 1,976
0.02 11,282
0.03 27,618
0.04 48,207
0.05 70,429
0.06 92,506
0.07 113,467
0.08 132,912
0.09 150,781
0.10 167,185
0
50,000
100,000
150,000
200,000
250,000
300,000
0.00 0.02 0.04 0.06 0.08 0.10
AT
I
Lot fraction defective, p
ATI for the First Proposed Tin Sheets Sampling Plan
Figure 2.126: ATI for the first proposed tin sheets sampling plan.
Page | 127
Table 2.66: Probability of acceptance for the second proposed tin sheets sampling plan at different
values of p.
p Pa
0.01 0.9731
0.02 0.8863
0.03 0.7833
0.04 0.6899
0.05 0.6109
0.06 0.5440
0.07 0.4863
0.08 0.4353
0.09 0.3898
0.10 0.3488
0.00
0.20
0.40
0.60
0.80
1.00
0.00 0.02 0.04 0.06 0.08 0.10
Pa
Lot fraction defective, p
Probablity of Acceptance for the Second Proposed Tin Sheets Sampling Plan
Figure 2.127: Probability of acceptance for the second proposed tin sheets sampling plan.
Page | 128
Table 2.67: AOQ for the second proposed tin sheets sampling plan at different values of p.
p AOQ
0.01 0.97%
0.02 1.77%
0.03 2.35%
0.04 2.76%
0.05 3.05%
0.06 3.26%
0.07 3.40%
0.08 3.48%
0.09 3.51%
0.10 3.49%
0.00%
0.50%
1.00%
1.50%
2.00%
2.50%
3.00%
3.50%
4.00%
0.00 0.02 0.04 0.06 0.08 0.10
AO
Q
Lot fraction defective, p
AOQ for the Second Proposed Tin Sheets Sampling Plan
Figure 2.128: AOQ for the second proposed tin sheets sampling plan.
Page | 129
Table 2.66: ATI of acceptance for the third proposed tin sheets sampling plan at different values
p ATI
0.01 11,308
0.02 47,749
0.03 91,018
0.04 130,271
0.05 163,444
0.06 191,512
0.07 215,776
0.08 237,178
0.09 256,302
0.10 273,504
0
50,000
100,000
150,000
200,000
250,000
300,000
0.00 0.02 0.04 0.06 0.08 0.10
AT
I
Lot fraction defective, p
ATI for the Second Proposed Tin Sheets Sampling Plan
Figure 2.129: ATI for the second proposed tin sheets sampling plan.
Page | 130
Table 2.67: Probability of acceptance for the third proposed tin sheets sampling plan at different values
of p.
p Pa
0.01 0.9562
0.02 0.8505
0.03 0.7511
0.04 0.6693
0.05 0.6000
0.06 0.5390
0.07 0.4841
0.08 0.4344
0.09 0.3894
0.10 0.3487
0.00
0.20
0.40
0.60
0.80
1.00
0.00 0.02 0.04 0.06 0.08 0.10
Pa
Lot fraction defective, p
Probablity of Acceptance for the Third Proposed Tin Sheets Sampling Plan
Figure 2.130: Probability of acceptance for the third proposed tin sheets sampling plan.
Page | 131
Table 2.68: AOQ for the third proposed tin sheets sampling plan at different values of p.
P AOQ
0.01 0.96%
0.02 1.70%
0.03 2.25%
0.04 2.68%
0.05 3.00%
0.06 3.23%
0.07 3.39%
0.08 3.48%
0.09 3.50%
0.10 3.49%
0.00%
0.50%
1.00%
1.50%
2.00%
2.50%
3.00%
3.50%
4.00%
0.00 0.02 0.04 0.06 0.08 0.10
AO
Q
Lot fraction defective, p
AOQ for the Third Proposed Tin Sheets Sampling Plan
Figure 2.131 : AOQ for the third proposed tin sheets sampling plan.
Page | 132
Table 2.69: ATI of acceptance for the third proposed tin sheets sampling plan at different values
p ATI
0.01 18,420
0.02 62,796
0.03 104,552
0.04 138,882
0.05 167,986
0.06 193,641
0.07 216,696
0.08 237,553
0.09 256,447
0.10 273,558
0
50,000
100,000
150,000
200,000
250,000
300,000
0.00 0.02 0.04 0.06 0.08 0.10
AT
I
Lot fraction defective, p
ATI for the Third Proposed Tin Sheets Sampling Plan
Figure 2.132: ATI for the third proposed tin sheets sampling plan.
Page | 133
Table 2.70: Probability of acceptance for the fourth proposed tin sheets sampling plan at
different values of p.
p Pa
0.01 0.9347
0.02 0.7845
0.03 0.6511
0.04 0.5477
0.05 0.4648
0.06 0.3957
0.07 0.3368
0.08 0.2863
0.09 0.2430
0.10 0.2059
0.00
0.20
0.40
0.60
0.80
1.00
0.0000 0.0200 0.0400 0.0600 0.0800 0.1000
Pa
Lot fraction defective, p
Probablity of Acceptance for the Fourth Proposed Tin Sheets Sampling Plan
Figure 2.133: Probability of acceptance for the fourth proposed tin sheets sampling plan.
Page | 134
Table 2.71: AOQ for the fourth proposed tin sheets sampling plan at different values of p.
p AOQ
0.01 0.93%
0.02 1.57%
0.03 1.95%
0.04 2.19%
0.05 2.32%
0.06 2.37%
0.07 2.36%
0.08 2.29%
0.09 2.19%
0.10 2.06%
0.00%
0.50%
1.00%
1.50%
2.00%
2.50%
0.0000 0.0200 0.0400 0.0600 0.0800 0.1000
AO
Q
Lot fraction defective, p
AOQ for the Fourth Proposed Tin Sheets Sampling Plan
Figure 10.17: AOQ for the fourth proposed tin
sheets sampling plan.
Page | 135
Table 2.72: ATI for the fourth proposed tin sheets sampling plan at different values of p.
p ATI
0.01 27,459
0.02 90,539
0.03 146,555
0.04 189,981
0.05 224,777
0.06 253,820
0.07 278,552
0.08 299,751
0.09 317,938
0.10 333,528
0
50,000
100,000
150,000
200,000
250,000
300,000
350,000
400,000
0.00 0.02 0.04 0.06 0.08 0.10
AT
I
Lot fraction defective, p
ATI for the Fourth Proposed Tin Sheets Sampling Plan
Figure 2.134: ATI for the fourth proposed tin sheets sampling plan.
Page | 136
Table 2.73: Probability of acceptance for the fifth proposed tin sheets sampling plan at different
values of p.
p Pa
0.01 0.9135
0.02 0.7236
0.03 0.5645
0.04 0.4482
0.05 0.3601
0.06 0.2905
0.07 0.2343
0.08 0.1887
0.09 0.1516
0.10 0.1216
0.00
0.20
0.40
0.60
0.80
1.00
0.00 0.02 0.04 0.06 0.08 0.10
Pa
Lot fraction defective, p
Probablity of Acceptance for the Fifth Proposed Tin Sheets Sampling Plan
Figure 2.135: Probability of acceptance for the fifth proposed tin sheets sampling plan.
Page | 137
Table 2.74: AOQ for the fifth proposed tin sheets sampling plan at different values of p.
p AOQ
0.01 0.91%
0.02 1.45%
0.03 1.69%
0.04 1.79%
0.05 1.80%
0.06 1.74%
0.07 1.64%
0.08 1.51%
0.09 1.36%
0.10 1.22%
0.00%
0.50%
1.00%
1.50%
2.00%
0.00 0.02 0.04 0.06 0.08 0.10
AO
Q
Lot fraction defective, p
AOQ for the Fifth Proposed Tin Sheets Sampling Plan
Figure 2.136: AOQ for the fifth proposed tin sheets sampling plan.
Page | 138
Table 2.75: ATI for the fifth proposed tin sheets sampling plan at different values of p.
p ATI
0.01 36,383
0.02 116,108
0.03 182,929
0.04 231,777
0.05 268,765
0.06 297,999
0.07 321,588
0.08 340,745
0.09 356,311
0.10 368,940
0
50,000
100,000
150,000
200,000
250,000
300,000
350,000
400,000
0.00 0.02 0.04 0.06 0.08 0.10
AT
I
Lot fraction defective, p
ATI for the Fifth Proposed Tin Sheets Sampling Plan
Figure 2.137: ATI for the fifth proposed tin sheets sampling plan.
Page | 139
Table 2.76: Probability of acceptance for the sixth proposed tin sheets sampling plan at different
values of p.
p Pa
0.01 0.9506
0.02 0.7794
0.03 0.5696
0.04 0.3876
0.05 0.2533
0.06 0.1624
0.07 0.1035
0.08 0.0662
0.09 0.0426
0.10 0.0277
0.00
0.20
0.40
0.60
0.80
1.00
0.00 0.02 0.04 0.06 0.08 0.10
Pa
Lot fraction defective, p
Probablity of Acceptance for the Sixth Proposed Tin Sheets Sampling Plan
Figure 2.138: Probability of acceptance for the sixth proposed tin sheets sampling plan.
Page | 140
Table 2.77: AOQ for the sixth proposed tin sheets sampling plan at different values of p.
p AOQ
0.01 0.95%
0.02 1.56%
0.03 1.71%
0.04 1.55%
0.05 1.27%
0.06 0.97%
0.07 0.72%
0.08 0.53%
0.09 0.38%
0.10 0.28%
0.00%
0.20%
0.40%
0.60%
0.80%
1.00%
1.20%
1.40%
1.60%
1.80%
0.00 0.02 0.04 0.06 0.08 0.10
AO
Q
Lot fraction defective, p
AOQ for the Sixth Proposed Tin Sheets Sampling Plan
Figure 2.139: AOQ for the sixth proposed tin sheets sampling plan.
Page | 141
Table 2.78: ATI for the sixth proposed tin sheets sampling plan at different values of p.
p ATI
0.01 20,796
0.02 92,709
0.03 180,801
0.04 257,219
0.05 313,617
0.06 351,813
0.07 376,531
0.08 392,202
0.09 402,093
0.1 408,368
0
50,000
100,000
150,000
200,000
250,000
300,000
350,000
400,000
450,000
0.00 0.02 0.04 0.06 0.08 0.10
AT
I
Lot fraction defective, p
ATI for the Sixth Propsed Tin Sheets Sampling Plan
Figure 2.140: ATI for the sixth proposed tin sheets sampling plan.
Page | 142
Comparison between the Proposed Double Sampling Plans for
Tin Sheets
Table 2.79: Comparison between the probability of acceptance for the proposed tin sheets
double sampling plans at different values of p.
p Plan 1 Plan 2 Plan 3 Plan 4 Plan 5 Plan 6
0.01 0.9953 0.9731 0.9562 0.9347 0.9135 0.9506
0.02 0.9732 0.8863 0.8505 0.7845 0.7236 0.7794
0.03 0.9343 0.7833 0.7511 0.6511 0.5645 0.5696
0.04 0.8852 0.6899 0.6693 0.5477 0.4482 0.3876
0.05 0.8323 0.6109 0.6000 0.4648 0.3601 0.2533
0.06 0.7798 0.5440 0.5390 0.3957 0.2905 0.1624
0.07 0.7299 0.4863 0.4841 0.3368 0.2343 0.1035
0.08 0.6836 0.4353 0.4344 0.2863 0.1887 0.0662
0.09 0.6410 0.3898 0.3894 0.2430 0.1516 0.0426
0.1 0.6019 0.3488 0.3487 0.2059 0.1216 0.0277
0.00
0.20
0.40
0.60
0.80
1.00
0 0.02 0.04 0.06 0.08 0.1
Pa
Lot fraction defective, p
Comparison between the Probablity of Acceptance for the Proposed Beans Double Sampling Plans
Plan 1
Plan 2
Plan 3
Plan 4
Plan 5
Plan 6
Figure 2.141: Comparison between the probability of acceptance for the proposed tin
sheets sampling plans.
Page | 143
Table 2.80: Comparison between the AOQ for the proposed tin sheets double sampling plans at
different values of p.
p Plan 1 Plan 2 Plan 3 Plan 4 Plan 5 Plan 6
0.01 1.00% 0.97% 0.96% 0.93% 0.91% 0.95%
0.02 1.95% 1.77% 1.70% 1.57% 1.45% 1.56%
0.03 2.80% 2.35% 2.25% 1.95% 1.69% 1.71%
0.04 3.54% 2.76% 2.68% 2.19% 1.79% 1.55%
0.05 4.16% 3.05% 3.00% 2.32% 1.80% 1.27%
0.06 4.68% 3.26% 3.23% 2.37% 1.74% 0.97%
0.07 5.11% 3.40% 3.39% 2.36% 1.64% 0.72%
0.08 5.47% 3.48% 3.48% 2.29% 1.51% 0.53%
0.09 5.77% 3.51% 3.50% 2.19% 1.36% 0.38%
0.1 6.02% 3.49% 3.49% 2.06% 1.22% 0.28%
0.00%
1.00%
2.00%
3.00%
4.00%
5.00%
6.00%
7.00%
0 0.02 0.04 0.06 0.08 0.1
AO
Q
Lot fraction defective, p
Comparison between the AOQ for the Proposed Tin Sheets Double Sampling Plans
Plan 1
Plan 2
Plan 3
Plan 4
Plan 5
Plan 6
Figure 2.142: Comparison between the AOQ for the proposed tin sheets sampling plans.
Page | 144
Table 2.81: Comparison between the ATI for the proposed tin sheets double sampling plans at
different values of p.
p Plan 1 Plan 2 Plan 3 Plan 4 Plan 5 Plan 6
0.01 1,976 11,308 18,420 27,459 36,383 20,796
0.02 11,282 47,749 62,796 90,539 116,108 92,709
0.03 27,618 91,018 104,552 146,555 182,929 180,801
0.04 48,207 130,271 138,882 189,981 231,777 257,219
0.05 70,429 163,444 167,986 224,777 268,765 313,617
0.06 92,506 191,512 193,641 253,820 297,999 351,813
0.07 113,467 215,776 216,696 278,552 321,588 376,531
0.08 132,912 237,178 237,553 299,751 340,745 392,202
0.09 150,781 256,302 256,447 317,938 356,311 402,093
0.1 167,185 273,504 273,558 333,528 368,940 408,368
0
100,000
200,000
300,000
400,000
500,000
0 0.02 0.04 0.06 0.08 0.1
AT
I
Lot fraction defective, p
Comparison between the ATI for the Proposed Beans Double Sampling Plans
Plan 1
Plan 2
Plan 3
Plan 4
Plan 5
Plan 6
Figure 2.143: Comparison between the ATI for the proposed tin sheets sampling plans.
Page | 145
Table 2.82: Comparison between the costs of the proposed tin sheets double sampling plans at
different values of p.
p Plan 1 Plan 2 Plan 3 Plan 4 Plan 5 Plan 6
0.01 21,114 21,345 21,522 21,747 21,968 21,581
0.02 41,843 40,921 40,540 39,838 39,191 39,783
0.03 61,109 56,325 55,304 52,134 49,389 49,550
0.04 78,202 67,894 66,812 60,394 55,143 51,948
0.05 92,943 76,594 75,796 65,814 58,082 50,199
0.06 105,488 83,120 82,639 69,043 59,063 46,905
0.07 116,126 87,881 87,627 70,550 58,669 43,501
0.08 125,156 91,141 91,019 70,729 57,355 40,568
0.09 132,829 93,113 93,058 69,914 55,471 38,240
0.1 139,334 93,986 93,963 68,383 53,279 36,461
Figure 2.144 shows that Plan 6 was the clear winner when it came to
minimizing the total cost of sampling and it was therefore chosen as the best
double sampling plan.
0
50000
100000
150000
0 0.02 0.04 0.06 0.08 0.1
To
tal C
ost
Lot fraction defective, p
Comparison between the Costs of the Proposed Tin Sheets Double Sampling Plans
Plan 1
Plan 2
Plan 3
Plan 4
Plan 5
Plan 6
Figure 2.144: Comparison between the costs of the proposed tin sheets sampling plans.
Page | 146
Comparison between the As-Is and Double Sampling Plans for
Tin Sheets
Table 2.83: Comparison between the probability of acceptance for the tin sheets as- is and
double sampling plans at different values of p.
p As-Is Double Sampling
0.01 0.9044 0.9506
0.02 0.8171 0.7794
0.03 0.7374 0.5696
0.04 0.6648 0.3876
0.05 0.5987 0.2533
0.06 0.5386 0.1624
0.07 0.4840 0.1035
0.08 0.4344 0.0662
0.09 0.3894 0.0426
0.10 0.3487 0.0277
0.00
0.20
0.40
0.60
0.80
1.00
0 0.02 0.04 0.06 0.08 0.1
Pa
Lot fraction defective, p
Comparison between the Probability of Acceptance for the Tin Sheets As-Is and
Double Sampling Plans
Double Sampling Plan
As is Plan
Figure 2.145: Comparison between the probability of acceptance for the tin sheets as-is and
double sampling plans.
Page | 147
Table 2.84: Comparison between the AOQ for the tin sheets as- is and double sampling plans at
different values of p.
p As-Is
Double
Sampling
0.01 0.90% 0.95%
0.02 1.63% 1.56%
0.03 2.21% 1.71%
0.04 2.95% 1.55%
0.05 2.99% 1.27%
0.06 2.69% 0.97%
0.07 2.42% 0.72%
0.08 2.17% 0.53%
0.09 1.95% 0.38%
0.10 1.74% 0.28%
0.00%
0.50%
1.00%
1.50%
2.00%
2.50%
3.00%
3.50%
0 0.02 0.04 0.06 0.08 0.1
AO
Q
Lot fraction defective, p
Comparison between the AOQ for the Tin Sheets As-Is and Double Sampling Plans
Double Sampling Plan
As is Plan
Figure 2.146: Comparison between the AOQ for the as-is and new tin sheets sampling plans.
Page | 148
Table 2.85: Comparison between the ATI for the tin sheets as- is and double sampling plans at
different values of p
p As-Is Double Sampling
0.01 40,169 20,796
0.02 76,838 92,709
0.03 110,289 180,801
0.04 140,777 257,219
0.05 168,536 313,617
0.06 193,787 351,813
0.07 216,732 376,531
0.08 237,561 392,202
0.09 256,449 402,093
0.1 273,559 408,368
.
0
50,000
100,000
150,000
200,000
250,000
300,000
350,000
400,000
450,000
0 0.02 0.04 0.06 0.08 0.1
AT
I
Lot fraction defective, p
Comparison between the ATI for Tin Sheets As-Is and Double Sampling Plans
Double Sampling Plan
As is Plan
Figure 2.147: Comparison between the ATI for the as-is and new tin sheets sampling plans.
Page | 149
Table 2.86: Comparison between the costs of the tin sheets as- is and double sampling plans at
different values of p.
p As-Is Double Sampling
0.01 22,063 21,581
0.02 40,184 39,783
0.03 54,871 49,550
0.04 72,691 51,948
0.05 75,699 50,199
0.06 71,261 46,905
0.07 67,228 43,501
0.08 63,567 40,568
0.09 60,247 38,240
0.1 57,240 36,461
0
10000
20000
30000
40000
50000
60000
70000
80000
0 0.02 0.04 0.06 0.08 0.1
To
tal c
ost
Lot fraction defective, p
Comparison between Costs of the Tin Sheets As-Is and Double Sampling Plans
Double sampling plan
As-is plan
Figure 2.148: Comparison between the costs of the tin sheets as-is and double sampling plans.
Page | 150
Figure 2.148 shows that the cost of the double sampling plan is less
than that of the as-is plan. Therefore, the cost of the double sampling was
compared with that of the new single sampling plan the one with minimum
cost was chosen.
Table 2.87: Comparison between the costs of the tin sheets new single sampling and double
sampling plans at different values of p.
p Double Sampling New Single Sampling
0.01 21,581 21,414
0.02 39,783 40,373
0.03 49,550 52,073
0.04 51,948 56,058
0.05 50,199 54,657
0.06 46,905 50,598
0.07 43,501 45,887
0.08 40,568 41,634
0.09 38,240 38,271
0.1 36,461 35,831
0
100000
00.020.040.060.080.1
To
tal c
ost
Lot fraction defective, p
Comparison between Costs of the Tin Sheets New Single
Sampling and Double Sampling Plans
Double sampling plan
Figure 2.149: Comparison between the costs of the tin sheets new single sampling and double sampling plans.
Page | 151
The double sampling plan has a lower cost as can be seen from figure 2,149
and therefore it was chosen as the best.
2. 9 Conclusion
The overfilling problem was exposed and the root cause analysis
indicated that the problem was with the culture in the factory rather than the
process itself. By eliminating overfilling, the company can save around 68,000
KD per year.
Also, the new quality control documentation will help the company track
quality characteristics of their products and therefore facilitate future quality
control efforts.
Furthermore, by changing the timing of the PH test, defects can be
detected sooner, thus minimizing cumulative costs of poor quality.
Finally, the new sampling plans developed will ensure better
relationships with suppliers as the chances of rejecting lots of good quality
have been reduced and will also save money by reducing the overall sampling
cost.
Page | 152
Page | 153
3. Cost Analysis
Page | 154
Page | 155
3.1 Introduction
"Emerging technologies are revealing unprecedented opportunities for
bringing new and improved products and systems into being that will be more
cost effective in private and public sectors world-wide." (Fabrycky, Life –Cycle
Cost and Economic Analysis) In these times of intensifying international
competition, producers are searching for ways to gain sustainable competitive
advantage in the marketplace. Hence, economic competitiveness is desired
by corporations. Moreover, analyzing the costs of the company may help find
areas of waste to be eliminated, therefore helping them generate more profit.
The National Canned Food Company owns the only factory in Kuwait
that fills canned food. It produces 35,869,495 cans, in twenty two different
varieties, to satisfy the demand of local customers, as well as that of regional
and international markets.
3.1.1 Problem Description
After analyzing the costs of The National Canned Food Company, two main
problems came to attention:
High costs due to overfilling:
The National Canned Food Company tends to overfill a lot of their
products which significantly increases their material costs.
Transportation Costs:
It was noticed that transportation costs are obscenely high due to high
costs of sending to certain markets with comparatively low demand.
Page | 156
3.1.2 Objectives
The main objective of cost analysis is to show substantial long-term
gains and cost savings by eliminating areas of “waste.” As such, the
objectives are as follows:
a. Finding current costs of the company.
b. Find the cost of overfilling.
c. Try to minimize the transportation costs.
d. Find the productivity of the system.
3.1.3 Solution Approach
The variable and fixed costs were found for the process. Using them,
the total cost, total revenue, and total profit of the company were
calculated. The breakeven point for the company, as well as the
breakeven point for each of the twenty-two varieties, separately, was
found. This would help the company decide whether the demand is worth
covering or not for a certain product, as well as offering a clear
understanding of the current situation and standing of the company
regarding how and where their money is being spent. After that, the cost of
overfilling was found, and the alternatives for sending demand to local or
regional areas that would cost less to ship to than the international
markets, therefore maintaining revenue, and at the same time lowering
their transportation costs. Moreover, the company’s current productivity
level and level that what would be achieved by taking the project’s analysis
and suggestions into consideration were found.
Page | 157
3.2 Analysis of As-Is System:
3.2.1 System
Every system has resources going into it, with the decisions being
made. The system also gets resource and system outputs. And overall, there
would be a value or outcome to that output. In the case of the National
Canned Food Company, the system is classified as follows:
Figure 3.1: The National Canned Food Company’s system.
National Canned
Food Company
Resource
Input
Resource
Output
Decisions
System Output
Outcome
Labor
Material
Equipment
Energy
Capital
Other
Labor
Material
Equipment
Energy
Capital
Other
Page | 158
1. Suppliers
The National Canned Food Company imports all their material from
numerous suppliers worldwide.
Carton Suppliers:
Carton Industries Company (Kuwait).
Arabian Packaging Company (UAE).
CeaserPac (Kuwait).
Interpack Company (Kuwait).
Labels Suppliers:
British Industries Press (Kuwait).
Ms Shahid Printing Press (Kuwait).
Integrated Plastic Packaging (UAE).
Aluminum Lids Supplier:
Express Flexi-Pack (UAE).
Glue Suppliers:
Henkels Ashawa Adhesives (Saudi Arabia).
Al Hashmi Trd. (Kuwait).
Master Batch Supplier:
Calrient (Kuwait).
Mushroom Suppliers:
Welton International Group Ltd (China).
Xiamen Continent Economic Development Ltd (China).
Xiamen Gulong Imp & Exp Co. (China).
Xiamen Huilon Imp & Export Trading Co. (China).
Page | 159
Frozen Sweet Corn Supplier:
Mirelite Foreign Trade (Hungary).
Sweet Kernal Corn Supplier:
Lamex Foods (The Netherlands).
Spare Parts Suppliers:
Intralox Inc. (The Netherlands).
Carnaid Metalbox Engineering (England).
Soudronic AG (Switzerland).
Electrolytic Tinplate Suppliers:
Containers Printers (Singapore).
Pacmetal Services (Australia).
Mitsui & Co Ltd (Japan).
Peter Cremer (Germany).
Al Rajhi Co. for Ind. & Trading (KSA).
Soudronic Wire Supplier:
Asia Countries W.L.L (Kuwait).
Lacquer and Thinner Supplier:
Holden Surface Coatings Ltd. (England).
White Wing Lok Closure Supplier:
Gulf Closures W.L.L (Bahrain).
Etimelt 103 Supplier:
National Adhesives Limited (KSA).
Seaming Chucks and Seaming Rolls Supplier:
T.A.J Engineers Ltd. (England).
Page | 160
Can Ends Suppliers:
A.C.P International (Italy).
Mivisa Envases S.A. (Spain).
Impress Metal Packaging Capolo SPA (Italy).
Al Rajhi Co. for Ind. & Trading (KSA).
Flavors and Ingredients Suppliers:
Ali Abdulkarim Trading Co. (Oman).
Tuncsan Salca Konserve Gisa San (Turkey).
Proguimac Color (Spain).
Crestar UK Ltd. (UK).
Food Specialties (UAE).
Leverbrook Ltd (England).
Aralco (France).
Beans and Peas Suppliers:
Pars Ram Brothers (Australia).
Muelle SA (Peru).
Midgulf International (Jordan).
Rizhao Sunway International (China).
Lamex Foods (The Netherlands).
P.S. International Ltd (USA).
Pars Ram Brothers (Australia).
Peters Commodities Ltd (Australia).
The Great Canadian Bean (Canada).
KBC Trading and Processing Co. (USA).
Export Packets Company Ltd (Canada).
Anny Frantzen (Denmark).
Page | 161
2. Customers
Local supermarkets (e.g. Co-ops).
Whole sale stores (e.g. Sultan Centers).
Small stores.
Regional and international markets.
3. Missions and Goals of The National Canned Food Company
Provide the local, regional, and international markets with their
demand for canned food, maintaining high quality standards and
reasonable prices.
Satisfy all of their customers’ demand, without any delays.
4. Resources
Labor
Maintenance, engineers, laborers, machine operators, forklift
operators, quality control, assistant operators, supervisors,
technicians, sales person, accountant, secretary, data entry
workers, messenger, invoice collector, senior accountant,
assistant general manager, store keeper, assistant store keeper,
watchman, transportation person.
Materials
Baked beans, black eye beans, broad beans, chick peas, chick
peas 10mm, chick peas with chili, green peas, hummus tehinah
- chick peas 7mm, hummus tehinah with garlic, lima beans,
mixed vegetables, mushroom pieces and stems, whole
mushrooms, peas and carrots, peeled fava beans with chili, red
kidney beans, red kidney beans with chili, sweet corn, fava
beans, white beans.
Page | 162
Equipments
Container and Product Technology, Electric Control Cabinet,
Line Control Equipment, Labeler, Case Packer, Treadle
Operated Case Stapler, Hand Case Taper, Crate Loader,
Crate Un-loader, Crate Frasers Horizontal Retorts, Associated
Equipment for Retorts, MetaMatic Slat Chain Conveyor,
MetaMatic Filled Can Washer, MetaMatic Gravity Changepart
Twist, MetaMatic Slat Chain Conveyor, Incline Filled Can
Magnetic Elevator, MetaMatic Gravity Roller Conveyor, Pea and
Bean Filler, Cannery Seamer, MetaMatic No.1 De-palletizer,
MetaMatic Vertical Magnetic Elevator and Change Parts Twist,
MetaMatic Empty Can Cable Conveyor, MetaMatic Empty Can
Rinse and Change Part Twist, Can Opening System, 2000 L
Storage Tank, 900 L open Top Tank, 3000L Steam Jacketed
Mixing Tanks, Alpha Laval Plate Heat Exchanger, Ancillary
Equipment, C.I.P. Plant, Hot Water Rotary Blancher, Vibrator
De-Watering Screen, Inspection Conveyor, Gooseneck
Elevator, Buffer Storage Hopper, Intake Sack Tip Hopper,
Gooseneck Elevator, Pneumatic Separator with Vibrator
Feeder, Belt Distribution Conveyor, Soaking Tanks, Flumes,
Suction Tank and Buffer Storage Hopper, Vibrator De-Watering
Screen.
Energy
Electricity, petrol, water.
Capital
Land, building, capital (money).
Other
maintenance, insurance, marketing, transportation.
Page | 163
5. Output
Number of cans.
Revenue from sales.
6. Outcome
Customer satisfaction.
Profit.
Assure canned food availability.
7. Performance Measures
Performance measures are set to have some standards to adhere to. Meeting
their performance measures allows The National Canned Food Company to
fulfill their objectives.
Utilization of machines (number or busy machines per hour).
Can production rate.
Can filling rate.
Amount of waste.
Number of defects.
Machine breakdowns.
8. Decisions The National Canned Food Company Should Consider
What should the working hours of the workers in the office be?
What should the working hours of the workers in the factory be?
What are the operating hours of the factory?
How many workers should the factory have?
How many office workers should they have?
Page | 164
How many hours is one shift?
How many shifts are there during the day?
What are the working hours of the workers in the factory?
What should the salaries/wages of all labor Involved?
What should the price of the products be?
What variety of products should the company offer?
How many of the products should they produce?
What quality standards of production should the company maintain?
What facility layout is appropriate for the factory?
Delivery Decisions.
Storage Decisions.
3.2.2 Productivity Indices
The productivity indices used to calculate The National Canned Food
Company’s productivity are the inputs and outputs of the company explained
in the previous section (labor, material, equipment, energy, other). The
numerical values for those inputs and outputs may be obtained by classifying
the costs as direct costs, indirect costs, technical overheads, company
overheads, and marketing overheads. And from that, the total cost and total
revenue of The National Canned Food Company was calculated.
1. Direct Cost
A direct cost is a cost that is directly attributable to the manufacture of a
product (or provision of a service). A good example of a direct cost is the cost
of the materials needed to make a product. The usage of the materials is
directly related to the manufacture of the product. Direct costs are very often
variable costs and vice-versa, but the two are not synonymous. There are
three types of direct cost:
Direct materials,
Direct labour, and
Direct expenses (mainly equipment).
Page | 165
Direct Labor Costs
The direct labor costs include most of the labor in the can filling plant. They
include all of the machine operators and the forklift operators, since those
laborers are necessary for the production line.
Table 3.2: Direct labor costs.
Designation Salary (KD/month)
Machine Operator 248
Machine Operator 195
Machine Operator 150
Machine Operator 135
Machine Operator 225
Machine Operator 150
Machine Operator 180
Machine Operator 113
Machine Operator 135
Machine Operator 135
Machine Operator 120
Forklift Operator 105
Forklift Operator 105
Forklift Operator 165
Total 2160
Page | 166
Direct Material Cost
(1) Can Making Direct Material Cost:
The National Canned Food Company produces the cans to be filled.
Each can requires all of the materials listed in table 3.2. Also given are the
cost of each of the materials individually, the quantity they require of each
material annually, and their annual production. To obtain the direct cost of
each can, certain calculations were used to convert the indiscrete units to
cost/unit.
Page | 167
Table 3.3: Can making costs.
*Quantity per unit = Quantity per year / Annual Production
**Cost/can = Quantity per unit * cost of material (KD/unit)
***Cost (KD/year) = cost (KD/unit) * Quantity per year
Description Unit Cost
(KD/unit)
Order
Quantity Per Year
Usage per year
Usage
Quantity *
Per can
Cost/can**
Cost***
(KD/Year)
Labels PCS 0.0048 35,869,496 35,869,496 1 0.0048 172,173.58
Copper Wires K.G 3.783 85,000 35,869,496 0.00237 0.0089646 321,555.00
Standard Lids PCS 0.009 48,851,442 35,869,496 1.36192 0.0122573 439,662.98
Easy Open Lids PCS 0.017 17,283,814 35,869,496 0.48185 0.0081915 293,824.84
Tin Sheets PCS 0.56 1,303,796 35,869,496 0.03635 0.0203551 730,125.76
Cartons PCS 0.018 2,880,000 35,869,496 0.08029 0.0014452 51,840.00
Shrink Film PCS 0.96 28,234 35,869,496 0.00079 0.0007556 27,104.64
Glue K.G 1.5 27,002 35,869,496 0.00075 0.0011292 40,503.00
Lacquer K.G 1.2 24,714 35,869,496 0.00069 0.0008268 29,656.80
Page | 168
(2) Can Filling Direct Material Cost:
(a) Beans Direct Cost
The National Canned Food Company produces different types of
products, including water, vinegar, ketchup and sausages which will not be
included in this study since they are produced in a different line. The products
presented in the table below, are the ones being considered. They are all
considered to be direct costs. Given the cost in KD/ton and the quantity in
kg/year, the cost in KD/year was calculated.
Table 3.4: Cost of direct material cost for the beans.
Description Production Cost
Cans/Year KD/year
Baked Beans 3,489,494 83,107.30
Black Eye Beans 494,928 14,005.60
Broad Beans 4,949,942 116,117.50
Chick Peas 6,581,088 126,880.54
Chick Peas 10mm 856,454 77,293.75
Chick Peas with Chili 46,080 888.40
Fava Beans 5,284,656 74,886.58
Fava Beans with Chili 66,960 948.86
Green Peas 7,272,720 52,628.31
Hummus Tehinah 3,925,008 29,292.47
Hummus Tehinah with Garlic 27,014 201.61
Lima Beans 94,464 23,661.92
Mixed Vegetables 351,936 32,008.32
Mushroom Pieces and Stems 182,534 35,191.80
Whole Mushrooms 234,864 43,989.75
Peas and Carrots 51,264 963.37
Peeled Fava Beans with Chili 230,918 4,632.81
Red Kidney Beans 772,934 48,588.55
Red Kidney Beans with Chili 21,600 1,357.83
Sweet Corn 631,238 40,057.24
Fava Beans 174,027 3,491.42
White Beans 129,370 26,165.11
TOTAL 35,869,496 836,359.04
Page | 169
(b) Additives Direct Cost:
Each can is filled with the raw materials and certain additives. The exact
ingredients and recipe of each product were considered confidential by The
National Canned Food Company. Given the cost of their annual order of
additives and the ingredients label on each can, the cost of each product with
its respective additives were obtained, as is shown in table 3.6. Since ratios
were used to obtain the relative costs, the following example on the broad
beans will demonstrate how the costs were obtained in table 3.4. To make
broad beans, only two additives were used; EDTA and citric acid:
Annual Production of broad beans = 4,949,942 cans/year
Annual Cost of EDTA = 2,400 KD/year
Productions and annual production rates of different variety that include
EDTA:
Table 3.5: Sample of additive calculation for broad beans.
Description Annual Production EDTA* KD/year
Black Eye Beans 494,928 62.82
Broad Beans 4,949,942 628.27
Chick Peas 6,581,088 835.30
Chick Peas 10mm 856,454 108.70
Chick Peas with Chili 46,080 5.85
Fava Beans 5,284,656 670.75
Fava Beans with Chili 66,960 8.50
Lima Beans 94,464 11.99
Peeled Fava Beans with Chili 230,918 29.31
Foul Medames 174,027 22.09
White Beans 129,370 16.42
TOTAL 18,908,887 2,400.00
EDTA cost = (Annual cost of EDTA / Total can production using EDTA)
* Broad bean annual production
= (2400/ 18,908,887)*4,949,942
= 628.27 KD/year (EDTA use for broad beans)
The same procedure was done to obtain the figures for the citric acid.
Page | 170
Table 3.5: Annual cost of additives.
Description Unit Cost per
Unit
Given
Order Quantity
(Unit/year)
Cost (KD/year)
Tomato Paste K.G 0.650 24,000 15,600.000
Lemon Juice Ltr 2.900 6,000 17,400.000
Green Color K.G 5.500 350 1,925.000
EDTA K.G 1.000 2,400 2,400.000
Citric Acid K.G 0.868 23,500 20,398.000
Camon Powder K.G 1.500 1,950 2,925.000
Chick Peas
Powder
K.G 0.650 5,205 3,383.250
Spices K.G 2.000 600 1,200.000
Whole Red Chili K.G 1.650 819 1,351.350
Onion Powder K.G 2.250 470 1,057.500
Powdered Red
Chili
K.G 0.950 624 592.800
Total 68,232.900
Page | 171
Ta
ble
3.6
: D
irec
t m
ate
ria
l co
st
of
ad
dit
ives
Page | 172
Ta
ble
3.6
: D
irec
t m
ate
ria
l co
st
of
ad
dit
ives
(c
on
tin
ued
).
Page | 173
(3) Total Direct Cost of Materials:
The cost of materials is the total cost of both the beans and the additives of
each product. The cost of the beans, shown in Table 3.3, and the cost of the
total additives, from Tables 3.5 and 3.6, is added to give us the total cost, in
KD, for each type. Then the following equation was used to give us the direct
cost in KD/unit:
Direct cost = Total cost (KD/Year) / Production (Units/Year)
Table 3.7: Direct costs of materials (beans and additives).
Description Annual Production Cans/year
Cost of Beans ( KD/year)
Total Additive
Cost (KD/year)
Total Cost
Direct Cost*
(KD/unit)
Baked Beans 34,89,494 83,107.3 16,674.33 99,781.63 0.0286
Black Eye Beans 494,928 14,005.6 62.82 14,068.42 0.0284
Broad Beans 4,949,942 116,117.5 7,274.02 123391.52 0.0249
Chick Peas 6,581,088 126,880.54 835.3 127715.84 0.0194
Chick Peas 10mm 856,454 77,293.75 108.7 77402.45 0.0904
Chick Peas with Chili 46,080 888.4 5.85 894.25 0.0194
Fava Beans 5,284,656 74,886.58 7,765.89 82,652.47 0.0156
Fava Beans with Chili 66,960 948.86 416.53 1365.39 0.0204
Green Peas 7,272,720 52,628.31 1,911.53 54,539.84 0.0075
Hummus Tahineh – Chick Peas 7mm
3,925,008 29,292.47 5,269.69 34,562.16 0.0088
HummusTahineh with Garlic
27,014 201.61 36.27 237.88 0.0088
Lima Beans 94,464 23,661.92 11.99 23,673.91 0.2506
Mixed Vegetables 351,936 32,008.32 472.51 32,480.83 0.0923
Mushroom Pieces and Stems
182,534 35,191.8 245.07 35,436.87 0.1941
Whole Mushrooms 234,864 43,989.75 0 43,989.75 0.1873
Peas and Carrots 51,264 963.37 13.47 976.84 0.0191
Peeled Fava Beans with Chili
230,918 4,632.81 15,481.58 20,114.39 0.0871
Red Kidney Beans 772,934 48,588.55 0 48,588.55 0.0629
Red Kidney Beans with Chili
21,600 1,357.83 696.01 2,053.84 0.0951
Sweet Corn 631,238 40,057.24 0 40,057.24 0.0635
Foul Medames 174,026 3,491.42 10,898.92 14,390.34 0.0827
White Beans 129,369 26,165.11 16.42 26,181.53 0.2024
TOTAL 35,869,495 836,359.04 904,555.9 0.0252
Page | 174
* Direct cost = Total cost (KD/Year) / Production (Units/Year)
Total Direct Material Cost:
The total material direct cost is the sum of the unit direct cost of each can,
bean and additive, as presented in Table 3.8 below. The Total Direct Cost in
KD per year was also obtained as shown the Table 8 below.
* Total Direct Cost (KD/year) = Total Material Direct Cost * Production
(KD/unit) (KD/Year)
Page | 175
Table 3.8: Total direct material costs.
Description Annual
Production
Direct Cost Direct Cost Direct Cost Total
Material
Total Direct
Cost
Beans +
Additives
Beans +
Additives Can Direct Cost * KD/year
Unit/Year KD/unit KD/Year KD/can KD/unit
Baked Beans 3,489,494.4 0.028594867 99,781.63 0.058725 0.084892 296,230.1586
Black Eye
Beans 494,928 0.028425185 14,068.42 0.058725 0.087464 43,288.38259
Broad Beans 4,949,942.4 0.02492787 123,391.52 0.058725 0.082686 409,290.9373
Chick Peas 6,581,088 0.019406493 127,715.84 0.058725 0.078038 513,574.9453
Chick Peas
10mm 856,454.4 0.090375448 77,402.45 0.058725 0.149229 127,807.8337
Chick Peas
with Chili 46,080 0.019406467 894.25 0.058725 0.08274 3,812.6592
Fava Beans 5,284,656 0.015640085 82,652.47 0.058725 0.073366 387,714.0721
Fava Beans
with Chili 66,960 0.020391129 1,365.39 0.058725 0.125798 8,423.43408
Green Peas 7,272,720 0.007499235 54,539.84 0.058725 0.066094 480,683.1557
Hummus
Tahineh
Chick Peas
7mm
3,925,008 0.008805628 34,562.16 0.058725 0.066766 262,057.0841
Hummus
Tahineh with
Garlic
27,014.4 0.008805674 237.88 0.058725 0.150086 4,054.483238
Page | 176
Table 3.8: Total direct material Costs (continued).
Description Annual
Production
Direct Cost Direct Cost Direct Cost Total
Material Total Direct
Cost
Beans + Additives
Beans + Additives
Can Direct Cost *
KD/year
Unit/Year KD/unit KD/Year KD/can KD/unit
Lima Beans 94,464 0.250613038 23,673.91 0.058725 0.311521 29,427.51974
Mixed Vegetables
351,936 0.092291866 32,480.83 0.058725 0.156114 54,942.1367
Mushroom Pieces and
Stems 182,534.4 0.194138036 35,436.87 0.058725 0.263937 48,177.58193
Peeled Fava Beans with
Chili 230,918.400 0.087 20,114.390 0.059 0.146 33,718.705
Red Kidney Beans
772,934.400 0.063 48,588.550 0.059 0.122 93,979.548
Red Kidney Beans with
Chili 21,600.000 0.095 2053.840 0.059 0.529 11,419.099
Sweet Corn 631,238.400 0.063 40,057.240 0.059 0.122 77,126.601
Foul Medames 174,026.900 0.083 14,390.340 0.059 0.164 28,578.698
White Beans 129,369.600 0.202 26,181.530 0.059 0.263 33,980.607
TOTAL 3,011,006.187
Page | 177
Equipment Direct Cost
Since the can filling production line is in series, and all the equipment are vital
and required to produce each unit of product, all the machines are considered to be
direct costs. All the equipment was bought in 1984 and have not been replaced
since. The lifespan of all machines is supposedly ten years. However, The National
Canned Food Company still uses the same machines, even though it has been 25
years.
Page | 178
Table 3.9: Direct equipment costs.
Process Machine Description Cost (KWD)
Container and Product
Technology
Metal box available to
undertake tests on the
compatibility of container
and product
10,226.4
Electrical Controls:
Electric Control Cabinet Dry product preparation 8,153.72
Soaking, blanching and
product feed
Filling, closing, and can
handling
Crate unloading, can
drying , labeling, and
case packing
Line Control Equipment To regulate flow of cans
and product
1,329.43
Labeling and Case
Packing
Labeler Labels the cans 3,573.51
Case Packer To collate cans in 3*4*2
configuration
6,274.92
Treadle Operated Case
Stapler
797.66
Hand Case Taper 5.32
Page | 179
Process Machine Description Cost (KWD)
Processing
Crate Loader Chain in-feed conveyor 3,589.47
Crate Un-loader Discharge conveyor 6,593.98
Crate Frasers Horizontal Retorts Steam retort 34,219.58
Associated Equipment for Retorts Flat top trucks and crates with
loose bottoms
7,147.026
Transporter trucks
Filled Can
Handling
MetaMatic Slat Chain Conveyor Conveys cans from seamed
discharge to filled can washer
1,239.03
MetaMatic Filled Can Washer Removes any slight traces of
sauce or brine adhering to the can
3031.1
MetaMatic Gravity Changepart
Twist
From crate un-loader to slat chain
conveyor
204.94
MetaMatic Slat Chain Conveyor Slat chain conveyor with fixed
speed drive
1,239.03
MetaMatic Alpine Conveyor Elevates cans to labeler in-feed 4,785.96
MetaMatic Gravity Changepart
Twist
Conveys cans to and from the
labeler and case packer
638.13
Incline Filled Can Magnetic
Elevator
Elevates filled cans to filled can
cable conveyor
3,759.63
MetaMatic Gravity Roller Conveyor For filled case conveying 265.87
Table 3.9: Direct equipment costs (continued).
Page | 180
Process Machine Description Cost (KWD)
Filling and Closing
Pea and Bean Filler Solids and liquid twin head filler
for peas and beans
29,247.50
Consists of guarding, level
control, combined support for
level control and/or mixer, duty
Cannery Seamer Closing cans 25,331.20
Empty Can Handling
MetaMatic Vertical Magnetic
Elevator and Change Parts
Twist
Discharge with gravity transfer to
cable conveyor
3,456.52
MetaMatic Empty Can Cable
Conveyor
Conveys cans from elevator to
filling area
2,233.45
MetaMatic Empty Can Rinse
and Change Part Twist
Pre-wash can prior to filling 1,967.56
Brine & Sauce Prep.
Can Opening System Opens tomato paste cans 439.74
2000 L Storage Tank Stores vegetable oil 2,197.86
900 L open Top Tank Premixes sugar, seasoning, etc. 1,475.87
3000L Steam Jacketed
Mixing Tanks
Preheat sauce or brine 12,741.28
Alpha Laval Plate Heat
Exchanger
Sauce and brine heater 3,929.80
Ancillary Equipment Control panel suitable for
temperature control, etc.
10,770.44
C.I.P. Plant Cleans brine and sauce
preparation equipment
5,158.20
Table 3.9: Direct equipment costs (Continued).
Page | 181
(1) Depreciation:
The National Canned Food Company use the straight line method to
depreciate their equipment.
Salvage value is assumed to be zero.
Table 3.10: Depreciation of machines.
Machine Life
Span
(n)
Cost
(KWD)
Depreciated
Value Per Year
Container and Product Technology 25 10,226.4 409.1
Electric Control Cabinet 25 8,153.7 326.1
Line Control Equipment 25 1,329.4 53.2
Labeler 25 3,573.5 142.9
Case Packer 25 6,274.9 251.0
Treadle Operated Case Stapler 25 797.7 31.9
Hand Case Taper 25 5.3 0.2
Crate Loader 25 3,589.5 143.6
Crate Un-loader 25 6,594.0 263.8
Crate Frasers Horizontal Retorts 25 34,219.6 1,368.8
Associated Equipment for Retorts 25 7,147.0 285.9
MetaMatic Slat Chain Conveyor 25 1,239.0 49.6
MetaMatic Filled Can Washer 25 3,031.1 121.2
MetaMatic Gravity Changepart Twist 25 204.9 8.2
MetaMatic Slat Chain Conveyor 25 1,239.0 49.6
MetaMatic Alpine Conveyor 25 4,786.0 191.4
MetaMatic Gravity Changepart Twist 25 638.1 25.5
Incline Filled Can Magnetic Elevator 25 3,759.6 150.4
MetaMatic Gravity Roller Conveyor 25 265.9 10.6
Pea and Bean Filler 25 29,247.5 1,169.9
Cannery Seamer 25 25,331.2 1,013.2
MetaMatic No.1 De-palletizer 25 7,976.6 319.1
Page | 182
Table 3.10: Depreciation of machines (continued).
Machine Life Span (n)
Cost (KWD)
Depreciated Value Per
Year
MetaMatic Vertical Magnetic Elevator and Change Parts Twist
25 3,456.50 138.3
MetaMatic Empty Can Cable Conveyor 25 2,233.40 89.3
MetaMatic Empty Can Rinse and Change Part Twist
25 1,967.60 78.7
Can Opening System 25 439.7 17.6
2000 L Storage Tank 25 2,197.90 87.9
900 L open Top Tank 25 1,475.90 59
3000L Steam Jacketed Mixing Tanks 25 12,741.30
509.7
Alpha Laval Plate Heat Exchanger 25 3,929.80 157.2
Ancillary Equipment 25 10,770.40
430.8
Vibrator De-Watering Screen 25 1,522.10 60.9
Inspection Conveyor 25 5,199.10 208
Gooseneck Elevator 25 1,527.40 61.1
Buffer Storage Hopper 25 4,254.20 170.2
Intake Sack Tip Hopper 25 1,063.50 42.5
Gooseneck Elevator 25 1,442.70 57.7
Pneumatic Separator with Vibrator Feeder
25 1,995.40 79.8
Gooseneck Elevator 25 1,662.80 66.5
Belt Distribution Conveyor 25 5,133.20 205.3
Suction Tank and Buffer Storage Hopper 25 2,083.30 83.3
Vibrator De-Watering Screen 25 1,522.10 60.9
Forklift 25 18,000 720
TOTAL 10,469.90
Page | 183
2. Indirect Costs
Indirect costs are those costs that are needed but not essential to produce
each part. In the case of the National Canned Food Company, all of the
indirect costs are labor costs. Indirect costs are very often variable costs.
There are three types of indirect cost:
Indirect materials,
Indirect labour, and
Indirect expenses (mainly equipment).
The indirect costs of The National Canned Food Company are the following:
a) Indirect Material: (none)
b) Indirect Labor:
Table 3.11: Indirect labor costs.
Designation Salary (KD/month)
Quality Controller 375
Quality Controller 270
Quality Controller 270
Quality Controller 255
Assistant Operator 128
Assistant Operator 105
Assistant Operator 173
Assistant Operator 98
Assistant Operator 98
Assistant Operator 98
Assistant Operator 180
Assistant Operator 90
Assistant Operator 90
Assistant Operator 98
Total 2,325
Page | 184
Workers may have the same designation with different salaries based
on their work experiences, how hard working they are, and their
nationality.
Office workers have no overtime.
Can plant workers are requested to stay overtime depending on the
work requirement.
A maximum of 4 overtime hours are allowed per day.
On average, each worker in the National Canned Food Company
works 40-50 overtime hours per month.
The overtime for plant workers is as follows:
Normal days per hour = Total salary / 30 / 8*1.25
Fridays per hour = Total salary / 30 / 8*1.50
Holidays per hour = Total salary / 30 / 8*1.75
The total overtime cost is 1,750 KD per month.
c) Indirect Equipment: (none)
Page | 185
3. Overheads
Overheads are those costs which are incurred in the running of the business
and which are not directly associated with a specific job. Overhead costs are
always fixed. There are three types of overheads:
Technical Overheads
Technical or factory overheads are any expenses related to
production but are not included in every unit.
Table 3.12: Technical overheads costs.
Designation Salary
(KD/month)
Spare Parts 5,000
Equipment Maintenance 1,458.33
Supervisor 525
Technical 210
Laborer 98
Laborer 180
Laborer 180
Laborer 180
Laborer 180
Laborer 135
Laborer 90
Laborer 150
Laborer 90
Laborer 75
Laborer 75
Laborer 90
Laborer 105
Total 8,821.33
Page | 186
Company Overheads
Company overheads are, as the name implies, those expenses that
are not related to manufacturing the product but rather related to
management and office.
Table 3.13: Company overheads costs.
Marketing Overheads
The Marketing costs are 12,000 KD/year. They mainly use this
amount for designs for the labels and posters. The National
Canned Food Company doesn't advertise in Kuwait. Every year
they attend a marketing exhibition in Dubai.
Designation Salary (KD/month)
Export and Import 451
Accountant 442
Data Entry 1 400
Secretary 255
Messenger 527
Invoice Collector 527
Senior Accountant 680
Assistant General Manager 1,275
Data Entry 170
Store Keeper 300
Assistant Store Keeper 180
Store Keeper 105
Watchman 135
Transportation 14,880
Insurance 833
Utilities: Water 600
Utilities: Petrol 2,450
Utilities: Electricity 700
Land 500
Total 25,409
Page | 187
4) Modeling Costs Overview:
a) Materials:
Direct Materials Cost = 3,011,006.187 KD/year.
Indirect Material Cost = 0 KD/year.
Total Material Cost = 3,011,006.187 KD/year.
b) Labors:
Direct Labors Cost = 2,160 KD/year.
Indirect Labors Cost = 2,325 KD/year.
Total Labors Cost = 4,485 KD/year.
c) Equipment:
Direct Machine Cost = 10,469.9 KD/year.
Indirect Machine Cost = 0 KD/year.
Total Machine Cost = 10,469.9 KD/year.
Total Direct Cost = 3,013,166.187 KD/year.
Total Indirect Cost = 2,325 KD/year.
d) Overheads: Technical Overhead Cost = 8,821.33 KD/year.
Company Overhead Cost = 25,409 KD/year.
Marketing Overhead Cost = 12,000 KD/year.
Total Overhead Cost = 46,230.33 KD/year.
Page | 188
5. Variable Cost
Variable costs are the costs that change according to the production rate. For
The National Canned Food Company, the only variable costs are the material
costs, utilities, and overtime since these are the costs that change with the
production rate. Hence, the total material direct cost + utility cost is the unit
variable cost. Multiplying the unit variable cost by the annual production rate
will result in the variable cost in KD/year.
Table 3.14: Variable costs.
Description
Annual
Production
Total
Material
Direct
Cost
Unit
Variable
Cost
Variable
Cost
Unit/Year KD/unit (KD/unit) KD/year
Baked Beans 3,489,494 0.0873 0.0873 304,632.83
Black Eye Beans 494,928 0.0872 0.0872 43,157.72
Broad Beans 4,949,942 0.0837 0.0837 414,310.15
Chick Peas 6,581,088 0.0781 0.0781 513,982.97
Chick Peas 10mm 856,454 0.1491 0.1491 127,697.29
Chick Peas with Chili 46,080 0.0781 0.0781 3,598.85
Fava Beans 5284656 0.0744 0.0744 393,178.41
Fava Beans with Chili 66,960 0.0791 0.0791 5,296.54
Green Peas 7,272,720 0.0662 0.0662 481,454.06
Hummus Tahineh - Chick Peas 7mm 3,925,008 0.0675 0.0675 264,938.04
Hummus Tahineh with Garlic 27,014 0.0675 0.0675 1,823.45
Lima Beans 94,464 0.3093 0.3093 29,217.72
Mixed Vegetables 351,936 0.151 0.151 53,142.34
Mushroom Pieces with Stems 182,534 0.2529 0.2529 46,162.85
Whole Mushrooms 234,864 0.246 0.246 57,776.54
Peas and Carrots 51,264 0.0778 0.0778 3,988.34
Peeled Fava Beans with Chili 230,918 0.1458 0.1458 33,667.84
Red Kidney Beans 772,934 0.1216 0.1216 93,988.77
Page | 189
Table 3.14: Variable costs (continued).
Description
Annual Production
Total Material Direct Cost
Unit Variable Cost
Variable Cost
Unit/Year KD/unit (KD/unit) KD/year
Red Kidney Beans with Chili
21,600 0.1538 0.1538 3,322.08
Sweet Corn 631,238 0.1222 0.1222 77,137.28
Foul Medames 174,026 0.1414 0.1414 24,607.28
White Beans 129,369 0.2611 0.2611 33,778.25
TOTAL 35869496 3,010,859
Variable Cost
Variable Cost Variable Cost
KD/month KD/year KD/unit
Utility: Water 600 7,200 0.000200728
Utility: Electricity 700 8,400 0.000234182
Utilities: Petrol 2,450 29,400 0.000819638
TOTAL 45,000 0.001254548
Variable Cost
Variable Cost Variable Cost
KD/month KD/year KD/unit
Total Overtime Cost
1,750 21,000 0.000585456
TOTAL VARIABLE COST
3,076,859.58 0.001840004 (Utilities +OT)
Page | 190
6. Fixed Costs
Fixed costs are those costs that do not vary or change with the
production rate. Therefore, the fixed cost in the case of the National Canned
Food Company would be the sum of the overheads and the direct labor and
equipment costs.
Total Overheads = Technical Overhead + Company Overhead + Marketing
Overhead
= (8,821.33*12) + (21,659*12) + 12,000
= 105,855.96 + 259,908 + 12,000
= 377,763.96 KD/year
Total Equipment Cost = 10,469.9 KD/Year
Total Labor Costs = Direct Labor + Indirect Labor
= (2160*12) + (2325*12)
= 25,920 + 27,900
= 53,820 KD/year
Total Fixed Cost = Total Overheads + Total Equipment Costs + Total Labor
Costs
= 377,763.96 + 10469.9 + 53,820
= 442,053.86 KD/year
7. Total Cost
The total cost is the sum of the variable and fixed cost.
Total Cost = Variable Cost + Fixed Cost
= 3,076,859.58+ 442,053.86
= 3,518,913.44 KD/year
Page | 191
8. Total Revenue:
The total revenue is how much money the company makes from selling
their products. The selling price is how much the product is being sold for, and
the total revenue per year is obtained from multiplying the selling price by how
much is being produced every year of each product.
Table 3.15: Total revenue.
Description
Annual
Production
Selling
Price Total Revenue; SP*X
Cans/Year KD/unit KD/Year
Baked Beans 3,489,494 0.135 471,081.74
Black Eye Beans 494,928 0.130 64,340.64
Broad Beans 4,949,942 0.120 593,993.09
Chick Peas 6,581,088 0.120 789,730.56
Chick Peas 10mm 856,454 0.170 145,597.25
Chick Peas with Chili 46,080 0.135 6,220.80
Fava Beans 5,284,656 0.110 581,312.16
Fava Beans with Chili 66,960 0.120 8,035.20
Green Peas 7,272,720 0.085 618,181.20
Hummus Tahineh - Chick
Peas 7mm
3,925,008 0.110 431,750.88
Hummus Tahineh with Garlic 27,014 0.120 3,241.73
Lima Beans 94,464 0.330 31,173.12
Mixed Vegetables 351,936 0.185 65,108.16
Mushroom Pieces with
Stems
182,534 0.300 54,760.32
Whole Mushrooms 234,864 0.300 70,459.20
Peas and Carrots 51,264 0.130 6,664.32
Peeled Fava Beans with Chili 230,918 0.170 39,256.13
Red Kidney Beans 772,934 0.155 119,563.29
Red Kidney Beans with Chili 21,600 0.170 3,665.25
Sweet Corn 631,238 0.165 104,154.34
Foul Medames 174,027 0.175 30,454.71
White Beans 129,370 0.280 36,223.49
TOTAL 35,869,496 3.714 4,274,967.57
Page | 192
9. Total Profit
Total profit = Total Revenue – Total Cost
= 4,274,967.57- 3,519,056.42
= 755,911.15 KD/Year
Profit Margin = Profit / Revenue
= 755,911.15 / 4,323,882.3
= 17.48 %
The following table, Table 3.16, shows how the allocation of the cost,
revenues and profits are for each of the products individually.
Page | 193
Table 3.16: Total profit.
Description
Annual
Production
Unit
Variable
Cost
Fixed Cost Total Cost Total
Revenue Total Profit
Cans/Year (KD/unit) KD/year KD/Year KD/Year KD/Year
Baked Beans 3,489,494 0.089 43,004.348 354,057.893 471,081.744 117,023.851
Black Eye Beans 494,928 0.089 6,099.468 50,167.859 64,340.640 14,172.781
Broad Beans 4,949,942 0.086 61,002.836 484,420.928 593,993.088 109,572.160
Chick Peas 6,581,088 0.080 81,104.997 607,197.198 789,730.560 182,533.362
Chick Peas 10mm 856,454 0.151 10,554.896 139,828.126 145,597.248 5,769.122
Chick Peas with
Chili 46,080 0.080 567.888 4,251.523 6,220.800 1,969.277
Fava Beans 5,284,656 0.076 65,127.834 468,030.029 581,312.160 113,282.131
Fava Beans with
Chili 66,960 0.081 825.212 6,244.954 8,035.200 1,790.246
Green Peas 7,272,720 0.068 89,628.635 584,464.532 618,181.200 33,716.668
Hummus Tahineh -
Chick Peas 7mm 3,925,008 0.069 48,371.601 320,531.671 431,750.880 111,219.209
Hummus Tahineh
with Garlic 27,014 0.069 332.919 2,206.098 3,241.728 1,035.630
Lima Beans 94,464 0.311 1,164.170 30,555.699 31,173.120 617.421
Mixed Vegetables 351,936 0.153 4,337.242 58,127.141 65,108.160 6,981.019
Page | 194
Table 3.16: Total profit (continued).
Description Annual
Production
Unit Variable
Cost Fixed Cost Total Cost
Total Revenue
Total Profit
Cans/Year (KD/unit) KD/year KD/Year KD/Year KD/Year
Mushroom Pieces and
Stems 182,534 0.255 2,249.54 48,748.35 54,760.32 6,011.97
Whole Mushroom 234,864 0.248 2,894.45 61,103.15 70,459.20 9,356.05
Peas and Carrots 51,264 0.08 631.775 4,714.44 6,664.32 1,949.88
Peeled Fava Beans with Chili
230,918 0.148 2,845.82 36,938.62 39,256.13 2,317.51
Red Kidney Beans
772,934 0.123 9,525.60 104,936.63 119,563.29 14,626.67
Red Kidney Beans with Chili
21,600 0.156 266.197 3,628.02 3,665.25 37.229
Sweet Corn 631,238 0.124 7,779.35 86,078.16 104,154.34 18,076.18
Foul Medames 174,027 0.143 2,144.69 27,072.30 30,454.71 3,382.41
White Beans 129,370 0.263 1,594.34 35,610.78 36,223.49 612.708
TOTAL 35,869,496 2.942 442,053.80 3,518,914.09 4,274,967.57 756,053.47
Page | 195
10. Productivity Analysis Results
All the previously collected data were used to calculate the productivity of the
National Canned Food Company.
Total Productivity = Total Output / Total Input
= Total Revenue /Total Cost
= 42,749,67.57 / 3,518,913.44
= 1.214 > 1
Since the total productivity is greater than 1, it means that The National
Canned Food Company is productive.
11. Break Even Point
The breakeven point is the point that the company covers its losses and from
then on starts making profit. This point is when the total profit is equal to zero.
To graphically show the breakeven point, the total cost is plotted against total
revenue. The point of intersection is the breakeven point. Figure 3.2 shows
the breakeven point for the company as a whole. Appendix V contains the
breakeven points for each product on its own. These can be helpful to show
the company how much of a certain product should be produced to make a
profit out of it.
Page | 196
a) Total Breakeven Point
Table 3.17: Total profit.
Annual Production Total Cost Total
Revenue Total Profit
Cans/Year KD/Year KD/Year KD/Year
0 442053.798 0 -442053.8
1000000 575781.0707 168818.182 -406962.89
2000000 709508.3435 337636.364 -371871.98
3000000 843235.6162 506454.545 -336781.07
4000000 976962.8889 675272.727 -301690.16
5000000 1110690.162 844090.909 -266599.25
6000000 1244417.434 1012909.09 -231508.34
7000000 1378144.707 1181727.27 -196417.43
8000000 1511871.98 1350545.45 -161326.53
9000000 1645599.253 1519363.64 -126235.62
10000000 1779326.525 1688181.82 -91144.707
11000000 1913053.798 1857000 -56053.798
12000000 2046781.071 2025818.18 -20962.889
13000000 2180508.343 2194636.36 14128.02
14000000 2314235.616 2363454.55 49218.929
15000000 2447962.889 2532272.73 84309.838
16000000 2581690.162 2701090.91 119400.75
17000000 2715417.434 2869909.09 154491.66
18000000 2849144.707 3038727.27 189582.57
19000000 2982871.98 3207545.45 224673.47
20000000 3116599.253 3376363.64 259764.38
21000000 3250326.525 3545181.82 294855.29
12597389 2126668.272 2126668.31 0.0341818
Page | 197
Total Breakeven Point
0
500000
1000000
1500000
2000000
2500000
3000000
3500000
4000000
0
2000
000
4000
000
6000
000
8000
000
1000
0000
1200
0000
1400
0000
1600
0000
1800
0000
2000
0000
Production
KD
Total Cost
Total Revenue
Figure 3.2: Total breakeven point.
Page | 198
4. New System
A. Overfilling:
The National Canned Food Company tends to over fill their products. When
over filling, the company is losing money. Depending on how much they over
fill and how much they produce of the products they over fill, the company
might actually have significant savings if they prevent over filling.
In the table on the following page, the annual cost of over filling for each type
of product is shown. The over filling is how many grams the product is being
overfilled per can. The target is how much the company aims to fill each
product. Although we’re working with the 400g cans, almost half of it is filled
with brine, and not the problem with increased costs when overfilling. Hence,
we’ll only consider the over filling of solid filling (the actually product itself.)
The cost per gram is needed to find how much it costs to overfill. This was
obtained by the following equation:
Cost per gram = Cost per year / (# cans produced per year * target)
Then the cost of overfilling in KD per year was obtained using the following
equation:
Cost of over filling = Amount over filled per year * cost per gram
As shown in table 3.40, 68,001.66 KD/year can be saved if they prevent
overfilling. This represents about 2.04% of their total cost.
Given that they tend not to record everything, and that not all variety of
products was covered, there is a very big possibility that costs of overfilling
are even higher than what was estimated.
Page | 199
Table 3.18: Costs of over filling.
OVER FILLING
Description Overfilling Production Target Overfilling Annual
Cost Cost Per
Gram
Cost of Over
Filling
g/can can/year g/can g/year KD/year KD/g KD/year
Baked Beans -0.17 3,489,494 170 -582,746 83,107 0.0001401 -81.6
Fava Beans -0.5 75,835 180 -37,918 75,835 0.0055556 -210.7
Green Peas 0.37 7,272,720 188 2,701,088 52,999 0.0000389 105
Hummos Tehina -1.5 29,494 408 -44,241 29,494 0.002454 -108.6
Mix Vegetables -2.5 351,936 233 -879,840 32,008 0.0003912 -344.2
Mushroom Pieces 0 182,534 215 0 35,192 0.0008967 0
Mushroom Whole 0 234,864 215 0 43,990 0.0008712 0
TOTAL 67,361.70
Page | 200
B. Transportation Costs
The transportation costs of The National Canned Food Company are very
high compared to the rest of their costs. It amounts to 14,880 KD/month, which is
178,560 KD/year representing 5.1% of the company’s total cost. Table 3.41 shows
the transportation costs and demand for The National Canned Food Company’s
different markets. Local transportation costs are considered to be zero since local
customers pick up their orders from the warehouse. Transporters for local and
regional markets are trucks, while for international markets they are ships.
Minimizing their transportation costs would lower their total cost.
Table 3.19: Transportation costs of The National Canned Food Company.
1. Transportation Forecast Cost for Year 1: 2009;
Avg. Demand
(transporter/month)
Capacity of
transporter (carton)
Cost
(KD/transporter)
Local 28 2100 0
KSA 6 2100 200
UAE 5 2100 300
Bahrain 4 2100 290
Qatar 3 2100 300
Oman 3 2100 400
Iraq 3 2100 150
Tunisia 2 1650 815
USA 3 1650 980
Kenya 3 1650 1300
Totals 122400 cartons/month 14,880
Page | 201
It was noticed that the three markets with the least demand and highest
transportation costs were Kenya, USA and Tunisia respectively. Due to increasing
yearly demand by approximately 10% annually (see Appendix), the company are
barely keeping up with demand, have huge amounts of overtime, and frequent
machine breakdowns. Reallocating their demand to local and regional markets
seems sensible especially since it costs more than twice the price to ship. Moreover,
the amount demanded by each of Tunisia, Kenya, and the US are very small to have
any substantial marketing value. The annual costs of the markets to be eliminated
and allocated to are represented in tables 3.42 and 3.43.
Table 3.20: Annual transportation costs to international markets.
Demand Shipping Cost
Cans/Year KD/year
Tunisia 950,400 19,560
USA 1,425,600 35,280
Kenya 1,425,600 46,800
Total 3,801,600 101,640
Table 3.21: Annual transportation costs to local and regional markets.
Demand Shipping Cost % Total Demand
Cans/Year KD/year Demand/Total Demand
Local 16,934,400.00 0.00 0.480392157
Regional
KSA 3,628,800 14,400 0.103
UAE 3,024,000 18,000 0.086
Bahrain 2,419,200 13,920 0.069
Qatar 1,814,400 10,800 0.058
Oman 1,814,400 14,400 0.051
Iraq 1,814,400 5,400 0.051
Total 14,515,200 76,920
In order to produce the 35,869,496 cans annually, The National Canned Food
Company is operating their regular 8 hours, and utilizing their maximum overtime
of 4 hours. Given these conditions, the maximum capacity the company can
produce is 36,691,200 cans annually. Given that the demand is increasing by 10%
every year, it can be noticed from Table 3.44 below that The National Canned
Page | 202
Food Company won’t be able to cover demand for their local and regional
customers. Therefore, it is only sensible to cover the difference in demand by
allocating it from the country that is most expensive to send to, Kenya, then the
second highest country to send to, US, and last Tunisia.
Table 3.22: 2009 shipping costs and allocated demand to local and regional markets.
* Demand = 2008Demand + (2008 Demand *0.1)
** Demand Difference = 2009 Demand – 2008 Demand
*** Extra Trucks Needed Yearly = (Demand Difference/24)/2100 24 cans in a carton 2100 KD per truck
**** Allocated Demand (see next page)
***** New Shipping Cost = Shipping Cost + (Extra Trucks*Truck Cost)
2009
Demand* Demand
Difference** Extra
Transporters Needed Yearly***
Allocated Demand****
New Shipping*****
Increase 10% Cans/year Cost KD/year
Local 18,627,840 1,693,440 1,693,440
Regional
KSA 3,991,680 362,880 7 362,880 15,840
UAE 3,326,400 302,400 6 302,400 19,800
Bahrain 2,661,120 241,920 5 241,920 15,312
Qatar 1,995,840 181,440 4 181,440 11,880
Oman 1,995,840 181,440 4 181,440 15,840
Iraq 1,995,840 181,440 4 181,440 5,940
Total 34,594,560 3,144,960 84,612
Page | 203
Allocated Demand:
The demand for 2009 including that for international markets is 38,776,320
cans annually, exceeding the company’s maximum capacity, taking into account a
maximum overtime of 4 hours daily, by 2,085,120 cans. Since Kenya is the
country that costs most to send to, we’re going to allocate the demand from Kenya
to the local and regional markets so satisfy all their demands. Kenya’s demand
for 2009 is 1,045,440 cans, but to satisfy the local demand only, Kenya’s entire
demand should be allocated to the local markets to cover the difference in
demand, as well as 125,280 cans from the US. And since the company won’t be
able to cover the demand for the regional markets for 2009, the difference in units
should be allocated from The US, since Kenya has already been entirely omitted.
The demands for KSA, UAE, Bahrain, Qatar and Oman can all be covered by
allocating the demand from the USA. The demand for Iraq, however, won’t be
covered from the US alone given that the demand of the US has already been
allocated to the other regional countries. Hence, 8640 cans will be allocated from
Tunisia to Iraq.
Table 3.45 shows the new shipping costs and demand that’s going to be sent to
international markets. Given that all the demand for Kenya and the US have been
allocated to cover the demand for the local and regional markets, no units will be
shipped to them, and Tunisia will have 26 transporters.
Table 3.23: 2009 shipping costs and demand for international markets.
New Demand Cans Shipped
Number of Transporters
Annually
New Shipping Cost
2009 2009 KD/year
Tunisia 1,045,440 1,036,800 26 21,338
Total 1,045,440 21,338
Page | 204
2. Transportation Forecasted Cost for Year 2: 2010;
Table 3.46 shows the shipping costs and demand for local and regional markets.
Demand forecasts (see appendix) suggests the demand will increase by 10%. In that
case, the demand for local and regional markets alone will be 38,054,016 cans.
Their maximum capacity, however, is 36,691,200 cans annually. Hence, the demand
to Tunisia will not be met, and will be allocated to the local market. Even after the
allocation, none of the demand will be met. So, it is going to be assumed that the
company will use up their 4 hours of overtime and produce with maximum capacity.
Hence, the difference between the maximum capacity and the demand in 2009 will
be divided by the number of markets they’re willing to send to, in this case 1 local
market, and 6 regional ones. This number will be added to each of the demand for
this year to be able to satisfy it as much as possible.
When adding those numbers, it can be seen in Table 3.46, that not all markets
require this increase. Consequently, the amounts with negative deficit (implying their
demand is being exceeded by the number given) will be removed from those
markets respectively and added to the local market since it’s the one with the highest
deficit.
Table 3.24: 2010 demand and demand deficit for local and regional markets.
Demand to Be Met Demand
Demand Deficit
Cans/year
Local 18927360 1563264
Regional
KSA 4291200 99648
UAE 3625920 33120
Bahrain 2960640 -33408
Qatar 2295360 -99936
Oman 2295360 -99936
Iraq 2295360 -99936
Page | 205
Table 3.47 shows the shipping costs and demand for local and regional markets
after readjusting the demand deficits for the regional customers. Table 3.48 shows
what’s left of the international market, Tunisia. Since all of its demand will be
allocated to the local market, and the company is already working at maximum
capacity, nothing will be sent to Tunisia.
So by 2010, The National Canned Food Company will be working at maximum
capacity and still won’t be satisfying their local and the two major regional markets.
Table 3.25: 2010 shipping costs and demand for local and regional markets.
2010 Demand* Demand To Be Met**
Demand Deficit***
Extra
Transporters
Needed
Yearly****
New Shipping*****
Increase 10% Cans/year Cans/year Cost KD/year
Local 20,490,624 19,260,576 1,230,048 - 0
Regional
KSA 4,390,848 4,291,200 99,648 6 15,589
UAE 3,659,040 3,625,920 33,120 6 19,189
Bahrain 2,927,232 2,927,232 0 5 14,976
Qatar 2,195,424 2,195,424 0 4 11,592
Oman 2,195,424 2,195,424 0 4 15,192
Iraq 2,195,424 2,195,424 0 4 6,192
Total 38,054,016 82,729
* 2010 Demand = 2009 Demand + (0.1* 2009 Demand) ** Demand To Be Met =Demand + (Shipped to Tunis/7) + (Capacity-Demand)/7 *** Demand Deficit = Demand 2010 - Demand to be met **** Extra Transporters Needed Yearly = (Demand Difference/24)/2100 24 cans in a carton 2100 KD per truck ***** New Shipping Cost = Shipping Cost + (Extra Trucks*Truck Cost)
Page | 206
Table 3.26: 2010 shipping costs and demand for international markets.
2010 Demand Demand Shipped
Increase 10% 2010
Tunisia 1,149,984 0
Since the National Canned Food Company is the only can filling company in
Kuwait, it is firmly believed that they should first cover their local customers. Since
there is a huge deficit in satisfying the local market with 1,230,048 cans annually, a
regional market should be omitted to firstly satisfy the local customers to minimize
transportation costs. Given all the transportation costs in Table 3.41, Oman’s
transportation cost is the most expensive from all the regional shipping costs
opposed to the average shipping cost of 248KD of all the other regional countries.
So, it is highly recommended that the demand from Oman should be reallocated to
the local market, and to KSA, and UAE.
Table 3.27: 2010 shipping costs and demand for local and regional markets, considering re-allocating
demands from Oman.
Year 2
Demand Demand To Be
Met Transporters
Needed Yearly New
Shipping
10% Cans/year Cost KD/year
Local 20,490,624 20,490,624 - 0
Regional
KSA 4,390,848 4,390,848 87 17,424
UAE 3,659,040 3,659,040 73 21,780
Bahrain 2,927,232 2,927,232 58 16,843
Qatar 2,195,424 2,195,424 44 13,068
Oman 2,195,424 832,608 17 6,608
Iraq 2,195,424 2,195,424 44 6,534
Total 17,563,392 82,257
Page | 207
3. Transportation Forecast Cost for Year 3: 2011;
With a 10% demand increase 3 years from now, the demand deficit for the
local customers is going to be very high. So as has been suggested previously, to
minimize their costs, the National Canned Food Company should start eliminating
one regional market at a time from the highest shipping cost to the lowest to try to
prioritize the local market.
Table 3.28: 2011 demand for local and regional markets.
2011 Demand Annual Demand To Be
Met
Demand
10% increase Deficit
Local 22,539,686 20,717,760 1,821,926
Regional
KSA 4,829,933 4,390,848 439,085
UAE 4,024,944 3,659,040 365,904
Bahrain 3,219,955 2,927,232 292,723
Qatar 2,414,966 2,195,424 219,542
Oman 2,414,966 832,608 1,582,358
Iraq 2,414,966 2,195,424 219,542
Total 41,859,418 36,918,336
Re-allocating all the demand from Oman wouldn’t cover the local market, so
the country with the second highest shipping cost will start to be omitted to satisfy
the local market. In this situation, two countries have a shipping cost of
300KD/month. However, since Qatar has lower demand than the UAE, it should be
eliminated first after totally depleting Oman’s demand.
Page | 208
Table 3.29: 2011 demand for local and regional Markets after Oman’s demand has been depleted.
2011 Demand Demand To Be Met
Demand
10% Deficit
Local 22539686 21550368 989318
Regional
KSA 4829932 4390848 439084
UAE 4024944 3659040 365904
Bahrain 3219955 2927232 292723
Qatar 2414966 2195424 219542
Oman 2414966 0 -
Iraq 2414966 2195424 219542
Since the local market will only require 989,318 cans to fully cover its
demand, it will come out of Qatar’s demand. Qatar will also fulfill the demands of
other countries with demand deficits. The priority is to provide for the local market of
course, and from then on, providing for countries with the least transportation cost.
So after the local market, satisfying Iraq’s demand will be prioritized followed by KSA
and Bahrain, and finally the UAE since it’s the most expensive to ship to from
remaining regions. By doing so, all the regional demands will be satisfied with the
exception of some of the UAE’s demands.
Table 3.30: 2011 demand and shipping costs for local and regional markets after Oman and Qatar’s
demands have been depleted.
Year 3 Demand
Demand To Be Met
Cans/year
Demand Deficit
cans/year
Transporters Needed
Yearly
Shipping Cost
10% increase KD/year
Local 22,539,686 22,539,686 0 0 0
Regional
KSA 4,829,933 4,829,933 0 96 19,200
UAE 4,024,944 3,686,659 338,285 73 21,900
Bahrain 3,219,955 3,219,955 0 64 18,560
Qatar 2,414,966 0 - 0 0
Oman 2,414,966 0 - 0 0
Iraq 2,414,966 2,414,966 0 48 7,200
TOTAL 41,859,418 36,691,200 66,860
Page | 209
4. Transportation Forecast Cost for Year 4; 2012
The UAE has the highest shipping cost from the remaining regional customers,
hence demand will be reallocated from the UAE to the local market initially, and then
to regional markets from the ones with lower shipping costs to higher ones.
Table 3.31: 2012 demand and demand to be met for local and the remaining regional markets.
2012 Demand
Demand To Be Met
Demand Deficit
Transporters Needed Yearly
Shipping Cost
KD/year
Local 24793655.04 24,793,655 0 0
Regional
KSA 5312926.08 5,312,926 0 106 21,200
UAE 4427438.4 386,205 4,041,233 8 2,400
Bahrain 3541950.72 3,541,951 0 71 20,590
Iraq 2656463.04 2,656,463 0 53 7,950
TOTAL 40732433.28 36,691,200 52,140
Page | 210
5. Transportation Forecast Cost for Year 5; 2013
The local demand deficit has been covered up by what was left of the UAE demand.
The next market that was eliminated was Bahrain since it had transportation costs of
290 KD, compared with 200KD, and 150KD for each of KSA and Iraq respectively.
Therefore, UAE and Bahrain are not going to be covered anymore, and the only
regional markets remaining are KSA, and Iraq.
Table 3.32: 2013 demand and shipping costs for local and the remaining regional markets.
2013 Demand
Demand To Be Met
Cans/year
Demand Deficit
Transporters Needed Yearly
Shipping Cost KD/year
Cans/year
Local 27,273,021 27,273,021 0
Regional
KSA 5,844,219 5,844,219 0 116 23,191
UAE 4,870,182 0 -
Bahrain 3,896,146 651,851 3,244,295 13 3,751
Iraq 2,922,109 2,922,109 0 58 8,697
TOTAL 44,805,677 36,691,200 35,639
6. Transportation Forecast Cost for Year 6; 2014
Bahrain has the highest transportation cost from the remaining regional customers.
Hence, its demand will be allocated first to the local market and then to Iraq. Finally,
what’s left is allocated to the KSA to cover their demand deficit.
Table 3.33: 2014 demand and shipping costs for local and the remaining regional markets.
2014 Demand Demand
To Be Met Demand Deficit
Transporters Needed
Shipping Cost
Cans/year Cans/year Trucks/year KD/year
Local 30,000,323 30,000,323 0
Regional
KSA 6,428,641 3,476,557 2,952,084 69 13,796
Iraq 3,214,320 3,214,320 0 64 18,495
TOTAL 43,929,044 36,691,200 7,237,844 728 32,291
Page | 211
6. Transportation Forecast Cost for after Year 6
The National Canned Food Company should follow the same procedure by
forecasting demand and eliminating the markets that have the highest transportation
costs by allocating their demands to the local market and then other regional
markets which are cheaper to send to. Eventually, the total shipping cost would go
down to 0 KD/year given that there is no transportation costs for the local market
because the customer picks up the products from the National Canned Food
Company’s warehouse.
New Fixed Cost = Total Fixed Cost – Transportation Cost
= 442,053.86 – 178,560 = 263,493.86 KD/year
New Total Cost = Total Cost – Total Fixed Cost + New Fixed Cost
= 3,518,913.44 - 442,053.86 + 263,493.86
= 3,340,353.44 KD/year
Savings in Total Cost = 3,518,913.44 - 3,340,353.44
= 178,560 KD
Page | 212
5. Conclusion
The costs of the National Canned Food Company were classified into
direct, indirect, technical overheads, company overheads, and marketing
overheads costs. From those costs, the variable and fixed costs were calculated.
The total cost was found to be 3,518,913.44 KD/year. The total revenue and total
profits were also calculated and found to be 4,274,967.57 KD/year and
755,911.15 KD/Year, respectively, with a profit margin of 17.48%. This number
suggests that the company is doing quite well. The total productivity of the
National Canned Food Company was calculated to be 1.214 which is greater
than 1, suggesting the company is productive. The breakeven point for the
company was also obtained as well as the breakeven point for each individual
product. This can help the company decide how much of each product to produce
in order to make a profit. The total breakeven point was 12,597,389 cans, which
means they broke even in a quarter of a year, which is quite reasonable.
Although the numbers seem rather outstanding, when further analysis was
done, it was noticed that the company has very high material costs due to
overfilling their products. The cost of overfilling for each product was calculated
and the total overfilling cost was found to be 68,001.8 KD/year. Another major
cost issue the company was facing is the very high transportation costs of
178,560 KD/year. When the transportation costs were analyzed in detail, it was
noticed that the National Canned Food Company had three major markets, local,
regional and international. The international markets were the smallest customers
with the highest transportation costs. Using demand forecasts, it was observed
that within the next 2 years, the company would not be able to meet even its local
customers because they’d already be producing at maximum capacity. Thus, it
only seemed logical to start re-allocating their demands from their international
markets to local and regional ones. The priority was given to the local market,
due to the company being the only supplier and the fact that there is no local
transportation cost, and then supplying markets with lower transportation costs.
By eliminating one market at a time through the year, eventually the National
Canned Food Company will only supply the local market and there would be no
transportation costs, lowering their total cost to 3,340,353.44 KD, saving 178,560
KD.
Page | 213
If the National Canned Food Company takes into consideration the analysis of
this study, they would eventually be saving 68,001.6 KD annually due to overfilling in
addition to 178,560 KD annually due to transportation costs. Overall, the company
would be saving 246,561.8 KD yearly. This figure represents 7% of their total costs,
and is considered substantial savings in the long run.
Page | 214
Page | 215
4. Production Line Analysis and
System Maintenance
Page | 216
Page | 217
4.1 Introduction
The factory has two lines (can making line and can filling line) and both lines are
continuous and the machines are connected in series, hence the failure of one
machine causes the stoppage of the whole line, adversely affecting the production
rate of the factory. Thus, it is important to analyze the maintenance system of the
factory.
The maintenance policies that the factory currently applies were studied and the
reliability and availability of the factory were calculated. The performance of the
factory was improved by introducing better maintenance policies to reduce the failure
rate of the different machines.
Since analytical methods assume very simple situations and do not apply to the
factory’s situation, the as-is layout was modeled using Arena simulation software to
analyze and improve it.
For both lines, only 400 g size cans were considered since most of the factory
production is of this size. For example, the production of the most recent four months
was as follows:
Table 4. 6: The production for July, August, September, and October.
Month 400 g
(cartons)
220 g
(cartons)
450 g
(cartons)
Total
(cartons)
400 g
(%)
220 g
(%)
450 g
(%)
July 38142 1340 7120 46602 81.8 2.9 15.3
August 61767 1671 0 63438 97.4 2.6 0
September 62006 2471 1558 66035 93.9 3.7 2.4
October 26685 1976 0 28661 93.1 6.9 0
Total of 4
months
188600 7458 8678 204736 92.1 3.6 4.2
Page | 218
Figure 4.2: Pie chart of the production of four months sample.
Problem Statement
The current maintenance schedule causes too much downtime and is not
optimized. The reliability of the can filling line is too low. The process can barely
keep up with demand.
Objectives
Improve the system reliability.
Increase the daily production.
Reduce the maintenance cost.
Solution Approach
New maintenance plans were proposed that increased machine reliability and
availability while minimizing the maintenance cost. These plans were evaluated
using Arena simulation software to choose the best alternative amongst them, after
verifying and validating the Arena models.
92%
4% 4%
400 g
200 g
450 g
Page | 219
4.2 Part List
Part lists provide a listing of the components of the product. A part list includes part
number, part name, and number of parts per product.
Table 4. 7: Part list of 400 g canned food.
Company National Canned Food Co. Prepared by: -
Product 400 g canned
food
Date: -
Part NO. Part Name Quantity Material Size (cm) Make/Buy
001 Sheet metal 1 Coated
Steel
23 x 11 Buy
002 Lid 2 Coated
Steel
8 cm
diameter
Buy
003 Label 1 Paper 23 x 8 Buy
004 Food 240 g - - Buy
Page | 220
4.3 Bill of Materials (BOM)
The Bill of materials is a product structure hierarchy refereeing to the level of the
product assembly.
Level 0: Final product.
Level 1: Subassemblies and components that feed directly to the final product.
Level 2: Subassemblies and components that feed directly to level 1.
Figure 4.3: BOM of 400 g cans.
Level 2
Level 1
Level 0400 g
Canned Food
Empty can
Sheet metal
001
Lower lid
002
Food
004
Upper lid
002
Label
003
Page | 221
002
001
4.4 Component Part Drawing
A component part drawing provides the part specifications and dimensions in
sufficient detail to allow part fabrication.
Figure 4.4: Component No. 002 (Lid)
23 cm
11 cm [Type a quote from the document or the summary of an interesting point. You
can position the text box anywhere in the document. Use the Text Box Tools tab to
change the formatting of the pull quote text box.]
Figure 4.5: Component No. 001 (400 g canned food).
D = 8
cm
Page | 222
Final Product
Figure 4.6: Final product (Canned food).
Page | 223
4.5 Process Description
The factory consists of two lines; the can making line and the can filling line.
The process of the Can Making Line can be described as follows:
Slitting: Tin sheets are cut into blanks of desired dimensions
Blanks are manually fed to the welder
Welding: the two ends of the blanks are welded to form a cylindrical shape
Welded blanks are transported to the lacquering machine by the conveyer belt
Lacquering: applying a varnish coat in the inner face of the welded blanks
Curing: in this process the welded blanks are moved to the flanging machine by a
magnetic belt and the varnished is cured and dried during this process
Flanging: can is flanged at both ends to prepare it for seaming
Seaming: one end of the can is seamed by a seamer
Palletizing: every 2940 cans are place in a pallet and moved by a forklift to the
empty can storage area.
Note:
The can production line follows FIFO (First in First out) procedure. Therefore, the
stored empty cans are taken to the filling line, first.
Page | 224
The process of the can filling line can be described as follows:
Soaking: the food is soaked for 8-14 hours in a hopper depending on the type of
food (Peas, kidney beans, mushroom, etc). The factory has a total of five hoppers
and the capacity of each hopper is 3000 Kg (meat and corn do not go into this
process).
Reel washing: the food is cleaned by showering and the excess water is drained.
The food is transported to the blancher by a bucket elevator.
Blanching: the food is blanched for 5 to 30 minutes to release gases and enzymes.
De-stoning: the food is moved to the de-stoner to remove stones.
Inspection belt: the food is sorted manually to remove any dark or broken pieces.
The food is held in the filling hopper.
Solid filling: the empty can is filled with solid food.
Liquid filling: a liquid solution is added to the can. The can is vacuumed by the
shower filler machine under a temperature of 75 °C to 85 °C. This process makes
the expiry date of the canned food longer and protects consumers.
Seaming: the other lid is seamed to the can using double seaming.
Coding: a code is printed on the lid of the can using the coding machine to show the
production and expiration dates of the product.
Crate loading: 700 cans are put on a crate, and 7 layers of crates are taken to
sterilizing the stage by a trolley.
Sterilizing: the can in the crates are sterilized under a temperature of 121ºC. This
process takes between 10 and 70 minutes depending on the type of product and the
type of liquid used. Then, it is cooled suddenly to kill the remaining bacteria. The
cans are then dried.
Crate unloading: the cans are unloaded from the crate to the labeler.
Labeling: the cans are labeled by the labeling machine.
Page | 225
Label inspection: The labels are checked to determine whether they were applied
correctly.
Packaging: 12 cans are kept in a tray. Two trays are then wrapped together by the
shrink wrapper.
Every 20 cartons are put in a pallet by two workers and one fork lift.
Storing: the final products are stored for four days before a sample is taken to carry
out three types of tests (physical, chemical and biological), ensuring that the product
meets standard and is ready for distribution.
Notes:
Cans are de-palletized before entering the filling line.
In the filling line, empty cans are sterilized by hot water and steam while preparing
the beans.
The liquid solution is prepared prior production hours.
Page | 226
4.6 Process Flow on the Factory Layout
Figure 4.7: Process flow on the factory layout.
Page | 227
4.7 Operation Process Chart
Company: National Canned Food Production and Trading Company Prepared by:__________
Products: Can Making Line Date:________________
011
021
031
041
SA1
Slitting
Welding
Lacquering
Seaming
Lid
002
Curing
051
Flanging
Sheet Metal
001
071
Palletizing
Figure 4.8: Operation Process Chart for the can making line.
Page | 228
Company: National Canned Food Production and Trading Company Prepared by:__________
Products: Can filling Line Date:________________
012
022
032
042
SA
2
072
A1
092
102
112
122
A2
152
I3
Soaking
Reel Washing
Blanching
De-stoning
Solid Filling
Liquid Filling
Seaming
Coding
Crate Loading
Sterilizing
Crate Unloading
Labeling
Packaging
Testing
Label
003
Lid
002
Food
004
Figure 4.9: Operation process chart for the can filling line.
I2 Label Inspection
I1
Inspection Belt
013
023
De-palletizing
Sterilizing
Empty Can
From store
Page | 229
4.8 Route sheets
Table 4. 8: Route sheet of sheet metal.
Company: National Canned Food Production and Trading co. Part Name: Sheet Metal Prepared By:
Produce: Part No.: 001 Date:
Operation No.
Operation Description Machine Type Dept.
Machine Rate
Materials or Parts Description
011 Slitting Slitting Machine Production 500 sheets/hr Coated Steel sheet metal 23x11 cm
021 Welding Welder Production 160 cans/min
031 Lacquering Lacquering Machine Production 160 cans/min
041 Curing Curing Machine Production 160 cans/min
051 Flanging Flanging Machine Production 160 cans/min
071 Palletizing Palletizer Production
Page | 230
Table 4. 9: Route sheet of lid.
Company: National Canned Food Production and Trading co. Part Name: Lid Prepared By:
Produce: Part No.: 002 Date:
Operation
No.
Operation
Description Machine Type Dept.
Operation
Time
Materials or Parts
Description
SA1/A1 Seaming Seamer Production 500 sheets/hr Lid 8 cm in diameter
Page | 231
Company: National Canned Food Production and Trading co. Part Name: Food Prepared By:
Produce: Part No.: 004 Date:
Operation No.
Operation Description Machine Type Dept. Machine Rate Materials or Parts Description
012 Soaking Hopper Production 8-14 hours
022 Reel Washing Shower Production
032 Blanching Blancher Production 5-30 min
042 Destoning Destoner Production
I1 Inspection Belt Inspection Belt Production
SA2 Solid Filling Solid Filler Production
072 Liquid Filling Liquid Filler Production
092 Coding Coding Machine Production 140 cans/min
102 Crate Loading Crate Loader Production
112 Sterilizing Retort Production 10-70 min
122 Crate Unloading Crate Unloader Production
A2 Labeling Labeler Production 140 cans/min
I2 Label Inspection Production
152 Packaging Shrink Wrapper Production 30 cartons/min
I3 Inspection - QC Lab 4 days
Page | 232
4.9 Data Collection and Fitting
The following table shows the demand inter-arrival distributions and the
quantity distributions of each product.
Table 4. 10: Distribution summary of inter-arrival and quantity of the demand.
Entity
Demand Inter-arrival1
(Days)
Quantity2
(Cartons)
Fava beans 0.5 + 8 * BETA(0.568, 1.52) 50 + 2.83e+003 * BETA(0.577, 0.802)
Peas 0.5 + WEIB(2.7, 1.5) UNIF(50, 2.31e+003)
Chickpeas 0.5 + WEIB(1.95, 1.33) 470 + 2.59e+003 * BETA(0.889, 0.774)
Beans 0.5 + 7 * BETA(0.827, 2.05) 79 + 3.1e+003 * BETA(0.603, 1.26)
Corn UNIF(1.5, 17.5) TRIA(103, 188, 957)
Mushroom 0.5 + EXPO(7.05) NORM(412, 230)
For more information about the daily production of the two lines, see Appendix (B).
1 See Appendix (F) for more details
2 See Appendix (E) for more details
Page | 233
Table 4. 11: Summary of the mean time between failure (MTBF) of the machines and their repair time.
Machine3 MTBF4 Distribution (Days) MTBF
(Days)
Repair time
(Min)
Can Plant -0.5 + EXPO(5.16) 4.66 60
Palletizer/De-Palletizer -0.5 + EXPO(12.2) 11.7 30
Process Line -0.5 + EXPO(8.37) 7.87 30
Fillers and Seamer -0.5 + EXPO(6) 5.5 60
Crate Loader 0.999 + EXPO(18.8) 19.799 5
Retort -0.5 + EXPO(18.8) 18.3 30
Crate Unloader 1.5 + EXPO(23.2) 24.7 5
Labeler -0.5 + EXPO(7.55) 7.05 60
Shrink Wrapper 0.999 + EXPO(13.5) 14.499 60
The MTBF in the table above is calculated as follows
MTBF = E(X+EXPO(1\λ)) = X + 1\λ
For example the MTBF of the can plant is E(-0.5 + EXPO(5.16)) = -0.5 + 5.16 = 4.66
days.
3 For more information about the machines, see Appendix (A)
4 See Appendix (H) for more details
Page | 234
4.10 Maintenance Types
The factory has two types of maintenance; corrective maintenance and
preventive maintenance.
Corrective Maintenance (CM)
Corrective maintenance is unscheduled maintenance actions performed as a
result of system failure, to restore the system to specified condition.
The failure rate λ = 1/MTBF
Table 4. 12: Summary of the MTBF and the failure rate of the machines.
Machine MTBF (Days) Failure Rate λ
(Failure/day)
Palletizer/De-Palletizer 11.7 0.085
Process Line 7.87 0.127
Fillers and Seamer 5.5 0.182
Crate Loader 19.799 0.051
Retort 18.3 0.055
Crate Unloader 24.7 0.04
Labeler 7.05 0.142
Shrink Wrapper 14.499 0.069
Can Plant 4.66 0.215
Page | 235
Preventive Maintenance (PM)
Preventive maintenance is all scheduled maintenance actions performed to
retain a system in a specified condition.
The factory performs preventive maintenance once a month (every 26 days)
during non-production hours and it takes 10 hours.
f = 1/26 = 0.0385 preventive maintenance/day
Page | 236
4.11 Maintenance Plan
Maintenance Model
Corrective maintenance is done by one mechanical technician, one electrician
and one helper.
Preventive maintenance is done by two mechanical technicians, two
electricians and two helpers.
Preventive maintenance is applied during non-production days, and lasts for
10 hours.
Mechanical technicians and electricians are paid 170 KD/month
Helpers are paid 50 KD/month.
26 days/month *12 month/year *10 hours/year = 3120 hours/year
Production rate of filling line = 140 cans/min
Production rate of can making line = 160 cans/min
Revenue/can = 0.232955 KD
CM Cost = (Mct/MTBF) * 3120 * cost/hr
PM Cost = fpt * Mpt * 3120 * cost/hr
Production Loss Cost= # units/min * Mct * λ * 3120 * Rev/unit
The new failure rate of the machine is calculated using the following equation:
𝑀𝑇𝐵𝑀 =1
𝜆+𝑓, by keeping the MTBM of the current maintenance plan the
same and changing the preventive maintenance rate.
Page | 237
Current Maintenance Plan
The factory currently applies preventive maintenance once a month (every 26
days). The following table shows the failure rate, PM rate and the mean time
between maintenance (MTBM) of each machine.
Table 4. 13: Summary of the failure rate, preventive maintenance rate, and mean time between maintenance
(MTBM) of the machines.
Machine Failure Rate
(failure/day) PM Rate (actions/day) MTBM (days)
Palletizer/De-Palletizer 0.085 1/26 8.07
Process Line 0.127 1/26 6.04
Fillers and Seamer 0.182 1/26 4.54
Crate Loader 0.051 1/26 11.23
Retort 0.055 1/26 10.74
Crate Unloader 0.040 1/26 12.66
Labeler 0.142 1/26 5.54
Shrink Wrapper 0.069 1/26 9.30
Can Plant 0.215 1/26 3.95
Page | 238
The annual corrective and preventive maintenance costs and the production
loss cost of the current maintenance plan were also calculated.
Table 4. 14: Summary of the corrective maintenance (CM) cost, preventive maintenance (PM) cost, and
production loss cost of the machines.
Machine
CM Cost
(KD/year)
PM Cost
(KD/year)
Production Loss Cost
(KD/year)
Palletizer/De-Palletizer 20 72.07 26,090.960
Process Line 29.733 72.07 38,788.340
Fillers and Seamer 85.091 36.04 111,005.175
Crate Loader 1.970 18.02 2,569.694
Retort 12.787 36.04 16,681.106
Crate Unloader 1.579 18.02 2,059.813
Labeler 66.383 18.02 86,599.782
Shrink Wrapper 32.278 18.02 42,108.315
Can Plant 100.429 72.07 131,014.692
Total 350.25 360.36 456,917.88
Total Cost = CM cost + PM cost + Production loss cost = 350.25 + 360.36 +
456,917.88 = 457,628.5 KD/year.
Page | 239
Proposed Maintenance Plans
Three alternative maintenance plans were proposed. They are as follows:
Alternative 1
Alternative proposed applying additional preventive maintenance actions
twice a month (every 13 days), instead of once a month (every 26 days), during non-
production days. This should reduce the failure rates of the machines.
By keeping the MTBM of the current maintenance plan the same, the
following results were obtained:
Table 4. 15: Summary of the new failure rate, preventive maintenance rate, and mean time between maintenance
(MTBM) of the machines.
Machine Failure Rate
(failure/day)
PM Rate (action/day) MTBM (days)
Palletizer/De-Palletizer 0.047 1/13 8.07
Process Line 0.089 1/13 6.04
Fillers and Seamer 0.143 1/13 4.54
Crate Loader 0.012 1/13 11.23
Retort 0.016 1/13 10.74
Crate Unloader 0.002 1/13 12.66
Labeler 0.103 1/13 5.54
Shrink Wrapper 0.031 1/13 9.30
Can Plant 0.176 1/13 3.95
Page | 240
The annual corrective and preventive maintenance costs and the production
loss cost of alternative 1 were also calculated as follows:
Table 4. 16: Summary of the corrective maintenance (CM) cost, preventive maintenance (PM) cost, and
production loss cost of alternative 1.
Machine
CM Cost
(KD/year)
PM Cost
(KD/year)
Production
Loss Cost
(KD/year)
Palletizer/De-Palletizer 11.010 143.99 14,362.708
Process Line 20.743 143.99 27,060.088
Fillers and Seamer 67.110 72.00 87,548.672
Crate Loader 0.471 36.00 614.985
Retort 3.797 72.00 4,952.854
Crate Unloader 0.081 36.00 105.104
Labeler 48.402 36.00 63,143.279
Shrink Wrapper 14.298 36.00 18,651.812
Can Plant 82.449 143.99 107,558.188
Total 248.360 719.97 323,997.689
Total Cost = CM cost + PM cost + Production loss cost = 248.360 + 719.97 +
323,997.689 = 324,966 KD/year.
Alternative 1 reduced costs by 29%.
Page | 241
Alternative 2
This alternative proposed applying preventive maintenance weekly (every 5
days) during non-production days. Once again, the same MTBM was used and the
following results were obtained:
Table 4. 17: Summary of the new failure rate, preventive maintenance rate, and mean time between maintenance
(MTBM) of the machines.
Machine Failure Rate
(failure/day) PM Rate (action/day) MTBM (days)
Palletizer/De-Palletizer -0.076 1/5 8.07
Process Line -0.034 1/5 6.04
Fillers and Seamer 0.020 1/5 4.54
Crate Loader -0.111 1/5 11.23
Retort -0.107 1/5 10.74
Crate Unloader -0.121 1/5 12.66
Labeler -0.020 1/5 5.54
Shrink Wrapper -0.093 1/5 9.30
Can Plant 0.053 1/5 3.95
Since only the fillers and seamer and the can plant have positive failure rates,
they are the only machines were performing preventive maintenance actions every
week is applicable. Thus, alternative 2 reduces to:
Applying PM weekly on the fillers and seamer and the can plant, and twice a
month on the remaining machines.
Page | 242
Table 4. 18: Summary of the new failure rate, preventive maintenance rate, and mean time between maintenance
(MTBM) of the machines.
Machine Failure Rate
(failure/day) PM Rate (action/day) MTBM (days)
Palletizer/De-Palletizer 0.047 1/13 8.07
Process Line 0.089 1/13 6.04
Fillers and Seamer 0.020 1/5 4.54
Crate Loader 0.012 1/13 11.23
Retort 0.016 1/13 10.74
Crate Unloader 0.002 1/13 12.66
Labeler 0.103 1/13 5.54
Shrink Wrapper 0.031 1/13 9.30
Can Plant 0.053 1/5 3.95
Page | 243
The annual costs of alternative were found to be as follows:
Table 4. 19: Summary of the corrective maintenance (CM) cost, preventive maintenance (PM) cost, and
production loss cost of alternative 2.
Machine CM Cost
(KD/year)
PM Cost
(KD/year)
Production
Loss Cost
(KD/year)
Palletizer/De-Palletizer 11.010 143.99 14,362.708
Process Line 20.743 143.99 27,060.088
Fillers and Seamer 9.50 187.2 12,404.828
Crate Loader 0.471 36.00 614.985
Retort 3.797 72.00 4,952.854
Crate Unloader 0.081 36.00 105.104
Labeler 48.402 36.00 63,143.279
Shrink Wrapper 14.298 36.00 18,651.812
Can Plant 24.847 187.2 32,414.344
Total 133.157 878.379 173,710.0026
Total Cost = CM cost + PM cost + Production loss cost = 133.157 + 878.379 +
173,710.0026 = 174,721.5 KD/year.
Alternative 2 reduced the cost by 61.8%.
Page | 244
Alternative 3:
In this alternative, it was suggested that PM be applied just before the failure
occurs (Reliability centered maintenance). Table 4. 16 shows the MTBF of the
current policy and the suggested mean time between preventive maintenance
(MTBPM).
Table 4. 20: Summary of the current MTBF and the proposed MTBPM.
Machine MTBF (days)
MTBPM
(days/action)
Palletizer/De-Palletizer 11.7 11.6
Process Line 7.87 7.77
Fillers and Seamer 5.5 5.4
Crate Loader 19.799 19.70
Retort 18.3 18.20
Crate Unloader 24.7 24.60
Labeler 7.05 6.90
Shrink Wrapper 14.499 14.40
Can Plant 4.66 4.56
Page | 245
Using the same MTBM of the current policy and the suggested mean time
between preventive maintenance, the following results are obtained:
Table 4. 21: Summary of the new mean time between failures.
Machine MTBFnew
(days)
Failure Rate
λ(Failure/day)
Palletizer/De-Palletizer 26.51 0.038
Process Line 27.15 0.037
Fillers and Seamer 28.49 0.035
Crate Loader 26.17 0.038
Retort 26.20 0.038
Crate Unloader 26.11 0.038
Labeler 28.27 0.035
Shrink Wrapper 26.33 0.038
Can Plant 29.62 0.034
Page | 246
The annual corrective and preventive maintenance costs and the production
loss cost for alternative 3 were found to be as follows:.
Table 4. 22: Summary of the corrective maintenance (CM) cost, preventive maintenance (PM) cost, and
production loss cost of alternative 3.
Machine CM Cost
(KD/year)
PM Cost
(KD/year)
Production
Loss Cost
(KD/year)
Palletizer/De-Palletizer 8.83 72 11,516.01
Process Line 8.62 72 11,241.73
Fillers and Seamer 16.42 36 21,426.21
Crate Loader 1.49 18 1,943.78
Retort 8.93 36 11,649.28
Crate Unloader 1.49 18 1,948.45
Labeler 16.56 18 21,599.26
Shrink Wrapper 17.78 18 23,189.42
Can Plant 15.80 72 20,608.73
Total 95.91 360.00 125,122.87
Total Cost = CM cost + PM cost + Production loss cost=125,578.78 KD/year.
The cost has been reduced by 72.56%.
Page | 247
4.12 The Reliability of the Lines
Reliability is the probability that the system will perform in a satisfactory
manner for a given period of time, when used under specified operating conditions. It
is calculated with the following equation:
R (T) = e-λt , where λ is the failure rate and t is the given period of time.
Table 4. 23: Summary of the mean failure rate of the machines and their reliability over one day.
Machine Failure Rate
λ(Failure/day)
Reliability over
one day (%)
Palletizer/De-Palletizer 0.085 91.81
Process Line 0.127 88.07
Fillers and Seamer 0.182 83.38
Crate Loader 0.051 95.07
Retort 0.055 94.68
Crate Unloader 0.040 96.03
Labeler 0.142 86.78
Shrink Wrapper 0.069 93.34
Can Plant 0.215 80.69
Page | 248
Alternative 1:
Table 4. 24: Summary of the failure rate of the machines and their reliability over one day for alternative 1.
Machine Failure Rate
λ(Failure/day)
Reliability over
one day (%)
Improvement
(%)
Palletizer/De-Palletizer 0.047 95.40 3.91
Process Line 0.089 91.52 3.92
Fillers and Seamer 0.143 86.64 3.91
Crate Loader 0.012 98.80 3.92
Retort 0.016 98.39 3.92
Crate Unloader 0.002 99.79 3.92
Labeler 0.103 90.17 3.91
Shrink Wrapper 0.031 96.99 3.91
Can Plant 0.176 83.85 3.91
Page | 249
Alternative 2:
Table 4. 25: Summary of the failure rate of the machines and their reliability over one day for alternative 2.
Machine Failure Rate
λ(Failure/day)
Reliability over
one day (%)
Improvement
(%)
Palletizer/De-Palletizer 0.047 95.40 3.92
Process Line 0.089 91.52 3.92
Fillers and Seamer 0.020 97.99 17.53
Crate Loader 0.012 98.80 3.92
Retort 0.016 98.39 3.92
Crate Unloader 0.002 99.79 3.92
Labeler 0.103 90.17 3.92
Shrink Wrapper 0.031 96.99 3.92
Can Plant 0.053 94.83 17.53
Page | 250
Alternative 3:
Table 4. 26: Summary of the failure rate of the machines and their reliability over one day for alternative 3.
Machine Failure Rate
λ(Failure/day)
Reliability over
one day (%)
Improvement
(%)
Palletizer/De-Palletizer 0.038 96.30 4.89
Process Line 0.037 96.38 9.44
Fillers and Seamer 0.035 96.55 15.80
Crate Loader 0.038 96.25 1.24
Retort 0.038 96.26 1.66
Crate Unloader 0.038 96.24 0.22
Labeler 0.035 96.52 11.23
Shrink Wrapper 0.038 96.27 3.15
Can Plant 0.034 96.68 19.82
Page | 251
4.13 Results
Can Making Line
Current Maintenance Plan
From Table 4. (19) and Figure (9), it was concluded that the reliability of the can
production line is 80.65%.
Proposed Maintenance Plan
Alternative 1:
From Table (20) and Figure (9), it was concluded that the reliability of the can
making line has become 83.85%, an increase of 3.91%.
Alternative 2:
From Table (21) and Figure (9), it was concluded that the reliability of the can
making line has become 94.83%, an increase of 17.53%.
Alternative 3:
From Table (22) and Figure (9), it was concluded that the reliability of the can
making line has become 96.68%, an increase in of 19.82%.
Can Plant
Figure 10: Schematic illustration of the can production line.
Page | 252
Can Filling Line
Current Maintenance Plan
From Table (19) and Figure (10), it was concluded that the reliability of the can filling
line is
R(1 day) = [1-(1-R1)(1-R2)] (R3) (R4) (R5) (R6) (R7) (R8)
= [1-(1-0.9181)(1-0.8807)](0.8338)(0.9507)(0.9468)(0.9603)(0.8678)(0.9334)
= 0.5781 = 57.81%
Proposed Maintenance Plan
Alternative 1:
From Table (20) and Figure (9);
R(1 day) = [1-(1-R1)(1-R2)] (R3) (R4) (R5) (R6) (R7) (R8)
= [1-(1-0.9540)(1-0.9152)](0.8664)(0.9880)(0.9839)(0.9979)(0.9017)(0.9699)
= 0.7322 = 73.22%
Palletizer/
De-
Palletizer
(1)
Fillers &
Seamer
(3)
Crate
Loader
(4)
Retort (5)
Crate
unloader
(6)
Labeler
(7)
Shrink
Wrapper
(8)
Process
Line (2)
Figure 11: Schematic illustration of the can filling line.
Page | 253
It can be concluded that the reliability of the can filling line has become 73.22%, an
increase of 26.65%.
Alternative 2:
From Table (20) and Figure (9);
R(1 day) = [1-(1-R1)(1-R2)] (R3) (R4) (R5) (R6) (R7) (R8)
= [1-(1-0.9540)(1-0.9152)](0.9799)(0.9880)(0.9839)(0.9979)(0.9017)(0.9699)
= 0.8281 = 82.81%
It can be concluded that the reliability of the can filling line has become 82.81%, an
increase of 43.24%.
Alternative 3:
From Table (20) and Figure (9);
R(1 day) = [1-(1-R1)(1-R2)] (R3) (R4) (R5) (R6) (R7) (R8)
= [1-(1-0.9630)(1-0.9638)](0.9655)(0.9625)(0.9626)(0.9624)(0.9652)(0.9627)
= 0.7989 = 79.89%
It can be concluded that the reliability of the can filling line has become 79.89%, an
increase of 38.19%.
Page | 254
4.14 Availability of the Machines
Availability is the percentage of time or the probability that a system will be
ready or available when required. Availability is expressed differently; three common
Figures of Merit (FOM) are defined below:
Inherent Availability (Ai):
Probability that an equipment (or system), when used under stated conditions
in an ideal support environment (i.e. readily available tools, spares, maintenance
personnel, etc), will operate satisfactorily at any time as required. It excludes:
Preventive/scheduled maintenance.
Logistic Delays (maintenance down time that is expended as a result of
waiting for a spare part to become available, waiting for the availability of testing
equipment, waiting for use of a facility, etc).
Administrative delays (portion of down time during which maintenance is delayed for
administrative reasons).
The Inherent Availability is calculated with the following equation:
Ai= 𝑀𝑇𝐵𝐹
𝑀𝑇𝐵𝐹+𝑀 𝐶𝑇
Where,
MTBF = mean time between failures
𝑀 CT = mean corrective maintenance time
Page | 255
Achieved Availability (Aa)
The probability that a system or equipment, when used under stated
conditions in an ideal support environment (i.e. readily available tools, spares,
personnel etc.) will operate satisfactorily at point in time.
This definition (Aa) is similar to that of Ai. However, preventive maintenance is
included. It excludes the logistic delays, administrative delays etc.
The Achieved Availability is calculated with the following equation:
Aa= 𝑀𝑇𝐵𝑀
𝑀𝑇𝐵𝑀+𝑀
Where,
MTBM = Mean time between maintenance
𝑀 =Mean active maintenance time
And MTBM & 𝑀 are a function of corrective and preventive maintenance actions.
Operational Availability (Ao)
Probability that system or equipment, when used under stated conditions in an actual
operational environment, will operate satisfactorily when called upon.
Ao=𝑀𝑇𝐵𝑀
𝑀𝑇𝐵𝑀+𝑀𝐷𝑇
Where
MDT=Mean Maintenance Down Time.
Page | 256
Table 4. 27: Summary of the availability of the machines.
Machine Ai (%) Aa (%) Ao (%)
Palletizer/De-Palletizer 99.57 95.90 60.15
Process Line 99.37 95.71 53.40
Fillers and Seamer 98.21 94.64 46.33
Crate Loader 99.96 96.25 67.39
Retort 99.73 96.04 66.36
Crate Unloader 99.97 96.26 69.75
Labeler 98.60 95.00 51.17
Shrink Wrapper 99.32 95.66 63.18
Can Plant 97.90 94.34 43.00
Page | 257
4.15 Spare Parts
Data related to the spare parts required for each machine and the number ordered
per year was collected. The factory orders some of the spare parts locally and some
others from the UK, Germany and Italy.
The following table shows each machine, its spare parts and the number ordered per
year.
Table 4. 28: Summary of the machines, spare parts, and the number ordered per year.
Machine Spare Part No. of orders per year
Plletizer/De-Palletizer
Sensors 2
Bearings 4
Pneumatics valves 2
Process Line
Sprocket 1
Shaft 10
Rollers 1
Belt 5
Fillers and Seamer
Sprocket 4
Bearings 7
Clutch 1
Seaming roller 4
Chuck 8
Crate Loader
Bearings 2
Sprocket 1
Page | 258
Machine Spare Part No. of orders per year
Electrical fuses 4
Conductors 1
Retort
Pipe fittings 10
Gasket 25
Valves 4
Crate Unloader
Bearings 2
Conductors 2
Electric motor 2
Driving belt 1
Labeler
Belt 3
Glue valves 2
Electrical fuses 4
Shrink Wrapper
Bearings 5
Glue nozzle 2
Glue Filters 2
Conductors 2
Belt 2
Can Plant
Bearings 12
Belt 5
Sprocket 4
Page | 259
Machine Spare Part No. of orders per year
Conductors 4
Cylinder 1
Page | 260
4.16 System Simulation
Nowadays, manufacturers are facing rapid and fundamental changes in the
ways business is done. Producers are looking for simulation systems increasing
throughput and profit, reducing cycle time, improving due-date performance and
reducing WIP. Manufacturing systems, often requiring large investments in capital,
equipment and supporting software, are costly and time-consuming to acquire,
integrate, and operate. Simulation technology is a tool of proven effectiveness in
improving the efficiency of manufacturing system design, operation, and
maintenance. Simulation models can be used to perform “what-if” analyses and
make better-informed decisions.
Manufacturing simulation has been one of the primary application areas of
simulation technology. It has been widely used to improve and validate the designs
of a wide range of manufacturing systems..
The following are some of the specific issues that simulation is used to
address in manufacturing systems:
The quantity of equipment:
Number and type of machines for a particular objective.
Number, type, and physical arrangement of transporters, conveyors, and
other support equipment (pallets and forklifts).
Location and size of inventory buffers.
Evaluation of a change in product volume or mix.
Labor-requirements planning.
Performance evaluation:
Throughput analysis.
Time-in-system analysis.
Bottleneck analysis.
Page | 261
Evaluation of operational procedures:
Production scheduling.
Control strategies.
Reliability analysis (effect of preventive maintenance).
Following are some of the performance measures commonly estimated by
simulation:
Throughput.
Time in system for parts.
Time parts spend in queues.
Queue sizes.
Timeliness of deliveries.
Utilization of equipment or personnel.
Arena was used to simulate the can making and can filling lines to study the
effect of changing the rate of the preventive maintenance on the daily production of
the lines.
Page | 262
Problem Formulation
System entities
Can Making Line:
The entities of this line are the boxes that contain the tin sheets. Every day,
two boxes containing 1300 sheets each, with 28 cans of size 400 g produced from
each sheet, are processed.
Can Filling Line:
The different products were split into separate categories. Products of the
same category undergo the exact same processes, with the only difference being the
sauces used. However, the model was not affected by this because one or two
workers come two hours prior to production hours to heat the holding tank and mix
the sauce. Therefore, the entities are the number of boxes ordered (each box
contains 24 cans).
Page | 263
Material handling system
Material handling is an activity that uses the right method to provide the right
amount of the right material at the right place, at the right time, in the right sequence,
in the right position and at the right cost.
Material handling for the can making line is as follows:
Conveyer Belt: The belt transports 160 welded blanks per minute to the
lacquering machine.
Magnetic Belt: In the curing process, 160 welded blanks are moved per
minute to the flanging machine by the magnetic belt. The varnish is cured and
dried during this process.
Palletizer: Every 2940 cans are put in a pallet, (14 layers with 210 cans in
each layer) and moved by a forklift to the empty can storage area.
The material handling for the filling line consists of:
Bucket elevator: All the solid material (depending on the demand) is
transported to the blancher by this elevator.
Inspection belt: All the solid material (depending on the demand) is sorted
manually to remove any dark or broken pieces.
Crate: Crate holding 720 cans (split into 6 layers) are loaded to the sterilizing
stage then unloaded to the labeler.
Forklift: Every 90 cartons are put in a pallet by two workers before being
transported by a single forklift.
Page | 264
Current Problems in the Layout
In the current layout, both lines are physically connected and the empty cans
are supposed to go to the filling line through this link automatically once they are
manufactured. However, this link is not being utilized, with the empty cans being
transported manually to the filling line, instead. The cans are then palletized before
they are filled.
The reasons behind not using this connection are:
The difference in production plans of both lines.
Some of the empty cans might be defective and thus cannot be filled.
The factory has to work overtime to meet demand.
Also, the failure rates of the machines are high because the machines are
very old. Therefore, the production lines are stopped in every breakdown. This
will cause a delay meaning the factory will not meet deadlines or work
overtime to do so.
Work Schedule
In our model we have a total of 4 workers and their schedule is:
26 days/month
5 days/week
1 shift/day
10 hours/shift
Workers have breaks from 8-9 AM and 12-1:30 PM. All machines in the model
are used for 10 hours.
Page | 265
Scrap Estimate
In the can making line, only 0.15% of the total cans produced are defective per day.
See Appendix (B) for details.
Policies
The factory has some policies related to processing the entities and they are:
The factory does not process the order as it is placed; but wait for other orders to
come before processing them together.
They store two containers for prime items and fill them again once they are used.
Page | 266
Simplification Assumptions
In this section we will list the assumptions we used to simplify the model
Can Making Line
Assumptions:
Lids already fed in the seamer.
Overtime is not included.
Setup times and warming up time are done outside of production hours.
Can Filling Line
Assumptions:
The entities are the number of cartons ordered from the following categories: Fava
beans, Peas, Chick peas, Beans, Mushroom, and Corn.
The soaking step is not considered since it is done overnight and is finished
before production starts at 6:30 AM.
Reel washing, De-stoning, Blanching, and Inspection belt are considered as
one process and are called the Process Line.
The rate of the process line is equivalent to 120 cans/minute.
Empty cans are ready to be filled.
Overtime is not included.
Soaking and mixing in the holding tank is done outside of production hours.
Setup times and warming up time are done outside of production hours.
Page | 267
Create 1O r iginal
Duplicat e
Separate 1
Sli tting Welding Lac quering Curing Flanging
SeamingO r iginal
Duplicat e
Separate 2D ecide 1
Tr ue
False
Dispose 3
Dispose 4
Create 2 Ass ign 1 Proc ess 8 Ass ign 2 Dispose 5
Scrap
Dai ly Produc tion
0
0
0 0 0 0 0 0
0
0
0
0
0
0
0
0 0
0
Coding the Arena Model of the As-Is System
Can Making line
Figure 12: Arena model code of the can production line.
N.Create 2 TBA : -0.5+LOGN(4.28,7.15) day Entity per arrival =1
Variable 1=IRF(Slitter)==1 Variable 2=IRF(Welder)==1 Variable 3=IRF(Lacquering machine)==1 Variable 4=IRF(Curing machine)==1 Variable 5=IRF(Flanger)==1 Variable 6=IRF(Seamer)==1
N. process 8 Delay Delay:
constant=1hr
Variable 1=IRF(Slitter)==0 Variable 2=IRF(Welder)==0 Variable 3=IRF(Lacquering machine)==0 Variable 4=IRF(Curing machine)==0 Variable 5=IRF(Flanger)==0 Variable 6=IRF(Seamer)==0
N.Create 1 TBA :constant=1 day Entity per arrival
=ANINT(DISC(0.18,1,0.94,2,1,3))
N.Separate 1 Type: dublicate
Size:1299
N.Slitting S-D-R Res:slitter , Q=1 Delay:
constant=7.2 sec
N.Wedling S-D-R Res:welder,Q=1 Delay: constant=10.5 sec
N.Lacquring S-D-R Res:lacquering machine,Q=1 Delay:
constant=10.5 sec
N.Curing S-D-R Res:curing machine,Q=1 Delay: constant=10.5 sec
N.Flanging S-D-R Res:flanger ,Q=1 Delay:
constant=10.5 sec
N.Seaming S-D-R Res:Seamer, Q=1 Delay: constant 10.5 sec
N.Separate 2 Type: dublicate Size:27
2 way by chance 99.85%
No. of replication:10 Rep. length:10 hours
Hours / day:24
N.Daily Production Type: count
Value=1
N.Scrap Type: count Value=1
Page | 268
Explanation of the As-is Model of the Can Making Line
As mentioned in the problem formulation section, the entities here are the
boxes that contain the sheet metals. One, two, or three boxes/day are processed
according to demand which follows the distribution ANINT(DISC(0.18, 1, 0.94, 2, 1,
3) (See Appendix (B) for more details). Each box contains 1300 sheets, with each
sheet capable of producing 28 cans.
First, the box arrives to the line. Then the module “separate” was used to
convert the box to 1300 sheets. Note that the process time per sheet (per 28 cans)
was used because the process time per can would be too small. The sheet is then
cut to the desired length by the slitter before it goes to the welding machine to be
welded, to the lacquering machine to add the varnish in the inner face, to the curing
machine to cure the varnish, to the flanger to flange both ends and finally to the
seamer to seam the lid onto one end. The process time from the welding machine to
the seamer is constant at 10.5 seconds/sheet. Again, the separate module was used
to convert one sheet into 28 cans.
In the decide module the scrap rate of this line, which is 0.15% of the total
production, was added. Finally, empty cans are palletized are transported to the
storage area.
The failure of the can making line was also modeled, where the mean time
between failures follows the distribution -0.5 + LOGN(4.28, 7.15) (See Appendix (H)
for more details).
Page | 269
Can Filling line
Chic k peas
Peas
Corn
M us hroom
Beans
PL FS
As s ign 1
As s ign 2
As s ign 3
As s ign 4
As s ign 5
As s ign 6
D ecide 2Tr ue
False
As s ign 7
As s ign 8
Tr ue
False
D ecide 3
Proc es s 9
Fav a Beans
0
0
0
0
0
0 0
0
0 0
0
0
0
N.FS
S-D-R
Res:Filler Seamers , Q=1
Delay:
constant=10.3 sec
N.PL
S-D-R
Res:Process line , Q=1
Delay:
constant=12 sec N.Process 9
Delay
Delay: constant=30 min
2 way by condition
IF(first item == following item)
Att, Following item= tupe
Var,Switch=1
Att, First item= tupe
Var, Switch=0
2 way by condition
IF(switch == following item)
N.Fava Beans
TBA :
0.5 + 8 * BETA(0.568, 1.52) days
Entity per arrival =ANINT(50 +
2.83e+003 * BETA(0.577, 0.802))
N.Chickpeas
TBA :
0.5 + WEIB(1.95, 1.33) days
Entity per arrival =anint(470 +
2.59e+003 * BETA(0.889, 0.774))
N.peas
TBA :
0.5 + WEIB(2.7, 1.5)days
Entity per arrival =anint(UNIF(50,
2.31e+003)) N.Corn
TBA :
UNIF(1.5, 17.5)days
Entity per arrival =anint(TRIA(103,
188, 957))
N.Mushroom
TBA :
0.5 + EXPO(7.05) days
Entity per arrival
=anint(NORM(412, 230))
Att, type=1
Att,proctime=52
Att, type=2
Att,proctime=52
Att, type=3
Att,proctime=27
Att, type=6
Att,proctime=45
Att, type=5
Att,proctime=30
Att, type=4
Att,proctime=27
N.Beans
TBA :
0.5 + 7 * BETA(0.827, 2.05) days
Entity per arrival =anint(79 +
3.1e+003 * BETA(0.603, 1.26))
Figure 13: Arena model code of the can filling line – Part 1.
Page | 270
Coding Crate Loading S terillizing
Crate Unloading S eparate 1 Labeling Decide 1T ru e
F a l s e
S hrink W rapping daily production
scrap
Dispose 2
0 0 0
0
0
0
0
0 0
0
N.Scrap
Type: count
Value=1
N.Daily Production
Type: count
Value=1
2 way by chance
95.8%
N.Shrink Wrapping
S-D-R
Res:Shrink Wrapper,Q=1
Delay: constant=10.3 sec
N.Labeling
S-D-R
Res:Labeller,Q=1
Delay: constant=10.3 sec
N.Crate Unloading
S-D-R
Res:Crate Unloader,Q=1
Delay: constant=5 Min
N.Separate 1
Type: Split Exiting
Batch
N.Sterilizing
S-D-R
Res:Retort,Q=1
Delay: expression=proctime min
N.Coding
S-D-R
Res:Coding machine,Q=1
Delay: 10.3 sec
N.Crate Loading
Type: Temporary
Size:30
No. of replication:32
Warm-up:2 hours
Rep. length:10 hours
Hours / day:24
variable , switch=1
Figure 14: Arena model code of the can filling line – Part 2.
Page | 271
Explanation of the As-is Model of the Can Filling Line
Entities were split into six categories (fava beans, chickpeas, peas, corn,
mushroom, beans); all the products which have the same properties (eg: process
time) were put in the same group. Each group belonged to the same create with TBA
that represents the demand in days and with entities per arrival that represents the
number of cartons (see Appendix (E) and Appendix (F) for more details about the
distributions).
An assign for each category was used to assign the type needed for the flag,
as is explained later, and for assigning the process time that is needed for sterilizing.
The flag: A decide module was added to check if the system variable changed
or not (since a variable called switch=1 was identified). Therefore, it allows the
entities with the same type to pass together with same variable value.
Then a second decide module was added to check the type; so the first type
will pass and the next one will be delayed for 30 min during which the line is cleaned.
The entity will pass through a process called “process line” which takes 12
sec for each carton, then through the fillers and seamer which takes 10.3 for each
carton. Finally, coding has the same process time for each carton.
After that a batch module was added to load every 30 cartons in the same
crate. The crate then goes to the sterilizing process, whose process time depends on
the type of the product identified in the assign module, as afore-mentioned.
Afterwards, the crate will be unloaded and this process will take 5 min/crate. A
separate module is used for this purpose. Each carton will then pass through the
labeler, which takes 10.3 sec, and a decide module is added to return the scrapped
cans to the labeler to be relabeled.
Finally, every two cartons will be packed together using the shrink wrapper
machine which takes 10.3 sec and a counter is added to count the daily production
in cartons.
Page | 272
Modeling the failures of the machines was done as follows:
Resource module:
Table 4.29: Summary of the resource module.
Resource Failure Failure Rule
Process Line Failure 1 Preempt
Fillers and seamers Failure 2 Preempt
Retort Failure 3 Preempt
Labeller Failure 4 Preempt
Shrink Wrapper Failure 5 Preempt
Failure module:
Table 4.30: Summary of failure module.
Name Up time (days) Down time (min)
Failure 1 EXPO(7.87) 30
Failure 2 EXPO (5.5) 60
Failure 3 EXPO(18.3) 30
Failure 4 EXPO (7.05) 60
Failure 5 EXPO (14.499) 60
Page | 273
Verification and Validation
Can Making Line
The Arena model that was coded for the can making line was verified and it was
observed that the model works properly.
Validating the daily production:
The replication parameters are:
Replication Length: 10 hours/day.
Number of replications: 33 (see Appendix (I) for more details about the sample size).
For validation, the following two performance measures were used:
The daily production.
The scrap cans.
Page | 274
Validating the Daily Production:
Since the daily production is normally distributed for both the real system and the as-
is model, see Appendix (C), hypothesis tests were applied to find the confidence
intervals.
Table 4.31: Real system and as-is model statistics summary.
Real system As-is model1
n 53 33
𝐱 (cans) 69,147.4 63,879.45
S (cans) 18,289.5 15,817.06
Testing the equality of two variances:
H0: 𝜎12= 𝜎2
2
H1: 𝜎12≠ 𝜎2
2
Test Statistic: f0
Decision Rule: Reject Ho if f0> f α/2, n1-1, n2-1
Significance: α= 0.05
f0= 1.337
f0.025, 52, 32 =1.65
p-value = 0.383
Since f0< f0.025, 52, 32, H0 was not rejected and both variances are equal.
1 See Appendix (J) for more details
Page | 275
Testing the equality of two means:
H0: μ1= µ2
H1: μ1≠ µ2
Test Statistic: t0
Significance Level: α= 0.05
Decision Rule: Reject H0 if | t0|> t α/2, n1+n2-2 or p-value < α
t0 = 1.413
p-value= 0.162
Since p-value > α. H0 was not rejected and both means are equal.
Confidence interval
𝑥 1-𝑥 2 - t α/2,v 𝑆1
2
𝑛1+𝑆2
2
𝑛2 ≤ µ1- µ2 ≤ 𝑥 1-𝑥 2 + t α/2,v
𝑆12
𝑛1+𝑆2
2
𝑛2
-2,156.64≤ µ1- µ2 ≤ 12,692.54
There is a 95% chance that the difference between the two means is within [-
2,156.64, 12,692.54]. Since zero is within this interval, both means are equal.
The power of this test is 90%.
Thus, the model is valid.
Page | 276
Validating the Daily Scrap
Since the daily scrap is normally distributed for both the real system and the
as-is model, see Appendix (C), hypothesis tests can be applied to find the
confidence intervals.
Table 4.32: Real system and as-is model statistics summary.
Real system As-is model1
n 53 33
𝐱 (cans) 97.94 96.56
S (cans) 34.09 25
Testing the equality of two variances:
H0: 𝜎12= 𝜎2
2
H1: 𝜎12≠ 𝜎2
2
Test Statistic: f0
Decision Rule: Reject Ho if f0> f α/2, n1-1, n2-1
Significance: α= 0.05
f0 = 1.86
f0.025, 53, 32 = 1.65
p-value = 0.064
Since f0< f0.025, 52, 32, H0 was not rejected and both variances are equal.
1 See Appendix (J) for more details
Page | 277
Testing the equality of two means:
H0: μ1= µ2
H1: μ1≠ µ2
Test Statistic: t0
Significance Level: α= 0.05
Decision Rule: Reject H0 if | t0|> t α/2, n1+n2-2 or P-value < α
t0 = 0.217
df = 82.06
P-value = 0.829
Since p-value > α, H0 was not rejected and both variances are equal.
Confidence interval:
𝑥 1-𝑥 2 - t α/2,v 𝑆1
2
𝑛1+𝑆2
2
𝑛2 ≤ µ1- µ2 ≤ 𝑥 1-𝑥 2 + t α/2,v
𝑆12
𝑛1+𝑆2
2
𝑛2
-11.34 ≤ µ1- µ2 ≤ 14.10
There is a 95% chance that the difference between the two means is within [-11.34,
14.10]. Since zero is within this interval, both means are equal.
The power of this test is 90%.
Thus, the model is valid.
Page | 278
Can Filling Line
The Arena model that was coded for the can filling line was verified and it was
observed that the model works properly.
Validating the daily production:
The replication parameters are:
Replication Length: 10 hours/day.
Number of replications: 32 (see Appendix (I) for more details about the sample size).
For validation, the daily production was used as a performance measure.
Page | 279
Validating the Daily Production:
Since the daily production is normally distributed for both the real system and the as-
is model, see Appendix (C), hypothesis tests were applied to find the confidence
intervals.
Table 4.33: Real system and as-is model statistics summary.
Real system As-is model
N 58 32
𝐱 (carton) 2,338.1 2364.375
S (carton) 599.1 99.18
Testing the equality of two variances:
H0: 𝜎12= 𝜎2
2
H1: 𝜎12≠ 𝜎2
2
Test Statistic: f0
Decision Rule: Reject Ho if f0> f α/2, n1-1, n2-1
Significance: α= 0.05
f0 = 36.49
f0.025, 57, 31 = 1.95
p-value = 1.071*10-17
Since f0> f0.025, 57, 31, H0 was rejected and there the variances are not equal.
Page | 280
Testing the equality of two means:
H0: μ 1= µ2
H1: μ1≠ µ2
Test Statistic: t0
Significance Level: α= 0.05
Decision Rule: Reject H0 if | t0|> t α/2, v or p-value < α
t0 = -0.362
p-value= 0.746
Since p-value > α, H0 was not rejected and both means are equal.
Confidence interval:
𝑥 1-𝑥 2 - t α/2,v 𝑆1
2
𝑛1+𝑆2
2
𝑛2 ≤ µ1- µ2 ≤ 𝑥 1-𝑥 2 + t α/2,v
𝑆12
𝑛1+𝑆2
2
𝑛2
-187.36 ≤ µ1- µ2 ≤ 134.81
There is a 95% chance that the difference between the two means is between [-
187.36, 134.81]. Since zero is within this interval, both means are equal.
The power of this test is 90%.
Thus, the model is valid.
Page | 281
4.17 Analysis of Daily Production Runs and Improvement
In this section, the statistical analysis used to compare between the daily
production of each alternative and the as-is model, based on the simulation models,
is shown.
Can Making Line
For the can making line, only the most common case (2 boxes of sheet metal
per day) was simulated to reduce the variability in the output.
Alternative 1
The same Arena code of the can making line that was described in section 20.1 was
run but with the new values of the mean time between failures obtained from
alternative 1.
Table 4. 34: As-is model and alternative 1 statistics summary1.
As-is model Alternative 1
N 33 33
𝐱 (carton) 72,691.06 72,691.06
S (carton) 2.086 2.086
Testing the equality of two variances:
H0: 𝜎12= 𝜎2
2
H1: 𝜎12≠ 𝜎2
2
Test Statistic: f0
Decision Rule: Reject Ho if p-value< α
Significance: α= 0.05
f0= 1
1 See Appendix (J) for more details
Page | 282
p-value = 1
Since p-value> α, H0 was not rejected and both variances are equal.
Testing the equality of two means:
H0: μ 1= µ2
H1: μ1≠ µ2
Test Statistic: t0
Significance Level: α= 0.05
Decision Rule: Reject H0 if | t0|> t α/2, v or p-value < α
t0 = 0
p-value= 1
Since p-value > α, H0 was not rejected and both means are equal.
Confidence interval:
𝑥 2-𝑥 1 - t α/2,v 𝑆1
2
𝑛1+𝑆2
2
𝑛2 ≤ µ2- µ1 ≤ 𝑥 2-𝑥 1 + t α/2,v
𝑆12
𝑛1+𝑆2
2
𝑛2
-1.03 ≤ µ2- µ1 ≤ -1.03
There is a 95% chance that there is no significant difference between the as-is
model and alternative 1. Thus, there is no improvement.
The power of this test is 90%.
Page | 283
Alternative 2
The same Arena code of the can making line that was described in section 20.1 was
used but with the new values of the mean time between failures obtained from
alternative 2.
Table 4. 35: As-is model and alternative 2 statistics summary1.
As-is model Alternative 2
N 33 33
𝐱 (carton) 72,691.06 72,691.06
S (carton) 2.086 2.086
Testing the equality of two variances:
H0: 𝜎12= 𝜎2
2
H1: 𝜎12≠ 𝜎2
2
Test Statistic: f0
Decision Rule: Reject Ho if p-value< α
Significance: α= 0.05
f0= 1
p-value = 1
Since p-value> α, H0 is not rejected and both variances are equal.
1 See Appendix (J) for more details
Page | 284
Testing the equality of two means:
H0: μ 1= µ2
H1: μ1≠ µ2
Test Statistic: t0
Significance Level: α= 0.05
Decision Rule: Reject H0 if | t0|> t α/2, v or p-value < α
t0 = 0
p-value= 1
Since p-value > α, H0 is not rejected and both means are equal.
Confidence interval:
𝑥 2-𝑥 1 - t α/2,v 𝑆1
2
𝑛1+𝑆2
2
𝑛2 ≤ µ2- µ1 ≤ 𝑥 2-𝑥 1 + t α/2,v
𝑆12
𝑛1+𝑆2
2
𝑛2
-1.03 ≤ µ2- µ1 ≤ -1.03
There is a 95% chance that there is no significant difference between the as-is
model and alternative 2. Thus, there is no improvement.
The power of this test is 90%.
Page | 285
Alternative 3
The same Arena code of the can making line that was described in section 20.1 was
used but with the new values of the mean time between failures obtained from
alternative 3.
Table 4. 36: As-is model and alternative 3 statistics summary1.
As-is model Alternative 3
N 33 33
𝐱 (carton) 72,691.06 72,691.06
S (carton) 2.086 2.086
Testing the equality of two variances:
H0: 𝜎12= 𝜎2
2
H1: 𝜎12≠ 𝜎2
2
Test Statistic: f0
Decision Rule: Reject Ho if p-value< α
Significance: α= 0.05
f0= 1
p-value = 1
Since p-value> α, H0 was not rejected and both variances are equal.
1 See Appendix (J) for more details
Page | 286
Testing the equality of two means:
H0: μ 1= µ2
H1: μ1≠ µ2
Test Statistic: t0
Significance Level: α= 0.05
Decision Rule: Reject H0 if | t0|> t α/2, v or p-value < α
t0 = 0
p-value= 1
Since p-value > α, H0 was not rejected and both means are equal.
Confidence interval:
𝑥 2-𝑥 1 - t α/2,v 𝑆1
2
𝑛1+𝑆2
2
𝑛2 ≤ µ2- µ1 ≤ 𝑥 2-𝑥 1 + t α/2,v
𝑆12
𝑛1+𝑆2
2
𝑛2
-1.03 ≤ µ2- µ1 ≤ -1.03
There is a 95% chance that there is no significant difference between the as-is
model and alternative 3. Thus, there is no improvement.
The power of the test is 90%.
Page | 287
Can Filling Line
Alternative 1
The same Arena code of the can making line that was described in section
20.2 was used but with the new values of the mean time between failures obtained
from alternative 1.
Table 4. 37: Summary of failure module of alternative 1.
Name Up time (days) Down time (min)
Failure 1 EXPO (11.24) 30
Failure 2 EXPO (6.99) 60
Failure 3 EXPO (62.5) 30
Failure 4 EXPO (9.71) 60
Failure 5 EXPO (32.26) 60
Table 4. 38: As-is model and alternative 1 statistics summary1.
As-is model Alternative 1
N 32 32
𝐱 (carton) 2,364.375 2,403.438
S (carton) 99.18433 88.25145
1 See Appendix (K) for more details
Page | 288
Testing the equality of two variances:
H0: 𝜎12= 𝜎2
2
H1: 𝜎12≠ 𝜎2
2
Test Statistic: f0
Decision Rule: Reject Ho if p-value< α
Significance: α= 0.05
p-value = 0.51
Since p-value> α, H0 was not rejected and both variances are equal.
Testing the equality of two means:
H0: μ 1= µ2
H1: μ1≠ µ2
Test Statistic: t0
Significance Level: α= 0.05
Decision Rule: Reject H0 if | t0|> t α/2, v or p-value < α
t0 = -1.69
p-value= 0.095
Since p-value > α, H0 was not rejected and both means are equal.
Page | 289
Confidence interval:
𝑥 2-𝑥 1 - t α/2,v 𝑆1
2
𝑛1+𝑆2
2
𝑛2 ≤ µ2- µ1 ≤ 𝑥 2-𝑥 1 + t α/2,v
𝑆12
𝑛1+𝑆2
2
𝑛2
-7.86 ≤ µ2- µ1 ≤ 85.99
There is a 95% chance that the difference between the two means is within [-7.86,
85.99]. Since zero is within this interval then both means are equal. Thus, there is no
improvement.
The power of this test is 90%.
Page | 290
Alternative 2
The same Arena code of the can making line that was described in section 20.2 was
used but with the new values of the mean time between failures obtained from
alternative 2.
Table 4. 39: Summary of failure module of alternative 2.
Name Up time (days) Down time (min)
Failure 1 EXPO (11.24) 30
Failure 2 EXPO (50) 60
Failure 3 EXPO (62.5) 30
Failure 4 EXPO (9.71) 60
Failure 5 EXPO (32.26) 60
Table 4. 40: As-is model and alternative 1 statistics summary1.
As-is model Alternative 2
N 32 32
𝐱 (carton) 2,364.375 2,426.281
S (carton) 99.18433 60.79221
1 See Appendix (K) for more details
Page | 291
Testing the equality of two variances:
H0: 𝜎12= 𝜎2
2
H1: 𝜎12≠ 𝜎2
2
Test Statistic: f0
Decision Rule: Reject Ho if p-value< α
Significance: α= 0.05
f0= 2.66
p-value = 7.02E-03
Since p-value< α, H0 was rejected and the variances are not equal.
Testing the equality of two means:
H0: μ 1= µ2
H1: μ1≠ µ2
Test Statistic: t0
Significance Level: α= 0.05
Decision Rule: Reject H0 if | t0|> t α/2, v or p-value < α
t0 = -3.05
p-value= 3.5E-03
Since p-value < α, H0 is not rejected and the means are not equal.
Page | 292
Confidence interval:
𝑥 2-𝑥 1 - t α/2,v 𝑆1
2
𝑛1+𝑆2
2
𝑛2 ≤ µ2- µ1 ≤ 𝑥 2-𝑥 1 + t α/2,v
𝑆12
𝑛1+𝑆2
2
𝑛2
20.63 ≤ µ2- µ1 ≤ 103.18
There is a 95% chance that the difference between the two means is within [20.63,
103.18] and the mean of alternative 2 is always greater than the mean of the as-is
model. Thus, there is an improvement.
The power of this test is 90%.
From the above confidence interval, it can be concluded that by applying the
maintenance plan of alternative 2, the factory can increase production by 21 to 103
cartons daily. This translates a reduction in overtime hours and cost by 3.51-17.22%.
Page | 293
Alternative 3
The same Arena code of the can making line that was described in section
20.2 was used but with the new values of the mean time between failures obtained
from alternative 3.
Table 4. 41: Summary of failure module of alternative 3.
Name Up time (days) Down time (min)
Failure 1 EXPO (27.15) 30
Failure 2 EXPO (28.49) 60
Failure 3 EXPO (26.20) 30
Failure 4 EXPO (28.27) 60
Failure 5 EXPO (26.33) 60
Table 4. 42: As-is model and alternative 1 statistics summary1.
As-is model Alternative 3
n 32 32
𝐱 (carton) 2,364.375 2,438.875
S (carton) 99.18433 51.271
1 See Appendix (K) for more details
Page | 294
Testing the equality of two variances:
H0: 𝜎12= 𝜎2
2
H1: 𝜎12≠ 𝜎2
2
Test Statistic: f0
Decision Rule: Reject Ho if p-value< α
Significance: α= 0.05
f0= 3.74
p-value = 3.4E-04
Since p-value< α, H0 was rejected and the variances are not equal.
Testing the equality of two means:
H0: μ 1= µ2
H1: μ1≠ µ2
Test Statistic: t0
Significance Level: α= 0.05
Decision Rule: Reject H0 if | t0|> t α/2, v or p-value < α
t0 = -3.83
p-value= 3.68E-04
Since p-value < α, H0 was rejected and the means are not equal.
Page | 295
Confidence interval:
𝑥 2-𝑥 1 - t α/2,v 𝑆1
2
𝑛1+𝑆2
2
𝑛2 ≤ µ2- µ1 ≤ 𝑥 2-𝑥 1 + t α/2,v
𝑆12
𝑛1+𝑆2
2
𝑛2
34.78 ≤ µ2- µ1 ≤ 114.22
There is a 95% confident that the difference between the two means is within [34.78,
114.22] and the mean of alternative 3 is always greater than the mean of the as-is
model. Thus, there is an improvement.
The power of this test is 90%.
From the above confidence interval, it is concluded that by applying the maintenance
plan of alternative 3, the factory can increase production by 35 to 114 cartons daily.
This translates to a reduction in overtime hours and cost of 5.85-19.06%.
Page | 296
4.18 Summary of the Proposed Alternatives
After analyzing each alternative and comparing it to the as-is situation; the
reduction in maintenance cost and the increase in both reliability and daily
production for both lines, under each alternative, are summarized in the following
table.
Table 4. 43: Summary of proposed alternatives.
Criteria Alternative 1 Alternative 2 Alternative 3
Maintenance Cost -29% -61.8% -72.65%
Reliability of Can Making
Line +3.91% +17.53% +19.82%
Reliability of Filling Line +26.65% +43.24% +38.19%
Daily Production of Can
Making Line No improvement No improvement No improvement
Daily Production of Filling
Line No improvement +0.89 to +4.36% +1.48 to +4.82%
Overtime cost No improvement -3.51 to -17.22% -5.85 to -19.06%
As shown, alternative 3 is the best in all criteria.
Page | 297
4.18 Conclusion
The maintenance policies that the factory currently applies were studied and both the
reliability and the maintenance cost were calculated. Then, the as-is system was
simulated using Arena software under the current operational conditions and failure
rates. Moreover, new maintenance policies were proposed to reduce the failure rates
of the machines, the reliability and the maintenance cost were calculated for each
alternative. The new policies were then simulated and compared with the as-is
model and the best policy was selected based on the following criteria: highest
increase in the reliability and production rate, and greatest reduction in the
maintenance cost.
Page | 298
Page | 299
5. Inventory Management
and Production Planning
Page | 300
Page | 301
5.1 Introduction
The National Canned Food Company produces a variety of canned
foods produced based on demand. The lead time between placing an order
and receiving it is 21 days. This period is set to ensure the availability of the
relevant raw materials. In addition to its factory in Subhan, the company has a
warehouse in Kabd for packing material, as well as a warehouse for exported
goods located in Mina Abdullah. The factory has three raw material
inventories. One is for labels (including can labels and special offers labels),
spices inventory (for example, sugar and salt) and can plant inventory (such
as copper wires and glue). The final product inventory has a capacity of
100,000 cans.
Figure 5.15: Inventory flow in the factory.
Problem description
Page | 302
The company cannot meet the demand on time due to poor production
plans.
Some processes take longer due to poor planning.
Excessive inventory is held in the system.
Lead time is relatively long for the final product.
Solution approach
1. Demand was forecasted for all 27 types of goods produced using past
data.
2. The current production capacity was calculated to determine if
demand can comfortably be covered.
3. Inventory plans were developed for raw material and production plans
for finished products.
Methodology
1. Collected data for past three years for all goods.
2. Applied forecasting methods to determine the demand for the next
year.
3. Selected best forecasting method.
4. Analyzed the current inventory system and order quantities for raw
material.
5. Applied inventory models to determine optimum order quantities and
compare with the current system.
6. Analyzed current production plan and lot sizes
7. Applied production planning models and determined optimum lot sizes
for all products.
8. Checked the production capacity and matched it with the plan.
9. Adjusted capacity according to the demand.
10. Applied service level calculation to determine safety stock.
5.2 Analysis
Page | 303
1- Demand forecasting
Demand forecasting is the activity of estimating the demand of
products that consumers will purchase in the future. It involves techniques
such as methods that can be used to predict the future demands or sales.
Forecasting depends on the trend of the historical data ,and the company’s
demand of the final products have a trend and seasonality in every
September of each year, considering year (2006-2007-2008) . In our project
the demand was forecasted for the next five years for capacity planning but
only the demand forecasted of year 2009 was used for production planning.
The appropriated method that will apply to forecast must be with least
error after testing the MAD (Mean Absolute Deviation) from each method. The
tested forecasting methods are:
Moving average method
Exponential smoothing with trend method
Regression method
Winter’s method
Holt’s method
In our project Holt's Method has the least error, therefore it was used.
Page | 304
Holt’s method
This method is designed to track time series with linear trend. Two smoothing
constant α and β must be specified for two smoothing equations. The
equations are:
St * = (α)*(Dt*) + (1-α)*(St-1* + Gt-1)
Gt* = (β)*(St* - St-1*) + (1-β)*(Gt-1*)
St-1* = Dt-1*
Gt-1* = (Di* - Dj*) / (i – j)
Ft,t+τ * =St* + τGt*
Ft = Ft* (CQt*)
Where St * is the value of the intercept, Gt* is the value of the slope, Ft*
symbolizes the forecast of the deseasonalized unit and Ft is the final forecast
of the original units. To compute the value of Gt-1*, an approximate trend line
should be obtained by eyeballing the data. The first point the trend line
through is the value of ( i ) and the last point is the value of ( j ).
Baked Beans
Page | 305
Table 5.1: The data of Avg. MA (12) and Ct for beaked beans.
Time Demand (Dt) Avg.MA(12) Index (Ct)
Jan-06 9330
Feb-06 9087
Mar-06 8481
Apr-06 9208
May-06 8724
Jun-06 9572
Jul-06 10299 10135.790 1.016
Aug-06 12480 10212.526 1.222
Sep-06 15751 10285.729 1.531
Oct-06 10299 10359.437 0.994
Nov-06 9208 10434.154 0.883
Dec-06 8724 10510.385 0.830
Jan-07 10263 10593.180 0.969
Feb-07 9996 10688.091 0.935
Mar-07 9330 10805.720 0.863
Apr-07 10129 10914.262 0.928
May-07 9596 10995.542 0.873
Jun-07 10529 11070.259 0.951
Jul-07 11329 11145.481 1.016
Aug-07 13728 11222.218 1.223
Sep-07 17326 11295.421 1.534
Oct-07 11329 11369.128 0.996
Nov-07 10129 11443.845 0.885
Dec-07 9596 11520.077 0.833
Jan-08 11195 11602.872 0.965
Page | 306
Figure 5.2: Forecasting model for seasonality & trend for baked beans.
Feb-08 10905 11697.783 0.932
Mar-08 10178 11815.412 0.861
Apr-08 11050 11923.954 0.927
May-08 10468 12005.234 0.872
Jun-08 11486 12079.951 0.951
Jul-08 12359
Aug-08 14976
Sep-08 18901
Oct-08 12359
Nov-08 11050
Dec-08 10468
Baked Beans
Page | 307
As mentioned previously the value of Gt-1* can only be determined if a
trend line passing through the deseasonalized demand is drawn. The trend
line passes through D10* and D30* which are the values of (i) and (j)
respectively. All the forecasting data can be seen in Appendix O (D10* is
10344).
Different values of α and β were generated. It happens to be that when α is
0.9 and β is 0.1, the error is at its minimum.
Figure 5.3: Forecasted demand for baked beans.
From the figure 5.3 above, it can be seen that the forecasted demand
is almost overlapping the actual demand. This indicates that the error is very
low. After applying Holt's method, the following results were achieved:
Mean Absolute Deviation = 12.542
Mean Square Error = 385.972
The following figures and tables pertain to the remaining products which were
dealt with in exactly the same manner as the baked beans.
Baked Beans
Page | 308
Black Eye Beans
Table 5.2. The data of Avg. MA (12) and Ct for black eye beans.
Time Demand (Dt) Avg.MA(12) Index (Ct)
Jan-06 1323
Feb-06 1289
Mar-06 1203
Apr-06 1306
May-06 1237
Jun-06 1358
Jul-06 1461 1437.597 1.016
Aug-06 1770 1448.481 1.222
Sep-06 2234 1458.863 1.531
Oct-06 1461 1469.318 0.994
Nov-06 1306 1479.915 0.883
Dec-06 1237 1490.727 0.830
Jan-07 1456 1502.470 0.969
Feb-07 1418 1515.932 0.935
Mar-07 1323 1532.616 0.863
Apr-07 1437 1548.010 0.928
May-07 1361 1559.539 0.873
Jun-07 1493 1570.136 0.951
Jul-07 1607 1580.805 1.016
Aug-07 1947 1591.689 1.223
Sep-07 2457 1602.072 1.534
Oct-07 1607 1612.526 0.996
Nov-07 1437 1623.123 0.885
Dec-07 1361 1633.935 0.833
Page | 309
Jan-08 1588 1645.679 0.965
Feb-08 1547 1659.140 0.932
Mar-08 1444 1675.824 0.861
Apr-08 1567 1691.219 0.927
May-08 1485 1702.747 0.872
Jun-08 1629 1713.345 0.951
Jul-08 1753
Aug-08 2124
Sep-08 2681
Oct-08 1753
Nov-08 1567
Dec-08 1485
Figure 5.4: Forecasting model for seasonality & trend for black eye beans.
It can clearly be seen in figure 5.4 above, that the trend line passes
through points D10* and D30*. The values that correspond to D10* and D30* are
1467 and 1713, respectively.
Black Eye Beans
Page | 310
Figure 5.5: Forecasted demand for balck eye beans.
The error, as shown below, is quite low. This indicates that the forecasting
method used is applicable.
Mean Absolute Deviation = 1.779
Mean Square Error = 7.765
Black Eye Beans
Page | 311
Broad Beans
Table 5.3: The data of Avg. MA (12) and Ct for broad beans.
Time Demand (Dt) Avg.MA(12) Index (Ct)
Jan-06 13234
Feb-06 12890
Mar-06 12031
Apr-06 13062
May-06 12375
Jun-06 13578
Jul-06 14609 14377.893 1.016
Aug-06 17703 14486.745 1.222
Sep-06 22343 14590.585 1.531
Oct-06 14609 14695.142 0.994
Nov-06 13062 14801.130 0.883
Dec-06 12375 14909.267 0.830
Jan-07 14558 15026.713 0.969
Feb-07 14180 15161.347 0.935
Mar-07 13234 15328.207 0.863
Apr-07 14369 15482.177 0.928
May-07 13612 15597.475 0.873
Jun-07 14936 15703.463 0.951
Jul-07 16070 15810.168 1.016
Aug-07 19473 15919.020 1.223
Sep-07 24578 16022.860 1.534
Oct-07 16070 16127.417 0.996
Nov-07 14369 16233.405 0.885
Dec-07 13612 16341.542 0.833
Page | 312
Jan-08 15881 16458.988 0.965
Feb-08 15469 16593.622 0.932
Mar-08 14437 16760.482 0.861
Apr-08 15675 16914.452 0.927
May-08 14850 17029.750 0.872
Jun-08 16294 17135.738 0.951
Jul-08 17531
Aug-08 21244
Sep-08 26812
Oct-08 17531
Nov-08 15675
Dec-08 14850
Figure 5.6: Forecasting model for seasonality & trend for broad beans.
It can clearly be seen in figure 5.6 above, that the trend line passes through
points D10* and D30*. The values that correspond to D10* and D30* are 14673
and 17127, respectively.
Broad Beans
Page | 313
Figure 5.7: Forecasted demand.
After applying Holt's Method, the following results were obtained:
Mean Absolute Deviation = 17.791
Mean Square Error = 776.660
Broad Beans
Page | 314
4. Chick Peas
Table 5.4: The data of Avg. MA (12) and Ct for chick peas.
Time Demand (Dt)
Avg.MA(12) Index (Ct)
Jan-06 17595
Feb-06 17138
Mar-06 15996
Apr-06 17367
May-06 16453
Jun-06 18052
Jul-06 19423 19115.814 1.016
Aug-06 23537 19260.537 1.222
Sep-06 29706 19398.595 1.531
Oct-06 19423 19537.605 0.994
Nov-06 17367 19678.520 0.883
Dec-06 16453 19822.290 0.830
Jan-07 19355 19978.439 0.969
Feb-07 18852 20157.438 0.935
Mar-07 17595 20379.284 0.863
Apr-07 19103 20583.990 0.928
May-07 18098 20737.283 0.873
Jun-07 19858 20878.197 0.951
Jul-07 21366 21020.064 1.016
Aug-07 25890 21164.787 1.223
Sep-07 32677 21302.845 1.534
Oct-07 21366 21441.855 0.996
Nov-07 19103 21582.770 0.885
Dec-07 18098 21726.540 0.833
Page | 315
Jan-08 21114 21882.689 0.965
Feb-08 20566 22061.688 0.932
Mar-08 19195 22283.534 0.861
Apr-08 20840 22488.240 0.927
May-08 19743 22641.533 0.872
Jun-08 21663 22782.447 0.951
Jul-08 23308
Aug-08 28244
Sep-08 35648
Oct-08 23308
Nov-08 20840
Dec-08 19743
Figure 5.8: Forecasting model for seasonality & trend for chick peas.
It can clearly be seen in figure 5.8 above, that the trend line passes through
points D10* and D30*. The values that correspond to D10* and D30* are 19508
and 22771, respectively.
Chick Peas
Page | 316
Figure 5.9: Forecasted demand for chick peas.
After applying Holt's Method, the following results were obtained:
Mean Absolute Deviation = 23.654
Mean Square Error = 1372.860
Chick Peas
Page | 317
5. Chick Peas 10mm
Table 5.5: The data of Avg. MA (12) and Ct. for chick peas 10 mm.
Time Demand (Dt) Avg.MA(12) Index (Ct)
Jan-06 2290
Feb-06 2230
Mar-06 2082
Apr-06 2260
May-06 2141
Jun-06 2349
Jul-06 2528 2487.708 1.016
Aug-06 3063 2506.542 1.222
Sep-06 3866 2524.508 1.531
Oct-06 2528 2542.599 0.994
Nov-06 2260 2560.937 0.883
Dec-06 2141 2579.648 0.830
Jan-07 2519 2599.969 0.969
Feb-07 2453 2623.263 0.935
Mar-07 2290 2652.134 0.863
Apr-07 2486 2678.774 0.928
May-07 2355 2698.724 0.873
Jun-07 2584 2717.062 0.951
Jul-07 2781 2735.524 1.016
Aug-07 3369 2754.358 1.223
Sep-07 4253 2772.325 1.534
Oct-07 2781 2790.416 0.996
Nov-07 2486 2808.754 0.885
Dec-07 2355 2827.464 0.833
Page | 318
Jan-08 2748 2847.785 0.965
Feb-08 2676 2871.080 0.932
Mar-08 2498 2899.951 0.861
Apr-08 2712 2926.591 0.927
May-08 2569 2946.540 0.872
Jun-08 2819 2964.879 0.951
Jul-08 3033 2859.3087
Aug-08 3676
Sep-08 4639
Oct-08 3033
Nov-08 2712
Dec-08 2569
Figure 5.10: Forecasting model for seasonality & trend for chick peas 10mm.
It can clearly be seen in figure 5.10 above, that the trend line passes
through points D10* and D30*. The values that correspond to D10* and D30* are
2539 and 2963, respectively.
Chick Peas 10mm
Page | 319
Figure 5.11: Forecasted demand for chick peas 10mm.
After applying Holt's Method, the following results were obtained:
Mean Absolute Deviation = 3.078
Mean Square Error = 23.251
Chick Peas 10mm
Page | 320
6. Chick Peas with Chili
Table 5.6: The data of Avg. MA (12) and Ct for chick peas with chilli.
Time Demand (Dt) Avg.MA(12) Index (Ct)
Jan-06 123
Feb-06 120
Mar-06 112
Apr-06 122
May-06 115
Jun-06 126
Jul-06 136 133.847 1.016
Aug-06 165 134.860 1.222
Sep-06 208 135.827 1.531
Oct-06 136 136.800 0.994
Nov-06 122 137.787 0.883
Dec-06 115 138.793 0.830
Jan-07 136 139.887 0.969
Feb-07 132 141.140 0.935
Mar-07 123 142.693 0.863
Apr-07 134 144.127 0.928
May-07 127 145.200 0.873
Jun-07 139 146.187 0.951
Jul-07 150 147.180 1.016
Aug-07 181 148.193 1.223
Sep-07 229 149.160 1.534
Oct-07 150 150.133 0.996
Nov-07 134 151.120 0.885
Dec-07 127 152.127 0.833
Page | 321
Jan-08 148 153.220 0.965
Feb-08 144 154.473 0.932
Mar-08 134 156.027 0.861
Apr-08 146 157.460 0.927
May-08 138 158.533 0.872
Jun-08 152 159.520 0.951
Jul-08 163
Aug-08 198
Sep-08 250
Oct-08 163
Nov-08 146
Dec-08 138
Figure 5.12: Forecasting model for seasonality & trend for chick peas with chili.
It can clearly be seen in figure 5.12 above, that the trend line passes through
points D10* and D30*. The values that correspond to D10* and D30* are 137 and
159, respectively.
ilihC htiw saeP kcihC
Page | 322
Figure 5.13: Forecasted demand for chick peas with chili.
After applying Holt's Method, the following results were obtained:
Mean Absolute Deviation = 0.166
Mean Square Error = 0.067
ilihC htiw saeP kcihC
Page | 323
7. Fava Beans
Table 5.7: The data of Avg. MA (12) and Ct for fava beans.
Time Demand (Dt) Avg.MA(12) Index (Ct)
Jan-06 14129
Feb-06 13762
Mar-06 12845
Apr-06 13946
May-06 13212
Jun-06 14496
Jul-06 15597 15350.121 1.016
Aug-06 18900 15466.335 1.222
Sep-06 23854 15577.196 1.531
Oct-06 15597 15688.823 0.994
Nov-06 13946 15801.978 0.883
Dec-06 13212 15917.427 0.830
Jan-07 15542 16042.815 0.969
Feb-07 15138 16186.553 0.935
Mar-07 14129 16364.696 0.863
Apr-07 15340 16529.077 0.928
May-07 14533 16652.171 0.873
Jun-07 15946 16765.327 0.951
Jul-07 17157 16879.246 1.016
Aug-07 20790 16995.460 1.223
Sep-07 26240 17106.321 1.534
Oct-07 17157 17217.948 0.996
Nov-07 15340 17331.103 0.885
Dec-07 14533 17446.552 0.833
Page | 324
Jan-08 16955 17571.940 0.965
Feb-08 16515 17715.678 0.932
Mar-08 15414 17893.821 0.861
Apr-08 16735 18058.202 0.927
May-08 15854 18181.296 0.872
Jun-08 17395 18294.452 0.951
Jul-08 18716
Aug-08 22680
Sep-08 28625
Oct-08 18716
Nov-08 16735
Dec-08 15854
Figure 5.14: Forecasting model for seasonality & trend for fava beans.
It can clearly be seen in figure 5.14 above, that the trend line passes through
points D10* and D30*. The values that correspond to D10* and D30* are 15665
and 18286, respectively.
snaeB avaF
Page | 325
Figure 5.15: Forecasted demand for fava beans.
After applying Holt's Method, the following results were obtained:
Mean Absolute Deviation = 18.994
Mean Square Error = 885.247
snaeB avaF
Page | 326
8. Fava Beans with Chili
Table 5.8: The data of Avg. MA (12) and Ct for fava beans with chili.
Time Demand (Dt) Avg.MA(12) Index (Ct)
Jan-06 179
Feb-06 174
Mar-06 163
Apr-06 177
May-06 167
Jun-06 184
Jul-06 198 194.496 1.016
Aug-06 239 195.968 1.222
Sep-06 302 197.373 1.531
Oct-06 198 198.788 0.994
Nov-06 177 200.221 0.883
Dec-06 167 201.684 0.830
Jan-07 197 203.273 0.969
Feb-07 192 205.094 0.935
Mar-07 179 207.351 0.863
Apr-07 194 209.434 0.928
May-07 184 210.994 0.873
Jun-07 202 212.428 0.951
Jul-07 217 213.871 1.016
Aug-07 263 215.343 1.223
Sep-07 332 216.748 1.534
Oct-07 217 218.163 0.996
Nov-07 194 219.596 0.885
Dec-07 184 221.059 0.833
Page | 327
Figure 5.16: Forecasting model for seasonality & trend for fava beans with chili.
It can clearly be seen in figure 5.16 above, that the trend line passes through
points D10* and D30*. The values that correspond to D10* and D30* are 198 and
232, respectively.
Jan-08 215 222.648 0.965
Feb-08 209 224.469 0.932
Mar-08 195 226.726 0.861
Apr-08 212 228.809 0.927
May-08 201 230.369 0.872
Jun-08 220 231.803 0.951
Jul-08 237
Aug-08 287
Sep-08 363
Oct-08 237
Nov-08 212
Dec-08 201
ilihC htiw snaeB avaF
Page | 328
Figure 5.17: Forecasted demand for fava beans with chili.
After applying Holt's Method, the following results were obtained:
Mean Absolute Deviation = 0.241
Mean Square Error = 0.142
ilihC htiw snaeB avaF
Page | 329
9. Egyptian Foul Medames
Table 5.9: The data of Avg. MA (12) and Ct for foul medames - Egyptian.
Time Demand (Dt) Avg.MA(12) Index (Ct)
Jan-06 1686
Feb-06 1642
Mar-06 1533
Apr-06 1664
May-06 1576
Jun-06 1730
Jul-06 1861 1831.608 1.016
Aug-06 2255 1845.475 1.222
Sep-06 2846 1858.703 1.531
Oct-06 1861 1872.023 0.994
Nov-06 1664 1885.524 0.883
Dec-06 1576 1899.300 0.830
Jan-07 1855 1914.262 0.969
Feb-07 1806 1931.413 0.935
Mar-07 1686 1952.669 0.863
Apr-07 1830 1972.283 0.928
May-07 1734 1986.971 0.873
Jun-07 1903 2000.473 0.951
Jul-07 2047 2014.066 1.016
Aug-07 2481 2027.933 1.223
Sep-07 3131 2041.161 1.534
Oct-07 2047 2054.481 0.996
Nov-07 1830 2067.983 0.885
Dec-07 1734 2081.758 0.833
Page | 330
Jan-08 2023 2096.720 0.965
Feb-08 1971 2113.871 0.932
Mar-08 1839 2135.127 0.861
Apr-08 1997 2154.742 0.927
May-08 1892 2169.430 0.872
Jun-08 2076 2182.932 0.951
Jul-08 2233
Aug-08 2706
Sep-08 3416
Oct-08 2233
Nov-08 1997
Dec-08 1892
Figure 5.18: Forecasting model for seasonality & trend for foul medames - Egyptain.
It can clearly be seen in figure 5.18 above, that the trend line passes through
points D10* and D30*. The values that correspond to D10* and D30* are 1869
and 2182, respectively.
semadeM luoF naitpygE
Page | 331
After applying Holt's Method, the following results were obtained:
Mean Absolute Deviation = 2.266
Mean Square Error = 12.604
10. Saudi Foul Medames
Table 5.10: The data of Avg. MA (12) and Ct Saudi Foul Medames.
Time Demand (Dt) Avg.MA(12) Index (Ct)
Jan-06 100
Feb-06 98
Mar-06 91
Apr-06 99
May-06 94
Jun-06 103
Jul-06 111 109.169 1.016
Aug-06 134 109.995 1.222
Sep-06 170 110.784 1.531
Oct-06 111 111.578 0.994
Nov-06 99 112.382 0.883
Dec-06 94 113.203 0.830
Jan-07 111 114.095 0.969
Feb-07 108 115.117 0.935
Mar-07 100 116.384 0.863
Apr-07 109 117.553 0.928
May-07 103 118.429 0.873
Jun-07 113 119.234 0.951
Jul-07 122 120.044 1.016
Aug-07 148 120.870 1.223
Page | 332
Sep-07 187 121.659 1.534
Oct-07 122 122.453 0.996
Nov-07 109 123.257 0.885
Dec-07 103 124.078 0.833
Jan-08 121 124.970 0.965
Feb-08 117 125.992 0.932
Mar-08 110 127.259 0.861
Apr-08 119 128.428 0.927
May-08 113 129.304 0.872
Jun-08 124 130.109 0.951
Jul-08 133
Aug-08 161
Sep-08 204
Oct-08 133
Nov-08 119
Dec-08 113
Figure 5.20: Forecasting model for seasonality & trend for Saudi Foul Medames.
Saudi Foul Medames
Page | 333
It can clearly be seen in figure 5.20 above, that the trend line passes through
points D10* and D30*. The values that correspond to D10* and D30* are 111 and
130, respectively.
Figure 5.21: Forecasted demand for Saudi Foul Medames.
After applying Holt's Method, the following results were obtained:
Mean Absolute Deviation = 570.825
Mean Square Error = 338502.937
Saudi Foul Medames
Page | 334
11. Lebanese Foul Medames
Table 5.11: The data of Avg. MA (12) and Ct for Lebanese foul medames.
Time Demand (Dt) Avg.MA(12) Index (Ct)
Jan-06 540
Feb-06 526
Mar-06 491
Apr-06 533
May-06 505
Jun-06 554
Jul-06 596 586.667 1.016
Aug-06 722 591.108 1.222
Sep-06 912 595.345 1.531
Oct-06 596 599.612 0.994
Nov-06 533 603.936 0.883
Dec-06 505 608.349 0.830
Jan-07 594 613.141 0.969
Feb-07 579 618.634 0.935
Mar-07 540 625.443 0.863
Apr-07 586 631.725 0.928
May-07 555 636.430 0.873
Jun-07 609 640.754 0.951
Jul-07 656 645.108 1.016
Aug-07 795 649.550 1.223
Sep-07 1003 653.787 1.534
Oct-07 656 658.053 0.996
Nov-07 586 662.378 0.885
Dec-07 555 666.790 0.833
Page | 335
Jan-08 648 671.582 0.965
Feb-08 631 677.076 0.932
Mar-08 589 683.884 0.861
Apr-08 640 690.167 0.927
May-08 606 694.871 0.872
Jun-08 665 699.196 0.951
Jul-08 715
Aug-08 867
Sep-08 1094
Oct-08 715
Nov-08 640
Dec-08 606
Figure5.22: Forecasting model for seasonality & trend for Lebanese foul medames.
It can clearly be seen in figure 5.22 above, that the trend line passes through
points D10* and D30*. The values that correspond to D10* and D30* are 599 and
699, respectively.
Lebanese Foul Medames
Page | 336
Figure 5.23: Forecasted demand for Lebanese foul medames.
After applying Holt's Method, the following results were obtained:
Mean Absolute Deviation = 0.726
Mean Square Error = 1.293
Lebanese Foul Medames
Page | 337
12. Green Peas
Table 5.12: The data of Avg. MA (12) and Ct for green peas.
Time Demand (Dt) Avg.MA(12) Index (Ct)
Jan-06 19444
Feb-06 18939
Mar-06 17677
Apr-06 19192
May-06 18182
Jun-06 19949
Jul-06 21465 21124.768 1.016
Aug-06 26010 21284.701 1.222
Sep-06 32828 21437.268 1.531
Oct-06 21465 21590.888 0.994
Nov-06 19192 21746.611 0.883
Dec-06 18182 21905.492 0.830
Jan-07 21389 22078.050 0.969
Feb-07 20833 22275.862 0.935
Mar-07 19444 22521.021 0.863
Apr-07 21111 22747.242 0.928
May-07 20000 22916.644 0.873
Jun-07 21944 23072.368 0.951
Jul-07 23611 23229.143 1.016
Aug-07 28611 23389.076 1.223
Sep-07 36111 23541.643 1.534
Oct-07 23611 23695.263 0.996
Nov-07 21111 23850.986 0.885
Dec-07 20000 24009.867 0.833
Page | 338
Jan-08 23333 24182.425 0.965
Feb-08 22727 24380.237 0.932
Mar-08 21212 24625.396 0.861
Apr-08 23030 24851.617 0.927
May-08 21818 25021.019 0.872
Jun-08 23939 25176.743 0.951
Jul-08 25758
Aug-08 31212
Sep-08 39394
Oct-08 25758
Nov-08 23030
Dec-08 21818
Figure 5.24: Forecasting model for seasonality & trend for green peas.
It can clearly be seen in figure 5.24 above, that the trend line passes through
points D10* and D30*. The values that correspond to D10* and D30* are 21559
and 25165, respectively.
Green Peas
Page | 339
Figure 5.25: Forecasted demand.
After applying Holt's Method, the following results were obtained:
Mean Absolute Deviation = 26.140
Mean Square Error = 1676.581
Green Peas
Page | 340
13. Hummus Tahineh - Chick Peas 7 mm
Table 5.13: The data of Avg. MA (12) and Ct for Hummus Tahineh - Chick Peas 7 mm.
Time Demand (Dt) Avg.MA(12) Index (Ct)
Jan-06 10494
Feb-06 10221
Mar-06 9540
Apr-06 10358
May-06 9813
Jun-06 10767
Jul-06 11584 11400.808 1.016
Aug-06 14037 11487.122 1.222
Sep-06 17717 11569.461 1.531
Oct-06 11584 11652.368 0.994
Nov-06 10358 11736.410 0.883
Dec-06 9813 11822.156 0.830
Jan-07 11543 11915.284 0.969
Feb-07 11244 12022.041 0.935
Mar-07 10494 12154.351 0.863
Apr-07 11393 12276.439 0.928
May-07 10794 12367.864 0.873
Jun-07 11843 12451.906 0.951
Jul-07 12743 12536.516 1.016
Aug-07 15441 12622.830 1.223
Sep-07 19489 12705.169 1.534
Oct-07 12743 12788.076 0.996
Nov-07 11393 12872.118 0.885
Dec-07 10794 12957.864 0.833
Page | 341
Jan-08 12593 13050.992 0.965
Feb-08 12266 13157.749 0.932
Mar-08 11448 13290.059 0.861
Apr-08 12429 13412.148 0.927
May-08 11775 13503.572 0.872
Jun-08 12920 13587.615 0.951
Jul-08 13901
Aug-08 16845
Sep-08 21260
Oct-08 13901
Nov-08 12429
Dec-08 11775
Figure 5.26: Forecasting model for seasonality & trend for Hummus Tahineh - Chick Peas 7 mm.
It can clearly be seen in figure 5.26 above, that the trend line passes through
points D10* and D30*. The values that correspond to D10* and D30* are 11635
and 13581, respectively.
Hummus Tahineh - Chick Peas 7
mm
Page | 342
Figure 5.27: Forecasted demand for Hummus Tahineh - Chick Peas 7 mm.
After applying Holt's Method, the following results were obtained:
Mean Absolute Deviation = 14.107
Mean Square Error = 488.328
Hummus Tahineh - Chick Peas 7
mm
Page | 343
14. Hummus Tahineh with Garlic
Table 5.14: The data of Avg. MA (12) and Ct for Hummus Tahineh with Garlic.
Time Demand (Dt) Avg.MA(12) Index (Ct)
Jan-06 72
Feb-06 70
Mar-06 66
Apr-06 71
May-06 68
Jun-06 74
Jul-06 80 78.468 1.016
Aug-06 97 79.062 1.222
Sep-06 122 79.628 1.531
Oct-06 80 80.199 0.994
Nov-06 71 80.777 0.883
Dec-06 68 81.368 0.830
Jan-07 79 82.009 0.969
Feb-07 77 82.743 0.935
Mar-07 72 83.654 0.863
Apr-07 78 84.494 0.928
May-07 74 85.124 0.873
Jun-07 82 85.702 0.951
Jul-07 88 86.284 1.016
Aug-07 106 86.878 1.223
Sep-07 134 87.445 1.534
Oct-07 88 88.016 0.996
Nov-07 78 88.594 0.885
Dec-07 74 89.184 0.833
Page | 344
Jan-08 87 89.825 0.965
Feb-08 84 90.560 0.932
Mar-08 79 91.471 0.861
Apr-08 86 92.311 0.927
May-08 81 92.940 0.872
Jun-08 89 93.519 0.951
Jul-08 96
Aug-08 116
Sep-08 146
Oct-08 96
Nov-08 86
Dec-08 81
Figure 5.28: Forecasting model for seasonality & trend for Hummus Tahineh with Garlic.
It can clearly be seen in figure 5.28 above, that the trend line passes through
points D10* and D30*. The values that correspond to D10* and D30* are 80 and
93, respectively.
Hummus Tahineh with Garlic
Page | 345
Figure 5.29: Forecasted demand for Hummus Tahineh with Garlic.
After applying Holt's Method, the following results were obtained:
Mean Absolute Deviation = 0.097
Mean Square Error = 0.023
Hummus Tahineh with Garlic
Page | 346
15. Hotdog Sausage
Table 5.15: The data of Avg. MA (12) and Ct for hotdog sausage.
Time Demand (Dt) Avg.MA(12) Index (Ct)
Jan-06 63
Feb-06 61
Mar-06 57
Apr-06 62
May-06 59
Jun-06 64
Jul-06 69 68.011 1.016
Aug-06 84 68.526 1.222
Sep-06 106 69.017 1.531
Oct-06 69 69.512 0.994
Nov-06 62 70.013 0.883
Dec-06 59 70.524 0.830
Jan-07 69 71.080 0.969
Feb-07 67 71.717 0.935
Mar-07 63 72.506 0.863
Apr-07 68 73.234 0.928
May-07 64 73.780 0.873
Jun-07 71 74.281 0.951
Jul-07 76 74.786 1.016
Aug-07 92 75.301 1.223
Sep-07 116 75.792 1.534
Oct-07 76 76.287 0.996
Nov-07 68 76.788 0.885
Dec-07 64 77.299 0.833
Page | 347
Jan-08 75 77.855 0.965
Feb-08 73 78.492 0.932
Mar-08 68 79.281 0.861
Apr-08 74 80.009 0.927
May-08 70 80.555 0.872
Jun-08 77 81.056 0.951
Jul-08 83
Aug-08 100
Sep-08 127
Oct-08 83
Nov-08 74
Dec-08 70
Figure 5.30: Forecasting model for seasonality & trend for hotdog sausage.
From It can clearly be seen in figure 5.30 above, that the trend line passes
through points D10* and D30*. The values that correspond to D10* and D30* are
69 and 81, respectively.
Hotdog Sausage
Page | 348
Figure 5.31: Forecasted demand for hotdog sausage.
After applying Holt's Method, the following results were obtained:
Mean Absolute Deviation = 0.084
Mean Square Error =0.017
Hotdog Sausage
Page | 349
16. Frankfurter Sausage
Table 5.16: The data of Avg. MA (12) and Ct for frankfurter sausage.
Time Demand (Dt) Avg.MA(12) Index (Ct)
Jan-06 103
Feb-06 100
Mar-06 94
Apr-06 102
May-06 96
Jun-06 106
Jul-06 114 111.929 1.016
Aug-06 138 112.777 1.222
Sep-06 174 113.585 1.531
Oct-06 114 114.399 0.994
Nov-06 102 115.224 0.883
Dec-06 96 116.066 0.830
Jan-07 113 116.980 0.969
Feb-07 110 118.028 0.935
Mar-07 103 119.327 0.863
Apr-07 112 120.526 0.928
May-07 106 121.424 0.873
Jun-07 116 122.249 0.951
Jul-07 125 123.079 1.016
Aug-07 152 123.927 1.223
Sep-07 191 124.735 1.534
Oct-07 125 125.549 0.996
Nov-07 112 126.374 0.885
Dec-07 106 127.216 0.833
Page | 350
Jan-08 124 128.130 0.965
Feb-08 120 129.178 0.932
Mar-08 112 130.477 0.861
Apr-08 122 131.676 0.927
May-08 116 132.574 0.872
Jun-08 127 133.399 0.951
Jul-08 136
Aug-08 165
Sep-08 209
Oct-08 136
Nov-08 122
Dec-08 116
Figure 5.32: Forecasting model for seasonality & trend for frankfurter sausage.
It can clearly be seen in figure 5.32 above, that the trend line passes through
points D10* and D30*. The values that correspond to D10* and D30* are 114 and
133, respectively.
Frankfurter Sausage
Page | 351
Figure 5.33: Forecasted demand for frankfurter sausage.
After applying Holt's Method, the following results were obtained:
Mean Absolute Deviation = 0.139
Mean Square Error = 0.047
Frankfurter Sausage
Page | 352
17. Cocktail Sausage
Table 5.17: The data of Avg. MA (12) and Ct for cocktail sausage.
Time Demand (Dt) Avg.MA(12) Index (Ct)
Jan-06 283
Feb-06 276
Mar-06 257
Apr-06 279
May-06 265
Jun-06 290
Jul-06 312 307.429 1.016
Aug-06 379 309.757 1.222
Sep-06 478 311.977 1.531
Oct-06 312 314.213 0.994
Nov-06 279 316.479 0.883
Dec-06 265 318.791 0.830
Jan-07 311 321.302 0.969
Feb-07 303 324.181 0.935
Mar-07 283 327.749 0.863
Apr-07 307 331.041 0.928
May-07 291 333.506 0.873
Jun-07 319 335.773 0.951
Jul-07 344 338.054 1.016
Aug-07 416 340.382 1.223
Sep-07 526 342.602 1.534
Oct-07 344 344.838 0.996
Nov-07 307 347.104 0.885
Dec-07 291 349.416 0.833
Page | 353
Jan-08 340 351.927 0.965
Feb-08 331 354.806 0.932
Mar-08 309 358.374 0.861
Apr-08 335 361.666 0.927
May-08 318 364.131 0.872
Jun-08 348 366.398 0.951
Jul-08 375
Aug-08 454
Sep-08 573
Oct-08 375
Nov-08 335
Dec-08 318
Figure 5.34: Forecasting model for seasonality & trend for cocktail sausage.
It can clearly be seen in figure 5.34 above, that the trend line passes through
points D10* and D30*. The values that correspond to D10* and D30* are 314 and
366, respectively.
Cocktail Sausage
Page | 354
Figure 5.35: Forecasted demand for cocktail sausage.
After applying Holt's Method, the following results were obtained:
Mean Absolute Deviation = 0.380
Mean Square Error = 0.355
Cocktail Sausage
Page | 355
18. Lima Beans
Table 5.18: The data of Avg. MA (12) and Ct for lima beans.
Time Demand (Dt) Avg.MA(12) Index (Ct)
Jan-06 253
Feb-06 246
Mar-06 230
Apr-06 249
May-06 236
Jun-06 259
Jul-06 279 274.386 1.016
Aug-06 338 276.463 1.222
Sep-06 426 278.445 1.531
Oct-06 279 280.440 0.994
Nov-06 249 282.463 0.883
Dec-06 236 284.526 0.830
Jan-07 278 286.768 0.969
Feb-07 271 289.337 0.935
Mar-07 253 292.521 0.863
Apr-07 274 295.460 0.928
May-07 260 297.660 0.873
Jun-07 285 299.683 0.951
Jul-07 307 301.719 1.016
Aug-07 372 303.796 1.223
Sep-07 469 305.778 1.534
Oct-07 307 307.773 0.996
Nov-07 274 309.796 0.885
Dec-07 260 311.860 0.833
Page | 356
Jan-08 303 314.101 0.965
Feb-08 295 316.670 0.932
Mar-08 276 319.855 0.861
Apr-08 299 322.793 0.927
May-08 283 324.993 0.872
Jun-08 311 327.016 0.951
Jul-08 335
Aug-08 405
Sep-08 512
Oct-08 335
Nov-08 299
Dec-08 283
Figure 5.36: Forecasting model for seasonality & trend for lima beans.
It can clearly be seen in figure 5.36 above, that the trend line passes through
points D10* and D30*. The values that correspond to D10* and D30* are 280 and
327, respectively.
Lima Beans
Page | 357
Figure 5.37: Forecasted demand for lima beans.
After applying Holt's Method, the following results were obtained:
Mean Absolute Deviation = 0.340
Mean Square Error = 0.283
Lima Beans
Page | 358
19. Mixed Vegetables
Table 5.19: The data of Avg. MA (12) and Ct for mixed vegetables.
Time Demand (Dt) Avg.MA(12) Index (Ct)
Jan-06 941
Feb-06 917
Mar-06 855
Apr-06 929
May-06 880
Jun-06 965
Jul-06 1039 1022.254 1.016
Aug-06 1259 1029.993 1.222
Sep-06 1589 1037.376 1.531
Oct-06 1039 1044.810 0.994
Nov-06 929 1052.346 0.883
Dec-06 880 1060.034 0.830
Jan-07 1035 1068.384 0.969
Feb-07 1008 1077.957 0.935
Mar-07 941 1089.820 0.863
Apr-07 1022 1100.767 0.928
May-07 968 1108.965 0.873
Jun-07 1062 1116.501 0.951
Jul-07 1143 1124.087 1.016
Aug-07 1385 1131.827 1.223
Sep-07 1747 1139.210 1.534
Oct-07 1143 1146.643 0.996
Nov-07 1022 1154.179 0.885
Dec-07 968 1161.867 0.833
Page | 359
Jan-08 1129 1170.218 0.965
Feb-08 1100 1179.790 0.932
Mar-08 1026 1191.654 0.861
Apr-08 1114 1202.601 0.927
May-08 1056 1210.798 0.872
Jun-08 1158 1218.334 0.951
Jul-08 1246
Aug-08 1510
Sep-08 1906
Oct-08 1246
Nov-08 1114
Dec-08 1056
Figure 5.38: Forecasting model for seasonality & trend for mixed vegetables.
It can clearly be seen in figure 5.38 above, that the trend line passes through
points D10* and D30*. The values that correspond to D10* and D30* are 1043
and 1218, respectively.
Mixed Vegetables
Page | 360
Figure 5.39 Forecasted demand for mixed vegetables.
After applying Holt's Method, the following results were obtained:
Mean Absolute Deviation = 1.265
Mean Square Error = 3.926
Mixed Vegetables
Page | 361
20. Mushroom Pieces and Stems
Table 5.20: The data of Avg. MA (12) and Ct for mushroom pieces and stems.
Time Demand (Dt) Avg.MA(12) Index (Ct)
Jan-06 488
Feb-06 475
Mar-06 444
Apr-06 482
May-06 456
Jun-06 501
Jul-06 539 530.200 1.016
Aug-06 653 534.214 1.222
Sep-06 824 538.043 1.531
Oct-06 539 541.899 0.994
Nov-06 482 545.807 0.883
Dec-06 456 549.795 0.830
Jan-07 537 554.126 0.969
Feb-07 523 559.091 0.935
Mar-07 488 565.244 0.863
Apr-07 530 570.922 0.928
May-07 502 575.174 0.873
Jun-07 551 579.082 0.951
Jul-07 593 583.017 1.016
Aug-07 718 587.031 1.223
Sep-07 906 590.860 1.534
Oct-07 593 594.716 0.996
Nov-07 530 598.624 0.885
Page | 362
Dec-07 502 602.612 0.833
Jan-08 586 606.943 0.965
Feb-08 570 611.907 0.932
Mar-08 532 618.061 0.861
Apr-08 578 623.738 0.927
May-08 548 627.990 0.872
Jun-08 601 631.899 0.951
Jul-08 646
Aug-08 783
Sep-08 989
Oct-08 646
Nov-08 578
Dec-08 548
Figure 5.40: Forecasting model for seasonality & trend for mushroom pieces and stems.
It can clearly be seen in figure 5.40 above, that the trend line passes through
points D10* and D30*. The values that correspond to D10* and D30* are 541 and
632, respectively.
Mushroom Pieces and Stems
Page | 363
Figure 5.41: Forecasted demand for mushroom pieces and stems.
After applying Holt's Method, the following results were obtained:
Mean Absolute Deviation = 0.656
Mean Square Error = 1.056
Mushroom Pieces and Stems
Page | 364
21. Whole Mushrooms
Table 5.21: The data of Avg. MA (12) and Ct for whole mushrooms.
Time Demand (Dt) Avg.MA(12) Index (Ct)
Jan-06 628
Feb-06 612
Mar-06 571
Apr-06 620
May-06 587
Jun-06 644
Jul-06 693 682.200 1.016
Aug-06 840 687.365 1.222
Sep-06 1060 692.292 1.531
Oct-06 693 697.253 0.994
Nov-06 620 702.281 0.883
Dec-06 587 707.412 0.830
Jan-07 691 712.985 0.969
Feb-07 673 719.373 0.935
Mar-07 628 727.290 0.863
Apr-07 682 734.596 0.928
May-07 646 740.066 0.873
Jun-07 709 745.095 0.951
Jul-07 762 750.158 1.016
Aug-07 924 755.323 1.223
Sep-07 1166 760.250 1.534
Oct-07 762 765.211 0.996
Nov-07 682 770.240 0.885
Dec-07 646 775.371 0.833
Page | 365
Jan-08 754 780.943 0.965
Feb-08 734 787.331 0.932
Mar-08 685 795.248 0.861
Apr-08 744 802.554 0.927
May-08 705 808.025 0.872
Jun-08 773 813.054 0.951
Jul-08 832
Aug-08 1008
Sep-08 1272
Oct-08 832
Nov-08 744
Dec-08 705
Figure 5.42: Forecasting model for seasonality & trend for whole mushrooms.
It can clearly be seen in figure 5.42 above, that the trend line passes through
points D10* and D30*. The values that correspond to D10* and D30* are 696 and
813, respectively.
Whole Mushrooms
Page | 366
Figure 5.43: Forecasted demand for whole mushrooms.
After applying Holt's Method, the following results were obtained:
Mean Absolute Deviation = 0.844
Mean Square Error = 1.748
Whole Mushrooms
Page | 367
22. Peas and Carrots
Table 5.22:The data of Avg. MA (12) and Ct for peas and carrots .
Time Demand (Dt) Avg.MA(12) Index (Ct)
Jan-06 137
Feb-06 134
Mar-06 125
Apr-06 135
May-06 128
Jun-06 141
Jul-06 151 148.904 1.016
Aug-06 183 150.032 1.222
Sep-06 231 151.107 1.531
Oct-06 151 152.190 0.994
Nov-06 135 153.288 0.883
Dec-06 128 154.408 0.830
Jan-07 151 155.624 0.969
Feb-07 147 157.018 0.935
Mar-07 137 158.746 0.863
Apr-07 149 160.341 0.928
May-07 141 161.535 0.873
Jun-07 155 162.633 0.951
Jul-07 166 163.738 1.016
Aug-07 202 164.865 1.223
Sep-07 255 165.941 1.534
Oct-07 166 167.023 0.996
Nov-07 149 168.121 0.885
Dec-07 141 169.241 0.833
Page | 368
Jan-08 164 170.457 0.965
Feb-08 160 171.852 0.932
Mar-08 150 173.580 0.861
Apr-08 162 175.174 0.927
May-08 154 176.368 0.872
Jun-08 169 177.466 0.951
Jul-08 182
Aug-08 220
Sep-08 278
Oct-08 182
Nov-08 162
Dec-08 154
Figure 5.44: Forecasting model for seasonality & trend for peas and carrots.
It can clearly be seen in figure 5.44 above, that the trend line passes through
points D10* and D30*. The values that correspond to D10* and D30* are 152 and
177, respectively.
Peas and carrots
Page | 369
Figure 5.45: Forecasted demand for peas and carrots.
After applying Holt's Method, the following results were obtained:
Mean Absolute Deviation = 0.184
Mean Square Error = 0.083
Peas and carrots
Page | 370
23. Peeled Fava Beans with Chilli
Table 5.23: The data of Avg. MA (12) and Ct for peeled fava with chilli .
Time Demand (Dt) Avg.MA(12) Index (Ct)
Jan-06 617
Feb-06 601
Mar-06 561
Apr-06 609
May-06 577
Jun-06 633
Jul-06 682 670.739 1.016
Aug-06 826 675.817 1.222
Sep-06 1042 680.661 1.531
Oct-06 682 685.539 0.994
Nov-06 609 690.483 0.883
Dec-06 577 695.528 0.830
Jan-07 679 701.007 0.969
Feb-07 661 707.288 0.935
Mar-07 617 715.072 0.863
Apr-07 670 722.255 0.928
May-07 635 727.634 0.873
Jun-07 697 732.578 0.951
Jul-07 750 737.556 1.016
Aug-07 908 742.634 1.223
Sep-07 1147 747.478 1.534
Oct-07 750 752.356 0.996
Nov-07 670 757.300 0.885
Dec-07 635 762.345 0.833
Page | 371
Jan-08 741 767.824 0.965
Feb-08 722 774.104 0.932
Mar-08 674 781.889 0.861
Apr-08 731 789.071 0.927
May-08 693 794.450 0.872
Jun-08 760 799.395 0.951
Jul-08 818
Aug-08 991
Sep-08 1251
Oct-08 818
Nov-08 731
Dec-08 693
Figure 5.46: Forecasting model for seasonality & trend for peeled fava beans with chili.
It can clearly be seen in figure 5.46 above, that the trend line passes through
points D10* and D30*. The values that correspond to D10* and D30* are 685 and
799, respectively
Peeled Fava Beans with Chili
Page | 372
Figure 5.47: Forecasted demand for peeled fava beans with chili.
After applying Holt's Method, the following results were obtained:
Mean Absolute Deviation = 0.830
Mean Square Error = 1.690
Peeled Fava Beans with Chilli
Page | 373
24. Red Kidney Beans
Table 5.24: The data of Avg. MA (12) and Ct for red kidney beans.
Time Demand (Dt) Avg.MA(12) Index (Ct)
Jan-06 2067
Feb-06 2013
Mar-06 1879
Apr-06 2040
May-06 1932
Jun-06 2120
Jul-06 2281 2245.111 1.016
Aug-06 2764 2262.108 1.222
Sep-06 3489 2278.323 1.531
Oct-06 2281 2294.649 0.994
Nov-06 2040 2311.199 0.883
Dec-06 1932 2328.085 0.830
Jan-07 2273 2346.424 0.969
Feb-07 2214 2367.447 0.935
Mar-07 2067 2393.502 0.863
Apr-07 2244 2417.545 0.928
May-07 2126 2435.549 0.873
Jun-07 2332 2452.099 0.951
Jul-07 2509 2468.761 1.016
Aug-07 3041 2485.758 1.223
Sep-07 3838 2501.973 1.534
Oct-07 2509 2518.299 0.996
Nov-07 2244 2534.849 0.885
Dec-07 2126 2551.735 0.833
Page | 374
Jan-08 2480 2570.074 0.965
Feb-08 2415 2591.097 0.932
Mar-08 2254 2617.152 0.861
Apr-08 2448 2641.195 0.927
May-08 2319 2659.199 0.872
Jun-08 2544 2675.749 0.951
Jul-08 2737
Aug-08 3317
Sep-08 4187
Oct-08 2737
Nov-08 2448
Dec-08 2319
Figure 5.48: Forecasting model for seasonality & trend for red kidney beans.
It can clearly be seen in figure 5.48 above, that the trend line passes through
points D10* and D30*. The values that correspond to D10* and D30* are 2291
and 2674, respectively.
Red Kidney Beans
Page | 375
Figure 5.49: Forecasted demand for red kidney beans.
After applying Holt's Method, the following results were obtained:
Mean Absolute Deviation = 2.778
Mean Square Error = 18.937
Red Kidney Beans
Page | 376
25. Red Kidney Beans with Chili
Table 5.25: The data of Avg. MA (12) and Ct for red kidney beans with chili.
Time Demand (Dt) Avg.MA(12) Index (Ct)
Jan-06 58
Feb-06 56
Mar-06 53
Apr-06 57
May-06 54
Jun-06 59
Jul-06 64 62.741 1.016
Aug-06 77 63.216 1.222
Sep-06 98 63.669 1.531
Oct-06 64 64.125 0.994
Nov-06 57 64.588 0.883
Dec-06 54 65.059 0.830
Jan-07 64 65.572 0.969
Feb-07 62 66.159 0.935
Mar-07 58 66.888 0.863
Apr-07 63 67.559 0.928
May-07 59 68.063 0.873
Jun-07 65 68.525 0.951
Jul-07 70 68.991 1.016
Aug-07 85 69.466 1.223
Sep-07 107 69.919 1.534
Oct-07 70 70.375 0.996
Nov-07 63 70.838 0.885
Dec-07 59 71.309 0.833
Page | 377
Jan-08 69 71.822 0.965
Feb-08 68 72.409 0.932
Mar-08 63 73.138 0.861
Apr-08 68 73.809 0.927
May-08 65 74.313 0.872
Jun-08 71 74.775 0.951
Jul-08 77
Aug-08 93
Sep-08 117
Oct-08 77
Nov-08 68
Dec-08 65
Figure 5.50: Forecasting model for seasonality & trend for red kidney beans with chili.
It can clearly be seen in figure 5.50 above, that the trend line passes through
points D10* and D30*. The values that correspond to D10* and D30* are 64 and
75, respectively.
Red Kidney Beans with Chili
Page | 378
Figure 5.51: Forecasted demand for red kidney beans with chili.
After applying Holt's Method, the following results were obtained:
Mean Absolute Deviation = 0.078
Mean Square Error = 0.015
Red Kidney Beans with Chili
Page | 379
26. Sweet Corn
Table 5.26: The data of Avg. MA (12) and Ct for sweet corn.
Demand (Dt) Avg.MA(12) Index (Ct)
1688
1644
1534
1666
1578
1732
1863 1833.532 1.016
2258 1847.413 1.222
2849 1860.656 1.531
1863 1873.989 0.994
1666 1887.505 0.883
1578 1901.295 0.830
1856 1916.272 0.969
1808 1933.442 0.935
1688 1954.720 0.863
1832 1974.355 0.928
1736 1989.059 0.873
1905 2002.575 0.951
2049 2016.182 1.016
2483 2030.063 1.223
3134 2043.306 1.534
2049 2056.639 0.996
1832 2070.155 0.885
1736 2083.945 0.833
Page | 380
2025 2098.922 0.965
1973 2116.092 0.932
1841 2137.370 0.861
1999 2157.005 0.927
1894 2171.709 0.872
2078 2185.225 0.951
2236
2709
3419
2236
1999
1894
Figure 5.52: Forecasting model for seasonality & trend for sweet corn.
It can clearly be seen in figure 5.52 above, that the trend line passes through
points D10* and D30*. The values that correspond to D10* and D30* are 1871
and 2184, respectively
Sweet Corn
Page | 381
Figure 5.53: Forecasted demand for sweet corn.
After applying Holt's Method, the following results were obtained:
Mean Absolute Deviation = 2.269
Mean Square Error = 12.630
Sweet Corn
Page | 382
27. White Beans
Table 5.27: The data of Avg. MA (12) and Ct for white beans.
Time Demand (Dt) Avg.MA(12) Index (Ct)
Jan-06 346
Feb-06 337
Mar-06 314
Apr-06 341
May-06 323
Jun-06 355
Jul-06 382 374.333 1.020
Aug-06 463 374.333 1.236
Sep-06 584 374.333 1.560
Oct-06 382 374.333 1.020
Nov-06 341 374.333 0.912
Dec-06 323 374.333 0.864
Jan-07 346 374.333 0.924
Feb-07 337 374.333 0.900
Mar-07 314 374.333 0.840
Apr-07 341 374.333 0.912
May-07 323 374.333 0.864
Jun-07 355 374.333 0.948
Jul-07 382 377.216 1.012
Aug-07 463 382.906 1.208
Sep-07 584 388.333 1.504
Oct-07 382 393.799 0.970
Nov-07 341 399.339 0.855
Dec-07 323 404.991 0.799
Page | 383
Jan-08 415 411.130 1.010
Feb-08 404 418.168 0.967
Mar-08 377 426.890 0.884
Apr-08 410 434.938 0.942
May-08 388 440.965 0.880
Jun-08 426 446.505 0.954
Jul-08 458
Aug-08 555
Sep-08 701
Oct-08 458
Nov-08 410
Dec-08 388
Figure 5.54: Forecasting model for seasonality & trend for white beans.
It can clearly be seen in figure 5.54 above, that the trend line passes through
points D10* and D30*. The values that correspond to D10* and D30* are 384 and
448, respectively
White Beans
Page | 384
Figure 5.55: Forecasted demand for white beans.
After applying Holt's Method, the following results were obtained:
Mean Absolute Deviation = 4.607
Mean Square Error = 119.103
White Beans
Page | 385
Five Year Forecasts
The following charts show the forecasted demands for the next five years for
each type of product.
Baked Beans
Figure 5.56: Forecasted demand for baked beans.
2. Black Eye Beans
Figure 5.57: Forecasted demand for black eye beans.
Baked Beans
Black Eye Beans
Page | 386
3. Broad Beans
Figure 5.58: Forecasted demand for broad beans.
4. Chick Peas
Figure 5.59: Forecasted demand for chick peas.
Broad Beans
Chick Peas
Page | 387
5. Chick Peas 10mm
Figure 5.60: Forecasted demand for chick peas 10mm.
6. Chick Peas with Chili
Figure 5.61: Forecasted demand for chick peas with chili.
Chick Peas with Chili
Chick Peas 10mm
Page | 388
7. Fava Beans
Figure 5.62: Forecasted demand for fava beans.
8. Fava Beans with Chili
Figure 5.63: Forecasted demand for fava beans with chili.
Fava Beans
Fava Beans with Chili
Page | 389
9. Egyptian Foul Medames
Figure 5.64: Forecasted demand for Egyptian foul medames.
10. Saudi Foul Medames
Figure 5.65: Forecasted demand for Saudi foul medames.
Egyptian Foul Medames
Saudi Foul Medames
Page | 390
11. Lebanese Fould Medames
Figure 5.66: Forecasted demand for Lebanese foul medames.
12. Green Peas
Figure 5.67: Forecasted demand for Green Peas.
Lebanese Foul Medames
Green Peas
Page | 391
13. Hummus Tahineh - Chick Peas 7mm
Figure 5.68: Forecasted demand for hummus tahineh – chick peas 7mm.
14. Hummus Tahineh with Garlic
Figure 5.69: Forecasted demand for hummus tahineh with garlic.
Hummus Tahineh – Chick Peas
7mm
Hummus Tahineh with Garlic
Page | 392
15. Hotdog Sausage
Figure 5.70: Forecasted demand for hotdog sausage.
16. Frankfurter Sausage
Figure 5.71: Forecasted demand for frankfurter sausage.
Hotdog Sausage
Frankfurter Sausage
Page | 393
17. Cocktail Sausage
Figure 5.72: Forecasted demand for cocktail sausage.
18. Lima Beans
Figure 5.73: Forecasted demand for lima beans.
Cocktail Sausage
Lima Beans
Page | 394
19. Mixed Vegetables
Figure 5.74: Forecasted demand for mixed vegetables.
20. Mushroom Pieces and Stems
Figure 5.75: Forecasted demand for mushroom pieces and stems.
Mixed Vegetables
Mushroom Pieces and Stems
Page | 395
21. Whole Mushrooms
Figure 5.76: Forecasted demand for whole mushrooms.
22. Peas and carrots
Figure 5.77: Forecasted demand for peas and carrots.
Whole Mushrooms
Peas and Carrots
Page | 396
23. Peeled Fava Beans with Chili
Figure 5.78: Forecasted demand for peeled fava beans with chili.
24. Red Kidney Beans
Figure 5.79: Forecasted demand for red kidney beans.
Peeled Fava Beans with Chili
Red Kidney Beans
Page | 397
25. Red Kidney Beans with Chili
Figure 5.80: Forecasted demand for red kidney beans with chili.
26. Sweet Corn
Figure 5.81: Forecasted demand for sweet corn.
Red Kidney Beans with Chili
Sweet Corn
Page | 398
27. White Beans
Figure 5.82: Forecasted demand for white beans.
White Beans
Page | 399
Economic Order Quantity (EOQ) for Production Planning
The EOQ is essentially an accounting formula that determines the point
at which the combination of order costs and inventory carrying costs are the
least. The result is the most cost effective quantity to order. In purchasing,
this is known as the order quantity, whilst in manufacturing it is known as the
production lot size.
While EOQ may not apply to every inventory situation, most
organizations will find it beneficial in at least some aspect of their operation.
Parameters:
Q = Order quantity.
Q * = Optimal order quantity.
D = Annual demand quantity of the product (average demand for three years
was used).
P = Purchase cost per unit.
C = A = Fixed cost per order.
H= ht = total annual holding cost per unit (also known as carrying cost)/
Equations:
TC = H Q/2 + A D/Q
TC*= √ (2ADH)
Q* = √ (2AD/H)
Page | 400
Table 5.28: The current and optimal quantities for the can plant.
The optimal quantities (Q*) for each item of the can plant’s raw materials are
less than the current quantities in the system.
Table 5.29: The difference between the current total cost and the optimal total cost of the can plant.
After applying the EOQ model to the can plant raw materials, it was
found that the optimal quantity saves a total of 143.58 KD/year.
Item Unit Q Q*
Labels CTN 2000 1474
Cooper Wire K.G 4250 812
Lids CTN 2000 1266
Tin-sheet CTN 1000 847
Cartoon CTN 1500 1030
Shrink Film PCS 30000 26857
Glue K.G 6751 3071
Lacquer K.G 6179 1593
Item Unit TC TC* TC-TC*
Labels CTN 112 106 6
Cooper Wire K.G 124 45 79
Lids CTN 20 18 2
Tin-sheet CTN 8 7 0
Cartoon CTN 10 9 1
Shrink Film PCS 8 7 0
Glue K.G 60 44 16
Lacquer K.G 75 36 39
Sum 143.58
Page | 401
Table 5.30: The current and optimal quantities for the spices.
The optimal quantities (Q*) for each item of the spices raw material are
less than the current quantities in the system.
Item Unit Q Q*
Tomato Pasta K.G 6000 3537
Lemon Juice Ltr 500 339
Green Color K.G 1000 405
Edta K.G 1000 775
Citric Acid K.G 3000 1960
Camon Powder K.G 1000 596
Chick Peas Powder K.G 2000 1695
Spices K.G 1000 548
Whole Red Chili K.G 500 381
Onion Powder K.G 2000 706
Powder Red Chili K.G 1200 1014
Page | 402
Table 5.31: The difference between the current total cost and the optimal total cost of the spices.
After applying the EOQ model to the spices, it was found that the optimal
quantities would save a total of 46.1 KD/year.
Item Unit TC TC* TC-TC*
Tomato Pasta K.G 40.0 34.49 5.51
Lemon Juice Ltr 16.0 14.75 1.25
Green Color K.G 48.0 33.37 14.63
Edta K.G 12.0 11.62 0.38
Citric Acid K.G 28.0 25.51 2.49
Camon Powder K.G 16.0 13.42 2.58
Chick Peas Powder K.G 17.0 16.52 0.48
Spices K.G 20.0 16.43 3.57
Whole Red Chili K.G 10.0 9.44 0.56
Onion Powder K.G 38.0 23.81 14.14
Powder Red Chili K.G 15.0 14.44 0.56
Sum= 46.1
Page | 403
Table 5.32: The current and optimal quantities for the beans.
The optimal quantities (Q*) for each item of the beans raw material are
less than the current quantities in the system.
Item Unit Q Q*
Black Eye Beans K.G 10553 2096
Broad Beans K.G 132234 17287
Chick Peas 8mm K.G 101930 18899
Chick Peas 7mm K.G 27500 4633
Chick Peas 10mm K.G 46309 6619
Whole Mushrooms K.G 18750 2972
Mushroom Stems and Pieces K.G 18750 2412
Green Peas K.G 61291 2419
Mixed Vegetables K.G 25811 2013
Navy Beans K.G 53905 5228
White Beans K.G 18766 2499
Peeled Fava Beans K.G 65000 11185
Fava Beans K.G 71153 7396
Red Kidney K.G 33869 2070
Sweet Corn K.G 33572 5806
Lima Beans K.G 19184 4229
Carrots K.G 12000 4883
Page | 404
Table 5.33: The difference between the current total cost and the optimal total cost of the beans.
Item Unit TC TC* TC-TC*
Black Eye Beans K.G 75.44 42.44 33.01
Broad Beans K.G 813.74 311.17 502.58
Chick Peas 8mm K.G 643.12 340.18 302.93
Chick Peas 7mm K.G 243.70 118.15 125.56
Chick Peas 10mm K.G 322.16 134.04 188.12
Whole Mushrooms K.G 291.85 133.72 158.12
Mushroom Stems and Pieces K.G 288.23 108.53 179.70
Green Peas K.G 261.10 30.84 230.26
Mixed Vegetables K.G 240.93 55.85 185.08
Navy Beans K.G 116.02 33.29 82.74
White Beans K.G 269.71 104.95 164.76
Peeled Foul K.G 594.01 293.61 300.41
Fava Beans K.G 397.68 122.04 275.65
Red Kidney K.G 263.42 48.03 215.39
Sweet Corn K.G 289.39 143.69 145.71
Lima Beans K.G 34.95 21.54 13.41
Carrots K.G 13.96 13.65 0.31
Sum= 3101.73
After applying the EOQ model to the beans, the optimal quantity (Q*) for each
was found to save a total of 3101.73 KD/year.
Page | 405
Economic Production Quantity (EPQ) for Production Planning
The EPQ is a method used to determine the optimal procedure for
producing multiple items in one system, to minimize the holding and the setup
costs. This procedure helps to avoid stock outs in a production cycle.
Parameters:
If (n) products are to be produced on a single machine:
λi = Demand rate for product i.
Pi = Production rate for product i.
ht,i = Total holding cost per unit time of product i.
Ki = Cost of setting up the production line to produce product i.
K: Setup Cost = setup time *production rate*selling price
The setup time for the 28 products is equal to 30 minutes each. Four workers
conduct the setup but the cost of their labor was not considered because it is
already considered in the selling price of each can.
Assumptions required for satisfying the demand with current capacity:
Feasibility: ∑λi/Pi ≤ 1.
Utilization of the rotation cycle so that in each cycle, there is exactly one setup
for each product.
The products are produced in the same sequence in each production cycle.
T = cycle time = √ ((2 ∑ Ki) / (hi * λi))
The setup time for each production type is not significant which will ensure
that T ≥ (∑Si / 1- ∑ (λi/Pi)) = Tmin
Page | 406
The production rate
160 cans/min which is the maximum production rate
The factory works 26 days per month and 12 hours per day to meet the
customers demand which includes the overtime shifts.
Table 5.34: Total holding cost.
Capital Cost (h0 = rv)
Storage (h1)
Insurance (h2)
Security (h3)
Total holding Cost (hT)
0.00219 0.005 0.003 0.004 0.01419
0.00208 0.005 0.003 0.004 0.01408
0.00169 0.005 0.003 0.004 0.01369
0.00141 0.005 0.003 0.004 0.01341
0.00186 0.005 0.003 0.004 0.01386
0.00242 0.005 0.003 0.004 0.01442
0.00146 0.005 0.003 0.004 0.01346
0.00169 0.005 0.003 0.004 0.01369
0.00276 0.005 0.003 0.004 0.01476
0.00219 0.005 0.003 0.004 0.01419
0.00264 0.005 0.003 0.004 0.01464
0.00129 0.005 0.003 0.004 0.01329
0.00242 0.005 0.003 0.004 0.01442
0.00283 0.005 0.003 0.004 0.01483
0.00416 0.005 0.003 0.004 0.01616
0.00630 0.005 0.003 0.004 0.01830
0.00450 0.005 0.003 0.004 0.01650
0.00495 0.005 0.003 0.004 0.01695
0.00276 0.005 0.003 0.004 0.01476
0.00585 0.005 0.003 0.004 0.01785
Page | 407
0.00585 0.005 0.003 0.004 0.01785
0.00321 0.005 0.003 0.004 0.01521
0.00203 0.005 0.003 0.004 0.01403
0.00225 0.005 0.003 0.004 0.01425
0.00180 0.005 0.003 0.004 0.01380
0.00327 0.005 0.003 0.004 0.01527
0.00420 0.005 0.003 0.004 0.01620
The set up cost (K) for all products is equal to 30
r is equal to 0.015 for all products
Cycle time (T) is equal to 1.0524 for all products
Tmin is equal to 0.8844 for all products
Page | 408
Table 5.35: shows the EPQ Model for the current demand in CTN. P
rod
uc
t
Dem
an
d (
λ)
P/y
ea
r
∆
h'=
∆h
T
λh
'
T
Tm
in
EP
Q (
Q*)
TV
C
λ /
P
Q
TV
C
Tj
TV
C(Q
) -
TV
C(Q
*)
Q*-
Q
Tj
(Hrs
)
Tj
(Min
)
(Q*)
(Q)
1 13,154 166,400 0.9209 0.0131 171.95 0.91 0.3931 11,975 111 0.0791 3,500 136 0.072 24 8,475 29.94 1796
2 1,866 166,400 0.9888 0.0139 25.98 0.91 0.3931 1,698 45 0.0112 1,000 63 0.0102 18 698 4.25 255
3 18,660 166,400 0.8879 0.0122 226.77 0.91 0.3931 16,987 136 0.1121 3,500 181 0.1021 45 13,487 42.47 2548
4 24,809 166,400 0.8509 0.0114 283.01 0.91 0.3931 22,584 162 0.1491 3,500 233 0.1357 71 19,084 56.46 3388
5 24,809 166,400 0.8509 0.0118 292.51 0.91 0.3931 22,584 166 0.1491 3,500 233 0.1357 67 19,084 56.46 3388
6 174 166,400 0.999 0.0144 2.5 0.91 0.3931 158 34 0.001 500 14 0.001 20- 342- 0.4 24
7 19,922 166,400 0.8803 0.0119 236.09 0.91 0.3931 18,135 140 0.1197 3,500 191 0.109 51 14,635 45.34 2720
8 252 166,400 0.9985 0.0137 3.45 0.91 0.3931 230 35 0.0015 500 19 0.0014 16- 270- 0.57 34
9 2,377 166,400 0.9857 0.0145 34.58 0.91 0.3931 2,164 49 0.0143 1,000 79 0.013 30 1,164 5.41 325
10 142 166,400 0.9991 0.0142 2.01 0.91 0.3931 129 34 0.0009 100 43 0.0008 9 29 0.32 19
11 761 166,400 0.9954 0.0146 11.1 0.91 0.3931 693 38 0.0046 500 49 0.0042 11 193 1.73 104
12 27,416 166,400 0.8352 0.0111 304.42 0.91 0.3931 24,958 172 0.1648 3,500 254 0.15 83 21,458 62.39 3744
13 14,796 166,400 0.9111 0.0131 194.37 0.91 0.3931 13,469 121 0.0889 3,500 150 0.0809 28 9,969 33.67 2020
14 102 166,400 0.9994 0.0148 1.51 0.91 0.3931 93 34 0.0006 100 31 0.0006 2- 7- 0.23 14
15 88 52,000 0.9983 0.0161 1.42 0.91 0.3931 80 34 0.0017 100 27 0.0015 6- 20- 0.64 39
16 145 52,000 0.9972 0.0182 2.65 0.91 0.3931 132 34 0.0028 100 44 0.0025 10 32 1.06 63
Page | 409
17 399 52,000 0.9923 0.0164 6.53 0.91 0.3931 363 36 0.0077 500 28 0.007 8- 137- 2.91 174
18 356 166,400 0.9979 0.0169 6.02 0.91 0.3931 324 36 0.0021 500 26 0.0019 10- 176- 0.81 49
19 1,327 166,400 0.992 0.0146 19.43 0.91 0.3931 1,208 42 0.008 1,000 47 0.0073 5 208 3.02 181
20 688 52,000 0.9868 0.0176 12.12 0.91 0.3931 626 38 0.0132 500 46 0.012 7 126 5.01 301
21 885 166,400 0.9947 0.0178 15.72 0.91 0.3931 806 40 0.0053 1,000 35 0.0048 5- 194- 2.01 121
22 193 166,400 0.9988 0.0152 2.94 0.91 0.3931 176 34 0.0012 500 15 0.0011 19- 324- 0.44 26
23 871 166,400 0.9948 0.014 12.14 0.91 0.3931 792 38 0.0052 1,000 33 0.0048 5- 208- 1.98 119
24 2,914 166,400 0.9825 0.014 40.79 0.91 0.3931 2,652 52 0.0175 2,000 58 0.0159 6 652 6.63 398
25 81 166,400 0.9995 0.0138 1.12 0.91 0.3931 74 33 0.0005 100 25 0.0004 8- 26- 0.19 11
26 2,380 166,400 0.9857 0.0151 35.82 0.91 0.3931 2,166 49 0.0143 1,000 79 0.013 30 1,166 5.42 325
27 493 166,400 0.997 0.0162 7.97 0.91 0.3931 449 37 0.003 500 34 0.0027 3- 51- 1.12 67
Sum 160,061 4,035,200 Since T>Tmin we will choose
T*=T 1,780
0.9793
2,174 394 Since
<1
Note: The product numbers are in the same order as they appear in the previous sections.
h’ represents the modified holding cost
Page | 410
Table 5.36: shows the EPQ Model for the forecasted demand of year 2009. D
es
cri
pti
on
Dem
an
d (
λ)
P/y
ea
r
∆
h'
λh
'
T
Tm
in
EP
Q (
Q*)
TV
C
λ /
P
Q
TV
C
Tj
TV
C(Q
) -
TV
C(Q
*)
(Q*)
(Q)
Q*-
Q
Tj
(Hrs
)
Tj
(Min
)
1 13,154 166,400 0.92 0.013 171.95 0.9103 0.393 11,975 111 0.0791 3,500 136 0.07 24 8,475 29.94 1796
2 1,866 166,400 0.99 0.014 25.98 0.9103 0.393 1,698 45 0.0112 1,000 63 0.01 18 698 4.25 255
3 18,660 166,400 0.89 0.012 226.77 0.9103 0.393 16,987 136 0.1121 3,500 181 0.1 45 13,487 42.47 2548
4 24,809 166,400 0.85 0.011 283.01 0.9103 0.393 22,584 162 0.1491 3,500 233 0.14 71 19,084 56.46 3388
5 24,809 166,400 0.85 0.012 292.51 0.9103 0.393 22,584 166 0.1491 3,500 233 0.14 67 19,084 56.46 3388
6 174 166,400 1 0.014 2.5 0.9103 0.393 158 34 0.001 500 14 0 20- 342- 0.4 24
7 19,922 166,400 0.88 0.012 236.09 0.9103 0.393 18,135 140 0.1197 3,500 191 0.11 51 14,635 45.34 2720
8 252 166,400 1 0.014 3.45 0.9103 0.393 230 35 0.0015 500 19 0 16- 270- 0.57 34
9 2,377 166,400 0.99 0.015 34.58 0.9103 0.393 2,164 49 0.0143 1,000 79 0.01 30 1,164 5.41 325
10 142 166,400 1 0.014 2.01 0.9103 0.393 129 34 0.0009 100 43 0 9 29 0.32 19
11 761 166,400 1 0.015 11.1 0.9103 0.393 693 38 0.0046 500 49 0 11 193 1.73 104
12 27,416 166,400 0.84 0.011 304.42 0.9103 0.393 24,958 172 0.1648 3,500 254 0.15 83 21,458 62.39 3744
13 14,796 166,400 0.91 0.013 194.37 0.9103 0.393 13,469 121 0.0889 3,500 150 0.08 28 9,969 33.67 2020
14 102 166,400 1 0.015 1.51 0.9103 0.393 93 34 0.0006 100 31 0 2- 7- 0.23 14
15 88 52,000 1 0.016 1.42 0.9103 0.393 80 34 0.0017 100 27 0 6- 20- 0.64 39
16 145 52,000 1 0.018 2.65 0.9103 0.393 132 34 0.0028 100 44 0 10 32 1.06 63
17 399 52,000 0.99 0.016 6.53 0.9103 0.393 363 36 0.0077 500 28 0.01 8- 137- 2.91 174
18 356 166,400 1 0.017 6.02 0.9103 0.393 324 36 0.0021 500 26 0 10- 176- 0.81 49
19 1,327 166,400 0.99 0.015 19.43 0.9103 0.393 1,208 42 0.008 1,000 47 0.01 5 208 3.02 181
Page | 411
20 688 52,000 0.99 0.018 12.12 0.9103 0.393 626 38 0.0132 500 46 0.01 7 126 5.01 301
21 885 166,400 0.99 0.018 15.72 0.9103 0.393 806 40 0.0053 1,000 35 0 5- 194- 2.01 121
22 193 166,400 1 0.015 2.94 0.9103 0.393 176 34 0.0012 500 15 0 19- 324- 0.44 26
23 871 166,400 0.99 0.014 12.14 0.9103 0.393 792 38 0.0052 1,000 33 0 5- 208- 1.98 119
24 2,914 166,400 0.98 0.014 40.79 0.9103 0.393 2,652 52 0.0175 2,000 58 0.02 6 652 6.63 398
25 81 166,400 1 0.014 1.12 0.9103 0.393 74 33 0.0005 100 25 0 8- 26- 0.19 11
26 2,380 166,400 0.99 0.015 35.82 0.9103 0.393 2,166 49 0.0143 1,000 79 0.01 30 1,166 5.42 325
27 493 166,400 1 0.016 7.97 0.9103 0.393 449 37 0.003 500 34 0 3- 51- 1.12 67
Sum 160061 4035200 Since T>Tmin we will choose
T*=T 1,780
0.9793
2,174 394
Since <1
Page | 412
Service Level
The service level expresses the probability that a certain level of safety
stock will not lead to a stock-out. Naturally, when safety stocks are increased,
the service level increases as well. Three scenarios of service level
percentages were applied to the average demand of the raw materials in
order to evaluate the safety stock for each item. If the company applies one of
the scenarios, it will consider the safety stock and the total cost for it.
Assumptions:
The labels, cartons and the spices are locally provided, but the other raw
materials are provided from different countries.
The local raw materials have an average lead time of one week, while the
other materials have an average lead time of three months.
The three different service levels tested were 90%, 95%, and 99%.
All raw materials follow a normal distribution.
Parameters:
D: Average demand.
Q: Order quantity.
L: Lead time.
DL: Demand during lead time.
µ: Mean.
σ: Standard deviation.
Page | 413
Equations:
TC(SS) = TC(Q) + h (SS)
𝑧 =𝑥 − 𝜇
𝜎
The mean and the standard deviation are obtained from the Arena input
analyzer.
Page | 414
Description Average
Demand Unit mean stand.dev Q TVC(Q) h
SS
For
90%
TC (SS)
90%
SS
For
95%
TC (SS)
95%
SS
For
99%
TC (SS)
99%
Black Eye Beans 88936 K.G 1853 794 10553 75.44 0.02 2869 132.82 3154 138.53 3694 149.32
Broad Beans 768446 K.G 15328 7133 132234 813.74 0.018 24458 1253.99 27026 1300.20 31876 1387.51
Chick Peas 8mm 1168924 K.G 17262 16829 101930 643.12 0.018 38802 1341.56 44860 1450.60 56304 1656.58
Chick Peas 7mm 608219 K.G 12671 5429 27500 243.70 0.026 19620 753.82 21574 804.63 25265 900.60
Chick Peas 10mm 161314 K.G 3361 1440 46309 322.16 0.02 5204 426.24 5722 436.61 6702 456.19
Whole Mushrooms 132455 K.G 3356 7122 18750 291.85 0.045 12471 853.04 15035 968.41 19877 1186.33
Mushroom Stems and
Pieces 109071 K.G 2272 974 18750 288.23 0.045 3518 446.56 3869 462.33 4531 492.12
Green Peas 24859 K.G 7392 5614 61291 261.10 0.013 14577 450.60 16598 476.87 20415 526.49
Mixed Vegetables 37465 K.G 1873 1824 25811 241 0.028 4208 358.75 4865 377.14 6105 411.87
Navy Beans 24859 K.G 3760 9203 53905 116 0.006 15540 209.26 18853 229.14 25111 266.69
White Beans 37465 K.G 518 222 18766 270 0.042 802 303.41 882 306.76 1033 313.10
Peeled Foul 820995 K.G 780.5 334.5 65000 594 0.026 1209 625.44 1329 628.57 1557 634.48
Table 5.37: Service levels of can plant.
Page | 415
After applying the three scenarios for the can plant, it was found that the 90% service level gives the least total cost, which
is equal to 728.72 KD/year, according to the safety stock. And the total cost of the current order quantity is equal to 416
KD/year.
Fava Beans 128946 K.G 15709 8098 71153 398 0.017 26075 840.95 28990 890.51 34497 984.13
Red Kidney 24859 K.G 3096 7061 33869 263 0.023 12134 542.51 14676 600.97 19478 711.40
Sweet Corn 208549 K.G 4345 1861.5 33572 289 0.025 6727 457.58 7398 474.33 8663 505.98
Lima Beans 26026 K.G 542.3 232.5 19184 35 0.005 840 39.15 924 39.57 1082 40.36
Carrots 16664 K.G 347.3 149 12000 14 0.003 538 15.57 592 15.73 693 16.04
Sum = 5159.43 9051.23 9600.91 10639.20
Page | 416
Description
Average
Demand Unit mean stand.dev Q TVC(Q) h
SS
For
90%
TC (SS)
90%
SS For
95%
TC (SS)
95%
SS For
99%
TC (SS)
99%
Black Eye Beans 88936 K.G 1853 794 10553 75.44 0.02 2869 132.82 3154 138.53 3694 149.32
Broad Beans 768446 K.G 15328 7133 132234 813.74 0.018 24458 1253.99 27026 1300.20 31876 1387.51
Chick Peas 8mm 1168924 K.G 17262 16829 101930 643.12 0.018 38802 1341.56 44860 1450.60 56304 1656.58
Chick Peas 7mm 608219 K.G 12671 5429 27500 243.70 0.026 19620 753.82 21574 804.63 25265 900.60
Chick Peas 10mm 161314 K.G 3361 1440 46309 322.16 0.02 5204 426.24 5722 436.61 6702 456.19
Whole Mushrooms 132455 K.G 3356 7122 18750 291.85 0.045 12471 853.04 15035 968.41 19877 1186.33
Mushroom Stems and
Pieces 109071 K.G 2272 974 18750 288.23 0.045 3518 446.56 3869 462.33 4531 492.12
Green Peas 24859 K.G 7392 5614 61291 261.10 0.013 14577 450.60 16598 476.87 20415 526.49
Mixed Vegetables 37465 K.G 1873 1824 25811 241 0.028 4208 358.75 4865 377.14 6105 411.87
Navy Beans 24859 K.G 3760 9203 53905 116 0.006 15540 209.26 18853 229.14 25111 266.69
White Beans 37465 K.G 518 222 18766 270 0.042 802 303.41 882 306.76 1033 313.10
Peeled Foul 820995 K.G 780.5 334.5 65000 594 0.026 1209 625.44 1329 628.57 1557 634.48
Table 5.38: Service levels of beans.
Page | 417
After applying the three scenarios of the service levels for the beans, it was found that the 90% service level once again
gives the least total cost, which is equal to 9051.23 KD/year, according to the safety stock. And the total cost of the
current order quantity is equal to 5159.43 KD/year.
Fava Beans 128946 K.G 15709 8098 71153 398 0.017 26075 840.95 28990 890.51 34497 984.13
Red Kidney 24859 K.G 3096 7061 33869 263 0.023 12134 542.51 14676 600.97 19478 711.40
Sweet Corn 208549 K.G 4345 1861.5 33572 289 0.025 6727 457.58 7398 474.33 8663 505.98
Lima Beans 26026 K.G 542.3 232.5 19184 35 0.005 840 39.15 924 39.57 1082 40.36
Carrots 16664 K.G 347.3 149 12000 14 0.003 538 15.57 592 15.73 693 16.04
Sum = 5159.43 9051.23 9600.91 10639.20
Page | 418
5.3 Conclusion
Were the EOQ model applied for the last three years, it would have reduced
the cost of the company’s total inventory by 3,291 KD/year.
Were the EPQ model applied for the last three years, it would have reduced
the cost of the company’s total inventory by 12,744 KD/year
If the EPQ Model is applied for the year of 2009, the total inventory cost will
be reduced by 4,728 KD/year
From the three different scenarios, the 90% service level minimized the company’s
total inventory costs.
Table 5.38: Total costs for the different service levels.
Service Level TC(KD/yr)
Scenario 1: 90% 10,079
Scenario 2: 95% 10,664
Scenario 3: 99% 11,768
Page | 419
6. Supply Chain Management
Page | 420
Page | 421
6.1 Introduction
A supply chain consists of all parties involved directly or indirectly in fulfilling a
customer request. It is dynamic and involves the constant flow of information,
product and funds between different stages. The value a supply chain generates is
the difference between what the final product is worth to the customer and the effort
the supply chain expends in filling the customer request.
Figure
6.16: Supply chain stages.
The National Canned Food Production and Trading Co.'s supply chain can be
classified as a pull system when it comes to meeting demand from its overseas and
gulf region customers; it orders its raw materials from its suppliers and manufactures
to meet the required demand. For its local customers, based on historical demand
from co-ops, wholesalers and small stores, the company keeps an inventory to
satisfy it.
The company uses two modes of transportation to fulfill its customer's orders;
truck loads for transportation by land and ship containers by sea with a capacity of
2100 and 1650 cartons, respectively.
Page | 422
Typical Supply Chain and its Cycles
Figure 6.17: A typical supply chain.
Customer Order Cycle
Occurs at the customer/distributor interface and includes all processes directly
involved in receiving and filling customer's order.
Customer arrives.
Customer Places Order.
Order is fulfilled.
Order is received.
Manufacturer markets product
Customer places orders
Manufacturer receives orders
Manufacturer order supplies
Supplier fulfill the order
Manufacturer fulfill customer’s order
Manufacturer sends final products to the customer
Page | 423
Manufacturing Cycle
Occurs at the distributor/manufacturer interface; related to production
scheduling and includes all processes involved in replenishing inventory triggered
by:
Customer order.
Replenishment orders.
Forecast of customer demand.
Procurement Cycle
Occurs at the manufacturer/supplier interface and includes all processes
necessary to ensure that materials are available for all manufacturing to occur
according to schedule.
Figure 6.18 - Supply chain cycles.
Cycles are very useful when considering operational decisions because it specifies
the roles and responsibilities of each member of the chain. Push/Pull view is very
useful when considering the strategic decisions relating to supply chain design.
Page | 424
Warehouses' Locations
There are two warehouses which belong to the National Canned Food
Production and Trading Co. One is located at Sabhan and is used for storing final
products and only the material/equipment needed for near production. The other
warehouse is located in Kabd and is used for storing the packing material until it is
needed.
Figure 6.19: Warehouses' location on Kuwait map.
Page | 425
Distribution Network
The National Canned Food Production and Trading Co. distributes its final
product, by land, to a local distributor who is then in charge of delivering to the co-
ops, wholesalers and small stores, to six Gulf Countries and ships to two countries in
Africa and to Houston, TX.
The imported packing and raw materials arrive at Shuwaikh Port. The packing
material is then transported to Kabd, and the raw materials to Sabhan. When the
packing material is needed, it is then sent to Sabhan.
The company manufactures for other gulf countries and the overseas customers
based on customer request, but does keep inventory for its local customers.
Figure 6.20: Customers in the Gulf region.
Page | 426
Figure 6.21: Overseas customers.
Page | 427
Figure 6.22: Supply chain network.
Page | 428
Current Average Demand and Costs
Based on historical data, table 6.1 was derived. Note that every truck
(sometimes called trailer) has a capacity of 2100 cartons (every carton holds 24
cans) and every container which is used for shipping modes has a capacity of 1650
cartons.
Table 6.44: Average demand and transportations costs for all customers.
Avg. Demand
(transporter/month)
Capacity
of
transporter
(carton)
Cost
(KD/transporter)
Total Cost (KD/month)
Local 28 2100 0 0
KSA (Dammam)
6 2100 200 1200
UAE 5 2100 300 1500
Bahrain 4 2100 290 1160
Qatar 3 2100 300 900
Oman 3 2100 400 1200
Iraq 3 2100 150 450
Tunisia 2 1650 815 1630
USA 3 1650 980 2940
Kenya 3 1650 1300 3900
Totals 122400 cartons/month 14880
Page | 429
Problem Statement
The National Canned Food Production and Trading Co. have to keep the
production line running overtime due to the large demand for their products. They
are incapable of satisfying demand with their official scheduled working hours. The
overtime includes working throughout nights, early mornings and during weekends.
The company is at risk of being unable to satisfy the current demand even with
overtime production. The company produces 4,000 cartons daily on average (without
considering overtime hours), which is equal to 104,000 cartons per month. The total
monthly demand on average is equal to 122,400 cartons. This means that the factory
produces almost 15% of the demand during overtime.
Overtime hours do not come free of charge, however. It costs the company, on
average, 1,750 KD every month which is considered as an extra, unnecessary
expense for the company and it is a work overload on the workers at the company!
The system is thereby risky and expensive.
Page | 430
Solution Approach
After studying the current supply chain of the company, Linear Programming (was
used to study the profitability of opening a new factory in 2 potential sites (KSA -
Dammam and Kuwait), the profitability of using a new mode of transportation, and
the profitability of increasing the capacity of the existing factory by replacing the
bottleneck machines.
The aim from this study is to raise the company's awareness of the necessity
of increasing the company's production capacity and look further into it.
6.2 Analysis and Studies
Assumptions
1. The establishing and fixed costs for the two alternatives are the same.
2. Any regulations regarding establishing a new factory in KSA were overlooked.
3. Costs of transportation from KSA are estimated using the obtained data for
transportation from/in Kuwait.
4. Sabhan (Kuwait) will remain to produce for the overseas markets and
therefore will not be included in the modeling.
5. The average monthly capacity is 50 truckloads. Since the overseas markets
will not be considered, their demand will be deducted from the total monthly
capacity. Therefore, the monthly capacity will be 42 cartons.
Page | 431
Table 6.45: Input data.
Demand City (j) Transportation Cost (Cij) per 2100 cartons (KD) Monthly Capacity
(x2100 cartons)
(Ki)
(i) Kuwait
(1)
KSA
(2)
UAE
(3)
Bahrain
(4)
Qatar
(5)
Oman
(6)
Iraq
(7)
Kuwait - Existing
(1)
0 200 300 290 300 400 150 42
Kuwait - Potential
(2)
0 200 300 290 300 400 150 90
KSA - Potential
(3)
200 0 100 90 100 200 350 90
Monthly Demand (Dj)
(x2100 cartons)
28 6 5 4 3 3 3 Total Demand
54
Page | 432
Study 1: Establishing a New Factory
The potential sites for establishing a new factory are Kuwait and KSA - Dammam.
Dammam is considered one of the most industrial cities in KSA. It is an easily
accessible city. Also, the distributor is located in Dammam, so the cost estimates are
valid.
The annual maintenance cost of the existing factory in Kuwait is 77,500 KD. The
annual equivalent of preventive maintenance costs is 10,800 KD and the annual
equivalent of the setup cost was estimated to be 53,070 KD:
Setup cost = 300,000 KD
A= P (A/P, i =12%, n=10) = 53,070 KD
Therefore, the annual equivalent of setup and maintenance costs either in Kuwait or
KSA is 63,870 KD.
Model
Input:
Cij : Cost of transporting one truck from i to j.
Dj : Demand of j.
Ki : Capacity of i.
Ai : Annual equivalent of running/establishing factory.
Decision Variables:
Yij : Whether j is covered by i or not.
Si : Whether a factory exists or is established at i or not.
Objective Function:
Min CijDjYij1≤ 𝑖 ≤ 31<𝑗<7
+ AiSi1≤ 𝑖 ≤ 31<𝑗<7
Page | 433
Constraints:
Yij = 1 3𝑖=1 j = 1, 2, … ,7
Ensures that the demand of every market is supplied by one factory.
Yij ≤ Si i = 1, 2, 3 and j = 1, 2, … ,7
Ensures that a factory can only cover a market’s demand if it exists or is established.
DjYij 7𝑗=1 ≤ KiSi i = 1, 2, 3
Ensures that the demand supplied by a factory does not exceed its capacity.
Si = 1 3i=2
Ensures that only one new factory is opened in either KSA or Kuwait.
S1 = 1
Ensures that Kuwait Plant Exists.
Yij = {0,1}
Whether a market i is supplied by a factory j or not.
Si = {0,1} i = 2,3
Whether a factory is established at KSA or Kuwait
min 0Y11 + 1200Y12 + 1500Y13 + 1160Y14 + 900Y15 + 1200Y16 + 450Y17 + 0Y21 + 1200Y22
+ 1500Y23 + 1160Y24 + 900Y25 + 1200Y26 + 450Y27 + 5600Y31 + 0Y32 + 500Y33 + 360Y34 +
300Y35 + 600Y36 + 1050Y37 + 6458S1 + 5323S2 + 5323S3
st Y11 + Y21 + Y31 = 1
Y12 + Y22 + Y32 = 1
Y13 + Y23 + Y33 = 1
Y14 + Y24 + Y34 = 1
Y15 + Y25 + Y35 = 1
Page | 434
Y16 + Y26 + Y36 = 1
Y17 + Y27 + Y37 = 1
Y21 - S2 <= 0
Y22 - S2 <= 0
Y23 - S2 <= 0
Y24 - S2 <= 0
Y25 - S2 <= 0
Y26 - S2 <= 0
Y27 - S2 <= 0
Y31 - S3 <= 0
Y32 - S3 <= 0
Y33 - S3 <= 0
Y34 - S3 <= 0
Y35 - S3 <= 0
Y36 - S3 <= 0
Y37 - S3 <= 0
S1= 1
S2 + S3 = 1
28Y11 + 6Y12 + 5Y13 + 4Y14 + 3Y15 + 3Y16 + 3Y17 - 42S1<= 0
28Y21 + 6Y22 + 5Y23 + 4Y24 + 3Y25 + 3Y26 + 3Y27 - 90S2 <= 0
28Y31 + 6Y32 + 5Y33 + 4Y34 + 3Y35 + 3Y36 + 3Y37 - 90S3 <= 0
end
int Y11
int Y12
int Y13
Page | 435
int Y14
int Y15
int Y16
int Y17
int Y21
int Y22
int Y23
int Y24
int Y25
int Y26
int Y27
int Y31
int Y32
int Y33
int Y34
int Y35
int Y36
int Y37
int S2
int S3
Page | 436
Output
Results showed that a new factory should be established in KSA and the distribution
plan is as follows.
Table 6.46: Model 1 output.
DjYij Kuwait KSA UAE Bahrain Qatar Oman Iraq Total Truck
loads
Kuwait 28 0 0 0 0 0 3 31
KSA 0 6 5 4 3 3 0 21
Total Cost = 13991 KD/month
S2 = 0
S3 = 1
*For more details refer to Appendix O for the Lindo output.
Page | 437
Study 2: Using New Trucks
KGL sends trucks with a capacity of 67.7 m3, to two of the existing customers. Thus,
the capacity of the new truck is 4130 cartons. We will study if using these trucks as a
mode of transportation from Kuwait to KSA - Dammam and UAE will help reduce
transportation costs in comparison to establishing a new factory.
Table 6.47: Price quotation from KGL.
KSA - Dammam UAE
Cost from Kuwait (KD/truck) 300 450
Average Demand (truck/month) 3 3
Model
Input:
Cij : Cost of transporting one truck from i to j.
Dj : Demand of j.
Ki : Capacity of i.
Decision Variables:
Yij : Whether j is covered by i or not.
Si : Whether a factory exists or is established at i or not.
Tij : Whether the new trucks are used to transport from i to j.
Objective Function:
Min CijDjYij1≤ 𝑖 ≤ 31<𝑗<7
+ AiSi3𝑖=1 + CijDjTij1≤ 𝑖 ≤ 3
1<𝑗<7
Page | 438
Constraints:
Yij + Tij = 1 3𝑖=1 j = 2, 3
Ensures that the demand of every market is supplied by one factory using one mode
of transportation.
Yij = 1 3𝑖=1 j = 1, 4, 5, 6, 7
Ensures that the demand of every market is supplied by one factory.
Yij ≤ Si i = 1, 2, 3 and j = 1, 2, … , 7
Ensures that a factory can only cover a market's demand if it exists or is established.
DjYij 7𝑗=1 + DjTij ≤ KiSi i = 1, 2, 3
Ensures that the demand supplied by a factory by one mode of transportation does
not exceed its capacity.
Si = 1 3i=2
Ensures that only one new factory is opened at either KSA or Kuwait.
S1 = 1
Ensures that Kuwait Plant Exists.
Yij = {0,1}
Whether a market i is supplied by a factory j or not.
Si = {0,1} i = 2,3
Whether a factory is established at KSA or Kuwait
Page | 439
min 0Y11 + 1200Y12 + 900T12 + 1500Y13 + 1125T13 + 1160Y14 + 900Y15 + 1200Y16 +
450Y17 + 0Y21 + 1200Y22 + 1500Y23 + 1160Y24 + 900Y25 + 1200Y26 + 450Y27 +
5600Y31 + 0Y32 + 500Y33 + 360Y34 + 300Y35 + 600Y36 + 1050Y37 + 6458S1 + 5323S2 +
5323S3
st
Y11 + Y21 + Y31 = 1
Y12 + Y22 + Y32 + T12 = 1
Y13 + Y23 + Y33 + T13 = 1
Y14 + Y24 + Y34 = 1
Y15 + Y25 + Y35 = 1
Y16 + Y26 + Y36 = 1
Y17 + Y27 + Y37 = 1
Y21 - S2 <= 0
Y22 - S2 <= 0
Y23 - S2 <= 0
Y24 - S2 <= 0
Y25 - S2 <= 0
Y26 - S2 <= 0
Y27 - S2 <= 0
Y31 - S3 <= 0
Y32 - S3 <= 0
Y33 - S3 <= 0
Y34 - S3 <= 0
Y35 - S3 <= 0
Y36 - S3 <= 0
Y37 - S3 <= 0
Page | 440
S1= 1
S2 + S3 = 1
28Y11 + 6Y12 + 3t12+ 3t13 + 5Y13 + 4Y14 + 3Y15 + 3Y16 + 3Y17 - 42S1 <= 0
28Y21 + 6Y22 + 5Y23 + 4Y24 + 3Y25 + 3Y26 + 3Y27 - 90S2 <= 0
28Y31 + 6Y32 + 5Y33 + 4Y34 + 3Y35 + 3Y36 + 3Y37 - 90S3 <= 0
end
int Y11
int Y12
int Y13
int Y14
int Y15
int Y16
int Y17
int Y21
int Y22
int Y23
int Y24
int Y25
int Y26
int Y27
int Y31
int Y32
int Y33
int Y34
int Y35
Page | 441
int Y36
int Y37
int S2
int S3
int T12
int T13
Output
Results showed that the best option is establishing a new factory in KSA again.
Table 6.48: Model 2 output.
DjYij Kuwait KSA UAE Bahrain Qatar Oman Iraq Total Truck loads
Kuwait 28 0 0 0 0 0 3 31
KSA 0 6 5 4 3 3 0 21
Total Cost = 13991 KD/month
S2 = 0
S3 = 1
T12 = 0
T13 = 0
*For more details refer to Appendix O for the Lindo output.
Page | 442
Justifications for Study 1 and Study 2
Current Situation
N.B. The following data was used to estimate the costs and was obtained from the
Cost Analysis Group.
Table 6.49: Annual costs.
Cost (KD/year)
Overtime 21,000
Maintenance 77,500
Operation Costs 178,560
Transportation 145,812
These are the costs considered when opening the new factory. A cash flow diagram
was developed to calculate the present worth of the current existing factory in
Kuwait. The interest rate used was 12% and calculated over a period of 10 years.
PW = 2,389,322 KD
Page | 443
Current (Kuwait) Factory in New Situation
Maintenance costs remain the same because the machines are untouched.
The transportation costs include only the costs involved in the new distribution plan.
The operation costs are equal to 65% of the current operation costs because the
current factory in the new situation will be responsible for producing only 65% of its
current production.
PW = 1,578,209 KD
Page | 444
New Factory
Since it is a new factory, no corrective maintenance should be applied in
normal conditions. However, the preventive maintenance will be carried on the same
schedule as the current factory which will result in constant costs. The new factory
will be shipping to KSA, Bahrain, UAE, Qatar and Oman. These locations demand
35% of the current production and operation costs are calculated based on that.
PW = 768,715 KD
Therefore, the Total Present Worth was calculated for the company by summing the
PW for the current factory in the new situation and that of the new factory.
PW = 1,578,209 + 768,715 = 2,346,924 KD
Total Cost Savings = ((2,389,322 - 2,346,924)/ 2,389,322) x 100
= 1.77 %
Page | 445
Study 3: Increasing Capacity of Existing Factory
The capacity of the existing factory in Kuwait could be increased if the bottle
neck machines were replaced. In the following model this option was included in
addition to the previous two alternatives and also relaxing the constraint so that more
than one alternative could be feasible.
The new average production speed would equal about 290 - 300 cans/min after
replacing the bottleneck machines. Therefore, the average monthly capacity is 90
truckloads.
Using average cost values obtained from Elmar, an industry leader in the
manufacturing and design of a wide variety of machines
(http://www.nov.com/elmar/), the annual equivalent of expanding the capacity cost
was estimated to be KD 11,522.
Model
Input:
Cij : Cost of transporting one truck from i to j.
Dj : Demand of j.
Ki : Capacity of i.
Ui : Increase in capacity of i.
Decision Variables:
Yij : Whether j is covered by i or not.
Si : Whether a factory exists or is established at i or not.
Tij : Whether the new trucks are used to transport from I to j.
Qi : Whether the capacity of factory i is increased or not.
Objective Function:
Min CijDjYij1≤ 𝑖 ≤ 31<𝑗<7
+ AiSi3𝑖=1 + CijDjTij1≤ 𝑖 ≤ 3
1<𝑗<7 + AiQi1
i=1
Page | 446
Constraints:
Yij + Tij = 1 3𝑖=1 j = 2, 3
Ensures that the demand of every market is supplied by one factory using one mode
of transportation.
Yij = 1 3𝑖=1 j = 1, 4, 5, 6, 7
Ensures that the demand of every market is supplied by one factory.
Yij ≤ Si i = 1, 2, 3 and j = 1, 2, … , 7
Ensures that a factory can only cover a market's demand if it exists or is established.
DjYij 7𝑗=1 + DjTij ≤ KiSi + QiUi i = 1, 2, 3
Ensures that the demand supplied by a factory by one mode of transportation does
not exceed its capacity.
Si = 1 3i=2
Ensures that only one new factory is opened at either KSA or Kuwait.
S1 = 1
Ensures that Kuwait Plant Exists.
Yij = {0,1}
Whether a market i is supplied by a factory j or not.
Si = {0,1} i = 2,3
Whether a factory is established at KSA or Kuwait
Page | 447
min 0Y11 + 1200Y12 + 900T12 + 1500Y13 + 1125T13 + 1160Y14 + 900Y15 + 1200Y16 +
450y17 + 0Y21 + 1200Y22 + 1500Y23 + 1160Y24 + 900Y25 + 1200Y26 + 450Y27 + 5600Y31 +
0Y32 + 500Y33 + 360Y34 + 300Y35 + 600Y36 + 1050Y37 + 6458S1 + 5323S2 + 5323S3 +
960Q1
st
Y11 + Y21 + Y31 = 1
Y12 + Y22 + Y32 + T12 = 1
Y13 + Y23 + Y33 + T13 = 1
Y14 + Y24 + Y34 = 1
Y15 + Y25 + Y35 = 1
Y16 + Y26 + Y36 = 1
Y17 + Y27 + Y37 = 1
Y21 - S2 <= 0
Y22 - S2 <= 0
Y23 - S2 <= 0
Y24 - S2 <= 0
Y25 - S2 <= 0
Y26 - S2 <= 0
Y27 - S2 <= 0
Y31 - S3 <= 0
Y32 - S3 <= 0
Y33 - S3 <= 0
Y34 - S3 <= 0
Y35 - S3 <= 0
Y36 - S3 <= 0
Y37 - S3 <= 0
Page | 448
S1= 1
28Y11 + 6Y12 + 3T12+ 3T13 + 5Y13 + 4Y14 + 3Y15 + 3Y16 + 3Y17 – 42S1 – 48Q1 <= 0
28Y21 + 6Y22 + 5Y23 + 4Y24 + 3Y25 + 3Y26 + 3Y27 – 90S2 <= 0
28Y31 + 6Y32 + 5Y33 + 4Y34 + 3Y35 + 3Y36 + 3Y37 – 90S3 <= 0
end
int Y11
int Y12
int Y13
int Y14
int Y15
int Y16
int Y17
int Y21
int Y22
int Y23
int Y24
int Y25
int Y26
int Y27
int Y31
int Y32
int Y33
int Y34
int Y35
int Y36
Page | 449
int Y37
int S2
int S3
int T12
int T13
int Q1
Output
Results showed that increasing the capacity of the existing plant in Kuwait is the best
option alongside using the new modes of transport.
Table 6.50: Model 3 output.
DjYij Kuwait KSA UAE Bahrain Qatar Oman Iraq Total
Truck loads
Kuwait (old
truck)
28 0 0 4 3 3 3 41
Kuwait
(new truck)
0 3 3 0 0 0 0 6
Total Cost = 13153 KD/month
S2 = 0
S3 = 0
Q1 = 1
T12 = 1
T13 = 1
*For more details refer to Appendix O for the Lindo output.
Page | 450
Study 4: Demand Increase
In the likely case of an increase in demand, decisions may change. Using the
demand forecasted for the next 5 years by the inventory control group, an average
monthly demand was calculated and the following results were obtained.
Using the same model as study 3, results were obtained in order to develop a
distribution plan in order to meet the forecasted demand.
Page | 451
Table 6.51: Forecasted average demand.
Demand City (j) Transportation Cost (Cij) per 2100 cartons (KD) Monthly Capacity
(x2100 cartons)
(Ki)
(i) Kuwait
(1)
KSA
(2)
UAE
(3)
Bahrain
(4)
Qatar
(5)
Oman
(6)
Iraq
(7)
Kuwait - Existing
(1)
0 200 300 290 300 400 150 42
Kuwait - Potential
(2)
0 200 300 290 300 400 150 90
KSA - Potential
(3)
200 0 100 90 100 200 350 90
FORECASTED-
Monthly Demand (Di)
(x2100 cartons)
33 8 7 5 4 4 7 Total Demand
68
Page | 452
min 0Y11 + 1600Y12 + 1500T12 + 2100Y13 + 2250T13 + 1450Y14 + 1200Y15 + 1600Y16 +
1050Y17 + 0Y21 + 1600Y22 + 2100Y23 + 1450Y24 + 1200Y25 + 1600Y26 + 1050Y27 +
6600Y31 + 0Y32 + 700Y33 + 450Y34 + 400Y35 + 800Y36 + 2450Y37 + 6458S1 + 5323S2
+ 5323S3 + 960Q1
st
Y11 + Y21 + Y31 = 1
Y12 + Y22 + Y32 + T12 = 1
Y13 + Y23 + Y33 + T13 = 1
Y14 + Y24 + Y34 = 1
Y15 + Y25 + Y35 = 1
Y16 + Y26 + Y36 = 1
Y17 + Y27 + Y37 = 1
Y21 - S2 <= 0
Y22 - S2 <= 0
Y23 - S2 <= 0
Y24 - S2 <= 0
Y25 - S2 <= 0
Y26 - S2 <= 0
Y27 - S2 <= 0
Y31 - S3 <= 0
Y32 - S3 <= 0
Y33 - S3 <= 0
Y34 - S3 <= 0
Y35 - S3 <= 0
Y36 - S3 <= 0
Page | 453
Y37 - S3 <= 0
S1= 1
33Y11 + 8Y12 + 5T12 + 5T13 + 7Y13 + 5Y14 + 4Y15 + 4Y16 + 7Y17 – 42S1 – 48Q1 <= 0
33Y21 + 8Y22 + 7Y23 + 5Y24 + 4Y25 + 4Y26 + 7Y27 – 90S2 <= 0
33Y31 + 8Y32 + 7Y33 + 5Y34 + 4Y35 + 4Y36 + 7Y37 – 90S3 <= 0
end
int Y11
int Y12
int Y13
int Y14
int Y15
int Y16
int Y17
int Y21
int Y22
int Y23
int Y24
int Y25
int Y26
int Y27
int Y31
int Y32
int Y33
int Y34
Page | 454
int Y35
int Y36
int Y37
int S2
int S3
int T12
int T13
int Q1
Output
Results showed that establishing a factory in KSA would be the most feasible
solution in the case of an increase in demand.
Table 6.52: Model 4 output.
DjYij Kuwait KSA UAE Bahrain Qatar Oman Iraq Total
Truck
loads
Kuwait
Existing
33 0 0 0 0 0 7 60
KSA
Potential
0 8 7 5 4 4 0 5
Total Cost = 15181.00 KD/month
S2 = 0
S3 = 1
Q1 = 0
Page | 455
T12 = 0
T13 = 0
*For more details refer to Appendix O for the Lindo output.
6.3 Conclusion
Throughout this analysis, alternatives were studied in order to overcome the
problem regarding the production capacity of the factory. The alternatives studied
were whether to increase the capacity of the current factory, establish a new factory,
and also, to reduce shipping costs, new modes of transportation were introduced
where the unit shipping cost is less than for the existing modes.
With the current average demand, it is suggested to increase the capacity of the
existing Kuwait factory and use the new modes of transportation introduced. The
initial associated transportation costs were 14880 KD/month; the cost resulting from
the suggested distribution plan is 13153 KD/month, resulting in savings of 11.6%.
Since the National Canned Food Production and Trading CO. is becoming more and
more known throughout the region and internationally, there is an expected increase
in demand, which the company may not be able to satisfy with their current
production capacity. It is safe to assume so because of the fact that they are already
working overtime to satisfy the current demand. Therefore, it would seem necessary
for the company to increase their production capacity in order to be able to satisfy
the future forecasted demand.
Page | 456
Page | 457
7. Safety & Human Factors
Page | 458
Page | 459
7.1 Introduction
The working conditions inside the factory were examined and it was
determined whether they are safe. It was attempted to remove all hazards from the
workplace and to try to minimize the chances of workers sustaining significant
injuries. By applying multiple human factors tools as RULA and the NIOSH lifting
equation, the aim was to eradicate any unhealthy postures during work or activities
that cause too much fatigue to the workers.
Also, the company was educated on the important role that safety and human
factors engineers can play in ensuring the safety of their workers and avoiding any
expensive accidents from occurring.
Problem Description
By observing the factory, it was noticed that there is no significant attention
paid to the safety and human factors aspects of the work being done. There were
wet floors, crammed machines, and no signs instructing workers to wear protective
equipment. Furthermore, many of the work activities were not ergonomically sound.
Page | 460
Objectives
It was immediately noticed that there are major opportunities for improvement
in the environment of the factory. The workers’ body positions as well as other areas
that safety and human factors can cover were studied with the aim to:
Improve operational performance.
Enhance effectiveness and efficiency.
Ensure the work environment can be used conveniently.
Make workers comfortable in their surrounding environment.
Reduce human errors.
Increase productivity.
Improve safety.
Reduce fatigue and stress.
Get workers’ acceptance.
Increase job satisfaction.
Improve the quality of life.
Note that, achieving the objectives above leads to a reduction in the number of
accidents which will go towards eliminating the direct and indirect costs of an
accident.
Solution Approach
Safety and human factors tools such as RULA and NIOSH were used to
evaluate all work activities. When activities were found to be unsafe,
recommendations to modify them were suggested.
Page | 461
7.2 Safety and Human Factors
Even though technology is advancing at an exponential rate, there are still
work activities with manual handling of material, supplies, and tools often requiring
workers to expend moderate to high level of physical energy to perform them.
Engineers must make sure that products, workplaces, environments,
buildings, vehicles and systems are safe since they affect the way a worker may act,
and may eventually cause an accident. The Domino Theory states that an accident
sequence is like a series of five dominos standing on end, one can knock the others
over. The five dominos in reverse sequence are injuries caused by an action which,
in turn, is caused by an unsafe act or condition, caused by undesirable traits
(nervousness, violent temper, lack of knowledge,…etc.), that are developed because
of unsafe environment.
Figure 7.1: Dominos theory.
At the same time, engineers work in an economic system that requires
businesses and enterprises to be competitive. Safety and human factors make
ergonomic sense as well as moral and legal sense.
Undesirable Traits
Unsafe Act
Accident Unsafe Environment
INJURY
Page | 462
So to achieve safety through engineering, engineers need to understand:
The duties and responsibilities for which they are accountable.
The hazards and engineering controls for them.
Human behavior, capabilities and limitations.
How to identify hazards and present the need for controls to the
managers.
Engineers work mainly on the preventive side of safety, where they must
identify the hazards during design and eliminate or reduce them. They also prevent
unsafe behavior by designing the product, workplace and environment in a way that
unsafe behaviors are not likely to occur.
Industrial engineers work mainly on fitting the job to people and designing
work methods to improve the fit between people and their equipment, environment,
system, workplace or information, to improve workers performance and safety.
Safety engineering is the application of scientific and engineering principals and
methods to the elimination and control of hazards. Also it is the state of being free
from harm, danger, injury or damage.
Human factors is a term that covers:
The science of understanding the properties of human capability (Human
Factors Science).
The application of this understanding to the design and development of
systems and services (Human Factors Engineering).
The art of ensuring successful application of Human Factors Engineering
to a program.
Page | 463
7.3 Hazard Categories
A hazard is a situation which poses a level of threat to life, health, property or
environment. Most hazards are dormant or potential, with only a theoretical risk of
harm. However, once a hazard becomes 'active', it can create an emergency
situation.
1. Biological Hazards include bacteria, viruses, insects, plants, birds, animals,
and humans. These sources can cause a variety of health effects ranging
from skin irritation and allergies to infections (e.g., tuberculosis, AIDS), cancer
and so on.
2. Chemical hazards are present when a worker is exposed to any chemical
preparation in the workplace in any form (solid, liquid or gas). Some are safer
than others, but to some workers who are more sensitive to chemicals, even
common solutions can cause illness, skin irritation or breathing problems.
Beware of:
Liquids, such as cleaning products, paints, acids, solvents especially
chemicals in an unlabelled container.
Vapors and fumes, for instance those that come from welding or
exposure to solvents.
Gases like acetylene, propane, carbon monoxide and helium.
Flammable materials like gasoline, solvents and explosive chemicals.
Page | 464
3. Ergonomic Hazards occur when the type of work, body position and working
conditions put strain on your body. They are the hardest to spot since the
strain on the body and the harm they pose are immediately noticeable. Short-
term exposure may result in "sore muscles" the next day or in the days
following exposure, but long term exposure can result in serious long-term
injuries. Ergonomic hazards include:
Poor lighting.
Improperly adjusted workstations and chairs.
Frequent lifting.
Poor posture.
Awkward movements, especially if they are repetitive.
Repeating the same movements over and over.
Having to use too much force, especially if repeated frequently.
4. Physical Hazards are the most common and will be present in most
workplaces at one time or another. They include unsafe conditions that can
cause injury, illness and death. They are typically easiest to spot but often
overlooked because of familiarity, lack of knowledge, resistance to spending
time or money to make necessary improvements or simply delays in making
changes to remove the hazards. None of these are acceptable reasons for
workers to be exposed to physical hazards. Examples of physical hazards
include:
Electrical hazards such as frayed cords, missing ground pins, improper
wiring.
Unguarded machinery and moving machinery parts, guards removed
or moving parts that a worker can accidentally touch.
Constant loud noise.
High exposure to sunlight/ultraviolet rays, heat or cold.
Working from heights, including ladders, scaffolds, roofs, or any raised
work area.
Working with mobile equipment such as forklifts since they require
significant additional training and experience.
Page | 465
7.4 Worker interaction with machine and material
The areas where the workers interact with the machine, raw materials, or final
product through the production process are discussed below.
Can Production Line:
1. Slitting: In the slitting process, a worker standing that feeds the tin sheets
into the slitting machine.
2. Blanks are manually fed by the same worker to the welder.
3. Welding: In this step there is a welding test applied by a single worker.
4. Seaming: A worker manually feeds the seaming machine with the lids.
Filling Line:
1. Soaking: Tanks are manually filled by a worker.
2. Inspection belt: The solid material is sorted manually by 4-6 workers to
remove any dark or broken pieces.
3. Crate loading: 700 cans are put on a crate manually and are taken to the
sterilizing stage by a trolley.
4. Sterilizing: The crates are pushed into the sterilizing machine manually.
5. Crate unloading: The cans are unloaded from the crate to the labeler
manually.
6. Label inspection: Checking the quality of the labels is done manually by a
specialized worker.
7. Every 20 cartons are put in a pallet by two workers and one fork lift.
Page | 466
Figure 7.2: Ventilation system.
7.5 Data Collection and Findings
To collect information accurately and easily identify the hazards around the factory,
steps were taken to summarize the findings to make it easier to improve the system
and reduce the hazards.
Safety Checklists: A checklist is used as an aid to memory. It helps to
ensure consistency and completeness in carrying out a task. A more
advanced checklist would be a schedule, which lays out tasks to be done
according to time of day or other factors.
Safety and Human factors Survey Table: A survey table is a technique
used to gather the findings and summarize them into categories.
Safety and Human Factors Checklists1:
Applying a number of safety and human factors checklists covered a large part of
the workplace which led to general conclusions regarding to safety hazards:
a. Work Environment:
The factory has a ventilation system but does
not have an air conditioning system which
causes an increase in temperature and
humidity in summer, adversely affecting worker
performance.
The noise level in the factory was very high.
1 For more details, Check Appendix (P)
Page | 467
Figure 7.3: Lighting system.
Figure 7.4: Wet ground.
Figure 7.5: Fire extinguishers.
The lighting of the factory was deemed
acceptable is the roof of the factory allows the
sun light through (which provides natural
lighting in addition to the electrical lighting
system in the factory). However, some areas
need some enhancement in the lightning
system because the illumination is not enough
or there are glare issues.
The poor machine layout and the unorganized raw material and final products
storage area cause some workers to face some difficulties in moving from one
machine to another.
Since the factory deals with the production of
caned food which involves the use of a
massive amount of fluids in the process line,
the ground is always wet, causing slipping
accidents.
b. Fire Protection:
The factory has an automatic fire fighting and
detection system that is sensitive to smoke and fire.
There are 4 fire hose reels distributed around the
factory plant and 8 fire extinguishers.
c. Emergency Exits:
The factory has 7 emergency exits distributed
in several places around the factory plant. Some
emergency exits are difficult to reach or access
because of the presence of obstacles in the way.
Stockpiles of raw material also hinder the
passage of workers.
Figure 7.6: Blocked emergency exit.
Page | 468
Figure 7.7: Instruction boards.
d. Safety Signs:
There are no information and warning signs that remind
the workers of the importance of wearing protective gear
(for example boots, gloves, eye protectors, coats, helmets
and earmuffs).
Uncomfortable Body Postures1:
The design of the machines and the working tasks forced the workers to adopt
uncomfortable postures that require further study by applying Human Factors
methods.
Safety and Human Factors Survey
Forming a safety and human factors survey table that contains all the findings that
were recognized when studying the factory made it easier to identify the type of
hazard and the way to remove or reduce it. The survey table contains the number of
findings, type, date, location (Fig.#), description, and data available. The information
gathered will be then used in:
Quick-Win Improvement Table contains the findings that can be easily
solved and the number of findings. The findings that can be solved by the
same recommendation are grouped together to faciliate their solution.
Long Term Improvement Table contains findings that need further studying
by applying human factors and safety tools where the findings can not be
solved easily and need further investigation.
1 For pictures, check Appendix (Q)
Page | 469
Location Layout
Figure 7.8: Location of hazard layout.
Page | 470
Safety and Human Factors Survey Table
Table 7.53: Safety and human factors survey1.
Finding Hazard Type Date Location Description Data
1 Chemical ET Out Doors
H2S Gas. Video
2 Physical ET EW Wet floor everywhere, except storage areas.
V+P
3 Physical ET EW Very high noise level. Video
4 Safety ET EW No safety signs. Picture
5 Ergonomic ET L 2 Workers are sorting beans to remove any dark or broken pieces.
Video
6 Ergonomic ET L 2 Workers standing/sitting for long periods of time.
Picture
7 Ergonomic ET L 2 Uncomfortable chairs. Picture
8 Ergonomic ET L 3 Operators standing all the time. Video
9 Ergonomic ET L 3 Hard to move and a need to bend under machines to pass.
V+P
10 Ergonomic ET L 4 Empty crates are pulled from the empty crate area to the crate loading
machine.
Video
11 Ergonomic ET L 4 700 cans are put on a crate. Video
12 Ergonomic ET L 4 Pushing full crate to sterilizing machine.
Video
13 Ergonomic ET L 5 Push full basket into retort. Video
1 ET: Every time, EW: Everywhere, Data: Represents the available data about the finding, Pictures: for more
details, see Appendix (Q), Video: For more details, Check attached CD. V+P: Video and Pictures are available
Page | 471
Table 7.54: Cont. safety and human factors survey.
Finding Hazard Type Date Location Description Data
14 Ergonomic ET L 5 Pull full basket from retort. -
15 Chemical ET L 5 Facing hot steam from sterilizing machine
Video
16 Ergonomic ET L 5 Push full basket to unloading machine.
Video
17 Ergonomic ET L 6 Pull & push to unload from basket to labeling machine.
Video
18 Ergonomic ET L 6 Pull & Push empty basket back to empty crate area.
Video
19 Ergonomic ET L 7 Labels are manually inspected by a single worker.
V+P
20 Ergonomic ET L 8 Stacking product on pallets. Video
21 Ergonomic ET L 8 Pulling empty pallet. V+P
22 Physical ET L 9 Very high noise level next to the welding machine.
Video
23 Ergonomic ET L 9 Loading welding machine with 5 to 10 kg group of blanks.
V+P
24 Ergonomic ET L 9 Feeding slitting machine with tin sheets.
Video
25 Ergonomic 8\11 L 9 Applying welding test on welded blanks.
Video
26 Ergonomic 8\11 L 9 Using old and heavy tools to apply test.
Video
27 Ergonomic 8\11 L 9 Operators setting up the seaming machine.
Video
28 Physical 17\11 EW High temperature & humidity levels. -
29 Physical 17\11 EW Glare on instruction boards. Picture
Page | 472
Table 7.55: Cont. safety and human factors survey.
Finding Hazard Type
Date Location Description Data
30 Safety 17\11 L 2 Emergency exit was blocked. video
31 Ergonomic 17\11 L 2 Filling machine from heavy oil drums. V+P
32 Physical 17\11 L 5 Unstable pressure gauge. Video
33 Ergonomic 17\11 L 5 Operator setting up sterilizing machine. Picture
34 Ergonomic 17\11 L 7 Operator setting up labeling machine. V+P
35 Safety 26\11 L 1 Emergency exit was blocked. Picture
36 Safety 26\11 L 1 Lifting worker on a forklift Video
37 Ergonomic 26\11 L 3 Manual can filling. Video
38 Safety 26\11 L 3 Emergency exit was blocked. V+P
39 Safety 26\11 L 9 Emergency exit was blocked. Picture
40 Safety 26\11 L 10 Emergency exit not obvious and hard to reach.
Video
41 Ergonomic 26\11 L 10 Control buttons are not classified. Picture
42 Safety 26\11 L 11 Emergency exit was blocked and located next to the main door.
Picture
43 Safety 26\11 L 11 Lifting worker on a forklift. Video
44 Ergonomic 28\11 L 1 Workers lifting 50 kg beans bags to fill tanks.
Video
45 Safety 5\12 L 8 Forklift bumps into worker. Video
Page | 473
7.6 Quick-win Improvements
Table 7.56: Quick win Improvement.
No. Finding # Hazard Description Recommendations
1 2 Slippery floor Try as much as possible to minimize the
amount of water while cleaning the factory.
Wear boots.
2 3,22 High noise level Wear ear muffs.
3 4 No safety signs Add instruction board that contains safety signs.
4 5,11,19,20,24,37 Repetitive motion
Educate workers on the importance of changing their body posture every once in a
while.
Change worker every so often.
5 7 Uncomfortable
chairs. Use chairs that are ergonomically designed.
6 8 Standing all the
time. Provide workers with chairs so that they
can rest every once in a while.
7 15 Hot steam. Wear protective masks.
8 26 Old, heavy, and un-
ergonomically designed tools.
Replace old tools with light, ergonomically designed tools.
9 28 High temperature
and humidity level. Add fans to the factory to reduce the
temperature and humidity levels.
10 29 Glare on instruction
board.
Change the material of the board to a type that does not reflect light.
Change the position of the board to reduce the glare effect.
11 30,35,38,39,40,42 Blocked emergency
exits. Educate workers to the importance of
clearing the area around the emergency exit.
12 32 Unstable pressure
gauge. Replace with new one.
13 36,43 Lifting workers on a
forklift. Educate workers to the risks of their action.
14 41 Control buttons
without instructions. Add instructions to show their use.
Page | 474
Figure 7.9: Safety instruction board
7.7 Long-term Improvement
Table 7.57: Long term improvement.
No. Finding # Tool Used Hazard Description Recommendations
1 1 - H2S Gas. The government should provide a sewage
system.
2 9 - Not easy to move from one machine to another.
Rearrange machine layout.
3 5,6,11,19,20,23,24,25,27,31,33,34,
44
RULA Uncomfortable\awkward body posture with repetitive motion.
1*
4 10,12,17,18,21 SNOOK tables
Push\pull heavy items (Create \Pallet).
*
5 20,23,44 NIOSH Repetitive lifting with body twisting.
*
6 5,11,13,19,20, 23 RRM Long working hours. *
* Note that recommendations will be explained separately for each case in the next section.
Page | 475
Methodologies
Human factors tools were applied on the findings introduced in the long term
improvement table, to rank the findings and determine whether to change it.
RULA
RULA is a quick survey method for use in ergonomic investigations of workplaces
where muscular skeletal disorders are reported. It is a screening tool that assesses
biomechanical and postural loading on the whole body. RULA scores indicate the
level of intervention required to reduce MSD (Muscular skeletal disorders) risks.
Furthermore, it compliments other ergonomic methods.
RULA can be applied manually, through a program from the following site
“http:\\www.rula.co.uk\survey.html”, or through Job Hazard Pro1. Most of the
postures have been assessed manually except for a posture that has two different
scores, one for the right hand and one for the left. The score was found using the
program as an example. Print screen of the final outcome is available below.
For the grand score “C” of the posture assessment:
A score of one or two shows an acceptable posture.
A score of three or four indicates further investigation is needed and changes
may be required.
A score of five or six indicates investigation and changes are required soon.
A score of seven or more indicates investigation and changes are required
immediately.
1 It includes five major risk assessment tools, which are recognized and recommended by OSHA.
Page | 476
Figure 7.10
Figure 7.11
By using RULA software the final score, action, and action level for each location in
the factory were obtained.1
Filling Line:
Case description:
In this case female workers repetitively separate the beans
from dark or broken ones.
Final RULA score: 4
Action: Investigate further.
Recommendation:
Use ergonomically designed chairs with back rest,
and lower the chair height so that the worker does
not need to bend.
Case description:
A male worker is filling a machine with oil. The process takes
more than one minute in the same body posture.
Final RULA score: 7
Action: Investigate and change immediately.
Recommendation:
Place the oil tank in a high place and use an alternative
method for filling.
1 For more details, see Appendix (R)
Page | 477
Figure 7.12
Figure 7.13
Case Description:
Male worker is repetitively loading cans into a crate,
with 700 cans fitting into one crate.
Final RULA score: 7
Action: Investigate and change immediately.
Recommendation:
Use an automated loading machine where the
worker only has to operate it and not apply too much
muscular force to load the cans into the crate.
Case Description:
Operator is setting up the labeling machine
Final RULA score: 3
Action: Investigate further.
Recommendation:
Educate the worker on the importance of changing
his body posture while setting up the machine; for
example, bending his knees rather than his back.
Page | 478
Figure 7.11
Figure 7.14
Figure 7.15
Case Description:
Male worker inspects lables.
Final RULA score: 4
Action: Investigate further.
Recommendation:
Educate the worker on the importance of changing
his body posture every once in a while.
Train different workers to do the same job to break
the repetitive sequence.
Case Description:
Male worker is stacking the final product which in a
box that contains 24 cans, weighing 400g each.
Final RULA score: 7
Action: Investigate and change
immediately.
Recommendation:
Introduce an automated machine that stacks the
boxes instead of the worker. The worker would only
have to operate it rather than repetitively lift the boxes.
Page | 479
Figure 7.16
Can Line:
Case Description:
Male worker is applying welding test on a welded
can to check the quality of the weld.
Final RULA score: 7
Action: Investigate and change
immediately.
Recommendation:
Change the tool into an ergonomically designed one
to make testing easier.
Page | 480
NIOSH
National Institute for Occupational Safety and Health have developed an
“occupational lifting” formula to compute recommended weight limits. This has great
influence on the health of the carrier. There are certain assumptions related to
applying the NIOSH equation such as the temperature being favorable for lifting,
smooth lifting and so on.
The measurements required are shown from figure 7.17 the calculations are done
for the origin and destination of a certain act. One could be safe, the other harmful.
NIOSH can be applied manually or through a program from the following site
“http:\\www.emcins.com\lc\niosh.htm”.
Figure 7.17: Diagram showing all the distances required to substitute into the equation.
Page | 481
The Recommended weight limit is calculated from the following equation:
RWL = LC * HM * VM * DM * AM * FM * CM
LI = W \ RWL
Where,
RWL: Recommended weight limit
LC: Load constant
HM: Horizontal multiplier
VM: Vertical multiplier
DM: Distance multiplier
AM: Asymmetric multiplier
FM: Frequency multiplier
CM: Coupling multiplier
LI: Lifting index
W: Load weight
Note that,
If the lifting index is less than one then the posture is fine for most workers. If
greater than one then the job has to be redesigned and finally if it is greater than 3
then it poses a significant risk.
Figure 7.18: All the factors in the equation, and how each multiplier is calculated from the real data
Page | 482
Figure 7.19
Case description:
Male worker is repetitively lifting 5-10 kg metal blanks from the slitting machine to the
wilding machine.
Table 7.58: Multipliers.
RWL = 23 * (25/36) * (1- (0.003*|110-75| ) * (0.82 + (4.5/64)) *0.57 * 0.15*0.9
= 23 * (0.695) * (0.895) * (0.891) * (0.77)
= 0.9815 ~ 1 Kg
W (actual weight of object) = 5 kg
LI = W/RWL
= 5 / .9815
= 5.094 > 3 (significant risk)
W (actual weight of object) = 10 kg
LI = W/RWL
= 10 / .9815
= 10.188 > 3 (significant risk)
Hand location Vert.
Dist.
Angle Freq. Time Object
coupling Origin Dest. Origin Dest. Lifts
/min hours
H V H V D A A F C
36 112 66 176 64 0 135 9 10 poor
Origin
Destination
483
Figure 7.20
Recommendation:
Reccomendation: Join the slitting machine with the welding machine by a conveyor
to eliminate the lifting operation.
SNOOK Tables
Snook tables19 were originally published by Snook in 1978 and by Snook and
Ciriello in 1991. Snook tables are used for lowering, lifting, pushing and pulling
efforts. Snook tables are less precise than NIOSH since they are based on
psychophysical measures rather than biomechanical. Data required include the type
of effort, whether the job is carried out by a male or female, the distance moved, and
the frequency.
Appropriate tables are then used in order to reach the maximum acceptable force.
Can Loading:
Case Discreption:
A male worker pulling a 30kg
create filled whith 700 cans, each
can weighing 400g, for 10 meters.
The height of his hand is 1.3 m,
and he repeats this process every
30 minutes.
• Result: maximum
acceptable weight is 28 kg.
From Snook pull table results, it
was concluded that the worker
exceeded the weight limit. It is
recommended a hoist is added to
carry the crates from the loading
machine to the sterilizing machine.
19 For more details about Snook tables, see Appendix (T)
Page | 484
Figure 7.21
Case Discreption:
A male worker pulling a 32kg pallet for
3 meters, where the height of his hand
is 0.7m, and he aproximatly does this
process every 30 min.
• Result: maximum acceptable
weight is 37 kg.
From Snook pull table results; we can
conclude that the worker did not
exceed the weight limit.
Page | 485
Rest Required in Minutes
To find the rest required in minutes we use the equation:
R = T [(W-S)/(W-1.5)]
Where;
• T: Total work time in min.
• W: Average energy consumption of work in kcal/min.
• S: Recommended average energy expenditure (4 or 5 kcal/min).
Working hours in the factory:
10 hrs/day = 600 min
55 min/day break
Total time = 600-55 = 545min.
The rest required for the beans inspection belt workers:
W = 1.6 kcal/min.
R=545[(1.6 - 4)/(1.6 -1.5)] = 22.71 minutes < 55 minutes. Therefore, the rest
time is acceptable.
The rest required for the label inspector:
W = 3.75 kcal/min.
R=545[(3.75 - 4)/(3.75 -1.5)] = 60.5 minutes > 55 minutes. Therefore, the
worker needs more breaks.
Calculating the rest required for the final product stacker:
W = 8.75 kcal/min.
R=545[(8.75 - 4)/(8.75 -1.5)] = 350 minutes >> 55 minutes. Therefore, the job
is very risky and the worker needs more rest.
Page | 486
Discomfort Survey
A survey20 was distributed amongst seventy workers to record the level of
discomfort for each body part. It contained questions about the type of discomfort
that they suffer and to which part of the body.
Figure 7.22
The Pareto Chart results show that most of the workers are complaining from their
right and left lower leg.
Suggested tips to minimize injury risk during standing work:
1. Remember to move around.
2. Take breaks and stretch.
3. Watch your posture.
20 For more details, check Appendix (U)
Discomfort Survey
2120
11
7 75 5
3 3 3 32 2 2
Rig
ht lo
wer
leg
Left
lower
leg
Left
shol
der
Mid
lower
bac
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Rig
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Left
uppe
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Rig
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igh
Left
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Rig
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pper
arm
Left
for a
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Upp
er b
ack
Rig
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rist
Butto
cks
Page | 487
7.6 Management Control
After analyzing the results of the checklist and the survey table, it was suggested a
new, specialized department to the management system, which consists of:
Departmental Safety officer (DSO).
Safety Supervisor (SS).
DSO responsibilities:
1. Apply and update OSHA regulations.
2. Develop training and refresher courses about safety and ergonomics. These
courses include:
Instructions about using personal protective equipment.
Instructions about doing the job in a safe way.
3. Develop a monthly journal which will be distributed to the workers. These
journals contain:
The accidents that occurred in the previous month, as well as the
causes of the accidents, the suggested corrective actions and the
suggested preventive actions.
An honors list, containing the names of the workers who are
following the safety rules.
Useful safety and ergonomics information that benefits the workers.
Workers comments and answers to workers questions.
4. Develop Safety Manual
5. Organize occupational safety and health committee which consists of the
supervisors of the factory shops. Also prepare regular committee meetings to
monitor the workers’ safety performance.
6. Develop yearly safety reports to monitor the safety performance in both the
filling line, and the can production line.
7. Develop monthly injury records.
Page | 488
Safety Supervisor responsibilities:
1. Investigate the factory using workplace safety checklists21.
2. Observe workers safety performance during working hours.
3. Apply training and refreshing courses to the workers.
4. Apply safety and ergonomics tools and analyze the results.
In order to do their job properly, it is imperative for the DSO and SS to
communicate with the other departments and workers regularly, to keep them
informed of what is expected. These departments are:
Management:
1. Approval on training courses.
2. Funding.
3. Assessment of staff requirements.
4. Reactive response to existing problems.
5. Funds for modifying existing equipment.
Engineering department:
1. Evaluation of basic workstation design and making appropriate
modifications to reduce or eliminate physical stress.
Line supervisor:
1. Record important information, such as high risk jobs.
2. Identify production trends.
3. Supervise workers and eliminate any risky actions.
Operators:
1. Attentive, open to new ideas, and asking questions.
2. Suggest improvements that might control the jobs’ physical stress.
3. Follow the company’s procedures for reporting an accident.
21 Provided in Appendix (P)
Page | 489
Purchasing department:
1. Purchase appropriate ergonomics equipment and tools.
Maintenance department:
1. Maintain factory machines.
2. Maintain safety and ergonomic equipment and tools.
Injury and Accident Record
It is important for the company to have a well recorded medical injury and accident
record because it helps in understanding what happened in an accident and why it
occurred, which can lead to preventive actions in similar situations. Record keeping
steps after an accident or an injury occur include:
1. Investigate the accident.
2. Compile data in a report.
3. Analyze the report.
4. Take preventive actions so that further accidents of the same type will not
occur again.
Keeping records will make it easier to point to the direct and indirect costs of an
accident..
Direct Costs:
oo Medical expenses.
oo Replacement of damaged items.
oo Compensation paid to an injured employee.
oo … Etc.
Page | 490
Indirect Costs:
oo Lost time of injured employees.
oo Time lost on investigation, and preparing reports.
oo Damage to tools, equipment, materials or property.
oo Losses resulting from reduced productivity of injured workers upon
return to work.
oo Loss of profit because of lost work time and idle machines.
oo Overhead costs that continue during lost work.
Also, laws and regulations that require record keeping and reporting injuries are
other reasons for keeping records. At the same time, records help in identifying
hazards, are used in establishing or adjusting insurance rates, and to assign legal
penalties.
Page | 491
7.7 Conclusion
In this project, the working conditions inside the factory were assessed. When
possible, hazards were removed from the workplace to try and minimize the chances
of workers sustaining significant injuries. This was done by applying multiple human
factors tools as RULA and Snook pull/push tables, to eradicate any unhealthy
postures during work or activities that cause too much fatigue to the workers.
Of the 45 problems identified, 61% were ergonomic, 22% safety, 13% physical,
and 4% were chemical hazards. It was found that 45% of the findings have
exceeded the maximum acceptable lifting weight, body posture score, or maximum
acceptable pulling weight.
It is hoped that the company has been educated as to the important role that safety
and human factors engineers can play in ensuring the safety of their workers and
avoiding any expensive accidents from occurring.
Page | 492
References
Safety and Health for engineers, Roger L.Brauer (1994)
Human Factors in engineering and design, Sanders and McCormick- Seventh Edition
http:\\ google.com
http:\\en.wikipedia.org
http:\\www.emcins.com\lc\niosh.htm
http:\\www.cdc.gov\niosh\
http:\\www.rula.co.uk\
http:\\www.osha.gov\
https:\\www.ekginc.com\?p=services_ergonomics
http:\\www.ccohs.ca\oshanswers\safety_haz\materials_handling\
http:\\libertymmhtables.libertymutual.com\CM_LMTablesWeb\taskSelection.do?action=initTas
kSelection
http:\\www.minerals.csiro.au\safety\physhaz.htm
http:\\www.saftek.com\osha\checklists.html
http:\\www.ccohs.ca\oshanswers\safety_haz\forklift\checks.html?print
http:\\www.labour.gov.on.ca\english\hs\guidelines\lifttrucks\index.html
http:\\www.labour.gov.on.ca\english\hs\alerts\i10.html
http:\\www.worksmartontario.gov.on.ca\scripts\default.asp?contentID=2-6-
1&mcategory=health#H2
http:\\www.stayingalive.ca\fire_checklist.html
http:\\www.stanford.edu\dept\EHS\prod\training\checklist\index_inspection.html
http:\\www.safety.uwa.edu.au\forms\workplace_safety_checklist
http:\\www.worksafesask.ca\topics\hazards.html
http:\\www.safety.uwa.edu.au\policies#physical
http:\\www.ccohs.ca\oshanswers\
http:\\www.cdc.gov\niosh\docs\2004-101\default.html
http:\\www.managementsuLort.com\factorytoolbox.htm
http:\\bfa.sdsu.edu\ehs\index.htm (A
Page | 493
8. Facilities Planning
Page | 494
Page | 495
8.1 Introduction
Facilities' planning determines how an activity’s fixed assets best support
achieving the facility objectives. In general, 20%-50% of total operating expenses are
attributed to material handling. With effective facilities planning, the material handling
costs can be reduced by at least 30%.
In this project the layout of the National Canned Food Production and Trading Co.
was studied with the aim of achieving the facility’s objectives, in order to best be able
to manufacture its products and deliver them to its customers by analyzing the
existing problems and if possible finding appropriate solutions.
Enhancing the satisfaction of the objectives and relationships of the fourteen major
departments was attempted. The function of each department and its relationship
with the others was studied. The flow of raw materials, semi-finished products and
final products between the departments was focused on.
Problem Statment
The following are the problems that were noticed regarding the current layout
of the factory:
The machines are too crammed.
Pathways are obstructed.
Inventory spread throughout the factory.
Wasted Space.
Floor area not clearly visible.
Throughout this study, the feasibility of eliminating these problems was studied.
Page | 496
Objectives
The following objectives are what were aimed to be achieved throughout this
study of the facility layout and the relationship and interactions that exists between
the departments.
A. Minimize the cost of distance traveled.
B. Smooth intradepartmental flow.
C. Improve the overall aesthetics of the layout.
D. Utilize space more efficiently.
Solution Approach
The current layout of the facility was studied and new layouts were proposed
by using the RDM and CRAFT software. Both layouts were scored based on their
ability to meet the criteria set in the objectives of the study, and the one that best met
the criteria was chosen. The costs of adopting the new layout were justified by
means of cash flow analysis.
Page | 497
8.2 Current Layout
Departments
1. Can Production;
The can production department includes all the machines used to make the empty
cans. After they are produced, an overhead conveyor is used to move the empty
cans to the empty can storage department.
Figure 8.23: Seaming machine (part of the can production department).
Page | 498
2. Empty Storage Can;
The produced empty cans arrive to this area by the overhead conveyors; they are
palletized and kept until they are needed.
Figure 8.24: Empty cans in storage.
3. Storage and Mixing tanks;
In the storage and mixing department, the beans are brought from the cold storage
area and are soaked in the tanks with the all the additives necessary until they are
ready to be taken to the hoppers in the raw material preparation department.
Page | 499
4. Raw Material Preparation;
In this department, the beans are brought from the storage and mixing tanks and are
left to soak until the beans are soft enough, and are then washed in the real washer
and manually inspected for any defective beans.
Figure 8.25: Workers manually inspect the beans.
Page | 500
5. Can Filling and Coding;
In this department, the empty cans are filled using a solid filler machine with the
beans that come from the raw material preparation, and with brine using the liquid
filler machine. The cans are then coded with the production and expiration dates by
the coding machine.
Figure 8.26: Codes showing production and expiry dates.
Page | 501
6. Can Sterilizing;
After the cans have been filled and coded, they are taken to the sterilizing
department by crates. There, the cans are put in four rotaries which use steam to
cook and sterilize the can.
Figure 8.27: Can Sterilizing Machine.
Page | 502
7. Labeling and Packaging;
After the cans have been through the sterilizing department, they are moved by
crates to the labeling and packaging department where the cans are manually
transported, from the crate to the conveyor, by a worker. The cans go through the
labeling machine, then each 12 cans are wrapped together and placed on a small
box that the packaging machine makes. Every two boxes are placed on top of each
other to form a carton.
Figure 8.28: Packed cartons wrapped in plastic.
Page | 503
8. Filled Cans Inventory Store:
After the cans have been packaged into cartons of 24 cans, they are palletized and
taken to the filled cans inventory store by a forklift.
Figure 8.29: Inventory Storage.
9. Labels Storage;
The labels storage department is a small space where the boxes of empty labels are
stored until they are ready to be used by the labeling machine. When needed, boxes
of labels are transported to the labeling machine by a worker using a crate.
Figure 8.30: Labels moved from storage by crates.
Page | 504
10. Cold Storage Area;
The beans are stored in the cold storage area until they are needed for production
and are taken to the storage and mixing tanks.
11. Office;
There is one office for one employee inside the can plant. It’s very small and is
currently located next to the raw material preparation department.
12. Maintenance Room;
The maintenance room is the room where all the maintenance tools and equipment
are kept.
13. Water Treatment Room;
The water treatment room is where the water that is to be used in the production line
is cleaned and purified. It also supplies the water needed through pipes.
14. Vinegar Production Line;
The National Canned Food Production and Trading Co. also produce vinegar. The
vinegar production line is inside the can plant, and occupies a very small area.
505
Blue Print of Factory
Figure 8.9: Blue Print of the Factory.
Page | 506
As-Is Layout
Figure 8.10: As-Is Layout of the Factory.
1.
12.25 m
#5 Can Filling
and
Coding
#10 Cold
Storage
#4 Raw
Material
Preparatio
n
#3 Storage
and Mixing
Tanks
#1 Can Production
#7 Labeling and
Packaging
#8 Filled
Cans
Inventor
y
Storage
#9
Labels
inventor
y
#12
Main
t.
#11
Offic.
#2
Empty
Cans
Storage
#13
Water
Treat-
ment
Room
#1
4 V
ine
ga
r
Lin
e
#6 Can Sterilizing
Page | 507
As-Is Layout with dimensions
Figure 8.11: As-Is Layout of the Factory with dimensions.
Page | 508
As-Is Layout showing flow between departments
Figure 8.12: As-Is Layout of the Factory with dimensions.
509
Department Areas
Table 8.59: Departments' Areas.
# Department name Area (m2)
1 Can Production 254.8
2 Empty Can Storage 107.8
3 Storage and Mixing Tanks 75.14
4 Raw Material Preparations 169.6
5 Can Filling and Coding 65
6 Can Sterilizing 147.6
7 Labeling and Packaging 171.15
8 Filled Cans Inventory Store 183.52
9 Labels Storage 43.4
10 Cold Storage Area 64.24
11 Office 6.25
12 Maintenance Room 6.25
13 Water Treatment Room 30.15
14 Vinegar Production Line 7.2
Total 1332.1
510
Grid Layout
For the grid layout, all areas were rounded to the nearest 25m2
Departments 10, 11 and 14 were ignored because they are not involved in can
production/filling, and they are small.
Table 8.60: Number of Grids.
# Area (m2) Rounded # Grids
1 254.8 250 10
2 107.8 100 4
3 75.14 75 3
4 169.6 175 7
5 65 75 3
6 147.6 150 6
7 171.15 175 7
8 183.52 175 7
9 43.4 50 2
10 64.24 75 3
11 6.25 0 0
12 6.25 0 0
13 30.15 25 1
14 7.2 0 0
Page | 511
Each Grid represents 25m2
10 5 5 6 6 6 6 6 6
10 5 4 3 1 1 7 7 8
10 13 4 3 1 1 7 7 8 8
2 4 3 1 1 7 7 8 8
2 4 4 1 1 7 8 8
2 4 4 1 1 9 9
2
Figure 8.13: Grid Blocks representing the As-Is Layout.
Page | 512
8.3 Material Handling
The following are the material handling modes that were considered. They represent
the way material andcans are moved from one department to the other. The material
handling modes are described in more detail in section 4.
Empty Can's Overhead Conveyors
Figure 8.14: Overhead Conveyor.
Conveyor
Figure 8.15: Conveyor linking raw material preparation department and can filling department.
Page | 513
Forklifts
Figure 8.16: Forklifts.
Crates
Figure 8.17: Crate.
Pipes: Flow through pipes was neglected because its cost represents a
negligible proportion of the total costs.
514
Material Handling Modes between Departments
Forklifts
Crates
Overhead Conveyor
Conveyor
Can Making Flow
Water Pipes
Can Filling Flow
11
Office
12
Maintenanc
e
14
Vinegar
Line
13
Water
Treatment
Room
1
Can
Production
2
Can Inventory
Storage
10
Cold
Storage
3
Storage and
Mixing
Tanks
4
Raw
Material
Prep.
5
Can Filling
and Coding
6 Can
Sterilizing
7
Labeling
and
Packaging
9
Label
Storage
8
Filled Can
Inventory
Storage
515
Table 8.3-Material Handling Modes.
1 2 3 4 5 6 7 8 9 10 11 12 13 14
1 ― conveyor 0 0 0 0 0 0 0 0 0 0 0 0
2 ― 0 0 conveyor 0 0 0 0 0 0 0 0 0
3 ― forklifts 0 0 0 0 0 0 0 0 pipes 0
4 ― conveyor 0 0 0 0 forklifts 0 0 pipes 0
5 ― crates 0 0 0 0 0 0 0 0
6 ― crates 0 0 0 0 0 pipes 0
7 ― forklifts crates 0 0 0 0 0
8 ― 0 0 0 0 0 0
9 ― 0 0 0 0 0
10 ― 0 0 0 0
11 ― 0 0 0
12 ― 0 0
13 ― 0
14 ―
516
Table 8.61: Average Number of trips or units per day.
1 2 3 4 5 6 7 8 9 10 11 12 13 14
1 ― 96000(1)
0 0 0 0 0 0 0 0 0 0 0 0
2 ― 0 0 84000(2)
0 0 0 0 0 0 0 0 0
3 ― 20(3)
0 0 0 0 0 0 0 0 0 0
4 ― 84000(2)
0 0 0 0 20(3)
0 0 0 0
5 ― 120(4)
0 0 0 0 0 0 0 0
6 ― 120(4)
0 0 0 0 0 0 0
7 ― 39(5)
1(6)
0 0 0 0 0
8 ― 0 0 0 0 0 0
9 ― 0 0 0 0 0
10 ― 0 0 0 0
11 ― 0 0 0
12 ― 0 0
13 ― 0
14 ―
N.B. (n) denotes that the data point will be explained in the Data Collection and Calculations section.
Page | 517
Table 8.62: Average Cost (KD) per trip or unit.
1 2 3 4 5 6 7 8 9 10 11 12 13 14
1 ― 3.3E-06(7)
0 0 0 0 0 0 0 0 0 0 0 0
2 ― 0 0 3.3E-06(7)
0 0 0 0 0 0 0 0 0
3 ― 0.0944(8)
0 0 0 0 0 0 0 0 0 0
4 ― 2.7E-05(9)
0 0 0 0 0.0944(8)
0 0 0 0
5 ― 0.03068(10)
0 0 0 0 0 0 0 0
6 ― 0.03068(10)
0 0 0 0 0 0 0
7 ― 0.0944(8)
0.03068(10)
0 0 0 0 0
8 ― 0 0 0 0 0 0
9 ― 0 0 0 0 0
10 ― 0 0 0 0
11 ― 0 0 0
12 ― 0 0
13 ― 0
14 ―
Page | 518
Table 8.63: Average Cost(KD) per day.
1 2 3 4 5 6 7 8 9 10 11 12 13 14
1 ― 0.32043 0 0 0 0 0 0 0 0 0 0 0 0
2 ― 0 0 0.28037 0 0 0 0 0 0 0 0 0
3 ― 1.89E+00 0 0 0 0 0 0 0 0 0 0
4 ― 0.45125 0 0 0 0 1.89E+00 0 0 0 0
5 ― 3.68208 0 0 0 0 0 0 0 0
6 ― 3.68208 0 0 0 0 0 0 0
7 ― 3.68E+00 3.07E-
02
0 0 0 0 0
8 ― 0 0 0 0 0 0
9 ― 0 0 0 0 0
10 ― 0 0 0 0
11 ― 0 0 0
12 ― 0 0
13 ― 0
14 ―
519
Data Collection and Calculations
Avg. Number of trips/units
(1) 96,000 empty cans are produced in the can production department, and are
moved by overhead conveyors to the empty can storage area.
(2) 84,000 empty cans are moved to join the can filling and coding department
through overhead conveyors.
(3) 20 forklift trips are needed to move the raw materials needed from the storage
and mixing tanks to the raw material preparation department.
(4) 120 crate trips are needed to move the filled cans from the can filling and coding
department to the can sterilizing department and from there to the labeling and
packaging department.
(5) 39 forklift trips are needed to move the cans to the final inventory storage.
(6) 1 crate load trip is needed to move the required labels from the labels storage to
the labeling and packaging department.
Avg. Cost/trip or Avg. Cost/unit
(7) Conveyor costs 0.3204 KD/day ; 3.33778E-06 KD/can.
(8) Forklifts' drivers' average salary is KD 95.735 /month; (÷ 26 days/month) = 3.682
KD/day; (÷ 39 trips/day) = 0.094414 KD/trip.
(9) Conveyor Costs 2.256 KD/day; 2.686E-05 KD/can.
(10) Worker's (pushing crate) salary is 3.682 KD/day; (÷ 120 trips/day) = 0.030684
KD/trip.
520
8.4 Method 1: Relationship Diagramming (RDM) Method
The Relationship Diagramming Method is a procedure applied in many layout
algorithms. It involves creating a relationship chart which identifies the priority of the
presence of one department next to the other by using letters.
Table 8.64: REL Key.
Letter Relation
A Absolutely Important
E Essential
I Important
O Ordinary
U Unimportant
X Undesirable
The following REL chart was created by studying the flow between the departments
and asking factory employees and management about the necessity of the proximity
between each department and the others.
521
REL Chart
Table 8.65: Deparment Relationships.
1.
Can
pro
du
ctio
n
2.
Em
pty
can
sto
rag
e
3.
Sto
rag
e a
nd
Mix
ing
tan
ks
4.
Raw
mate
rial
pre
para
tion
s
5.
Can
filling
an
d
Co
din
g
6.
Can
ste
rilizin
g
7.
Lab
elin
g a
nd
packag
ing
8.
Fille
d c
an
s
inven
tory
sto
re
9.
Lab
els
sto
rag
e
10. C
old
sto
rag
e
are
a
11. O
ffice
12. M
ain
ten
an
ce
roo
m
13. W
ate
r treatm
en
t
roo
m
14. V
ineg
ar
pro
du
ctio
n lin
e
1. Can production - E O O E O O U U U X U I U
2. Empty can storage - I O E U U E U U U U O U
3. Storage and Mixing tanks - E O O O U U E X U I U
4. Raw material preparations - A I I I U E O U E U
5. Can filling and Coding - A I I U U X U I U
6. Can sterilizing - A I U U X U E U
7. Labeling and packaging - A E U O U O U
8. Filled cans inventory store - O U U U O U
9. Labels storage - U U U O U
10. Cold storage area - U U O U
11. Office - U O U
12. Maintenance room - O U
13. Water treatment room - U
14. Vinegar production line -
522
REL Diagram
Figure 8.18: REL Diagram.
523
Relationship Diagramming Worksheet
Table 8.66:REL Diagramming Worksheet.
1 2 3 4 5 6 7 8 9 10 11 12 13 14
A 5 4,6 5,7 7,8
E 2,5 1,5,8 4,10 3,10,1
3
1,2 13 9 2 7 3,4 4,6
I 13 3 2,13 6,7,8 7,8,13 4,8 4,5 4,5 5
O 3,4,6,
7
4,13 5,6,7 1,2,11 3 1,3 1,3,11,1
3
9,13 8,13 13 4,7,13 13 2,7,8,9
10,11,1
2
U 8,9,1
0
14
6,7,9,1
0
11,12,1
4
8,9,1
2
14
9,12,1
4
9,10,1
2
14
2,9,1
0
12,1
4
2,10,12
14
1,3,10
11,12,1
4
1,2,3,4,
5
6,10,11
12,14
1,2,5,6
7,8,9,1
1
12,14
2,8,9,1
0
12,14
1,2,3,
4
5,6,7,
8
9,10,1
1
14
14 1,2,3,4,
5
6,7,8,9
10,11,1
2
13
X 11 11 11 11 1,3,5,6
Page | 524
Iteration 1
Start with department #5 since it’s one of the departments with the highest number of
“A” relationships and it has the largest E relationships.
5
Figure 8.19: Iteration 1.
Iteration 2
Place department #6 because it has the highest number of “A” relationships with
department 5.
6 5
Figure 8.20: Iteration 2.
The next iterations are based on the following ranking hierarchy: “AA”, “AE”, “AI”,
“EE”, “EI”, “E*”, “II”, “I*”. Where * corresponds to “O” and “U”.
Page | 525
Iteration 3
From the table below, department #4 was selected.
Table 8.67: Iteration 3.
4
6 5
Figure 8.21: Iteration 3.
Dept. 1 E5*6 Dept. 9 *5*6
Dept. 2 E5*6 Dept.
10
*5*6
Dept. 3 *5*6 Dept.
11
*5*6
Dept. 4 A5I6 Dept.
12
*5*6
Dept. 7 I5 Dept.
13
E6I5
Dept. 8 I5 Dept.
14
*5*6
Page | 526
Iteration 4
From the table below, department #13 was selected.
Table 8.68: Iteration 4.
4 13
6 5
Figure 8.22: Iteration 4.
Dept. 1 E5*4*6 Dept. 10
E4*5*6
Dept. 2 E5*4*6 Dept. 11
*4*5*6
Dept. 3 E4*5*6 Dept. 12
*5*6*4
Dept. 7 I4I5 Dept. 13
E6E4I5
Dept. 8 I4I5 Dept. 14
*4*5*6
Dept. 9 *4*5*6
Page | 527
Iteration 5
From the table below, department #1 was selected.
Table 8.69: Iteration 5.
Figure 8.23: Iteration 5.
Dept. 1 E5I13*4*6 Dept. 9 *4*5*6*13
Dept. 2 E5*13*4*6 Dept.
10
E4*5*6*13
Dept. 3 E4I13*5*6 Dept.
11
*4*5*6*13
Dept. 7 I4I5*13 Dept.
12
*5*6*4*13
Dept. 8 I4I5*13 Dept.
14
*4*5*6*13
4 13
6 5 1
Page | 528
Iteration 6
From the table below, department #2 was selected.
Table 8.70: Iteration 6.
Figure 8.24: Iteration 6.
Dept. 2 E1E5*13*4*6 Dept.
10
E4*1*5*6*13
Dept. 3 E4I13*5*6 Dept.
11
*4*5*6*13
Dept. 7 I4I5*1*13 Dept.
12
*1*5*6*4*13
Dept. 8 I4I5*1*13 Dept.
14
*1*4*5*6*13
Dept. 9 *1*4*5*6*13
4 13 2
6 5 1
Page | 529
Iteration 7
From the table below, department #10 was selected.
Table 8.71: Iteration 7.
Figure 8.25: Iteration 7.
Dept. 3 E4I2I13*5*6 Dept.
10
E2E4*1*5*6*13
Dept. 7 I4I5*1*2*13 Dept.
11
*4*5*6*13
Dept. 8 I4I5*2*9*13 Dept.
12
*1*2*5*6*4*13
Dept. 9 *1*2*4*5*6*13 Dept.
14
*1*2*4*5*6*13
10
4 13 2
6 5 1
Page | 530
Iteration 8
From the table below, department #3 was selected.
Table 8.72: Iteration 8.
Figure 8.26: Iteration 8.
Dept. 3 E4E10I2I13*5*6 Dept.
11
*4*5*6*10*13
Dept. 7 I4I5*1*10*2*13 Dept.
12
*1*2*4*5*6*10*13
Dept. 8 I4I5*2*9*10*13 Dept.
14
*1*2*4*5*6*10*13
Dept. 9 *1*2*4*5*6*10*13
3 10
4 13 2
6 5 1
Page | 531
Iteration 9
From the table below, department #7 was selected.
Table 8.73: Iteration 9.
Figure 8.27: Iteration 9.
Dept. 7 I4I5*1*3*10*2*13 Dept.
11
*4*5*6*10*13
Dept. 8 I4I5*2*3*1*10*13 Dept.
12
*1*2*3*4*5*6*10*13
Dept. 9 *1*2*3*4*5*6*10*13 Dept.
14
*1*2*3*4*5*6*10*13
3 10
7 4 13 2
6 5 1
Page | 532
Iteration 10
From the table below, department #9 was selected.
Table 8.74: Iteration 10.
Figure 8.28: Iteration 10.
Dept. 8 I4I5*2*3*9*10*13 Dept.
12
*1*2*3*4*5*6*7*10*13
Dept. 9 E7*1*2*3*4*5*6*10*13 Dept.
14
*1*2*3*4*5*6*7*10*13
Dept.
11
*4*5*6*7*10*13
3 10
7 4 13 2
9 6 5 1
Page | 533
Iteration 11
From the table below, department #8 was selected.
Table 8.75: Iteration 11.
Figure 8.29: Iteration 11.
Dept. 8 I4I5*2*3*1*9*10*13 Dept. 12 *1*2*3*4*5*9*6*7*10*13
Dept.
11
*4*5*6*7*10*9*13 Dept. 14 *1*2*3*4*5*6*7*9*10*13
3 10
7 4 13 2
9 6 5 1
8
Page | 534
Iteration 12
All other departments were randomly assigned since they have the same ranking
code and they are not necessary in the can production/filling line.
Figure 8.30: Iteration 12.
3 10
7 4 13 2
9 6 5 1
14 11 8 12
Page | 535
8.5 Method 2: CRAFT
CRAFT (computerized Relative Allocation of Facilities Technique) is the first
computer aided layout algorithm. It was introduced by Armour and Buffa in 1963.
The input data is represented in the form of an initial block layout and flow and cost
matrices. The main objective behind CRAFT is to minimize total transportation cost.
CRAFT uses the input data and calculates the centroid of each department and the
rectilinear distances between the centroids, then stores them in a matrix. It then
determines the initial layout score by multiplying the from-to-chart i.e. the flow matrix,
by the distance and cost matrices.
Next, CRAFT aims to improve the layout by performing all-possible two-way
exchanges, which involve switching the place of two departments, and three-way
exchanges, which involve changing three. It selects the interchange that results in
the least cost at each iteration, unless no further reduction in cost is possible.
CRAFT was used to develop a layout alternative for the factory's current layout, if
possible, resulting in lower material handling costs.
Page | 536
CRAFT Output
Initial Layout
Figure 8.31: CRAFT Initial Layout.
Initial MH Cost (KD/day) 124.1587
CRAFT Alternatives
Figure 8.32: 2-way Exchange.
2-way Exchange MH Cost (KD/day) 94.50639
Page | 537
Figure 8.33: 3-way Exchange.
3-way Exchange MH Cost (KD/day) 110.7229
Figure 8.34: 2-way followed by 3-way Exchange.
2-way followed by 3-way Exchange MH Cost (KD/day) 94.50639
Figure 8.35: 3-way followed by 2-way Exchange.
2-way followed by 3-way Exchange MH Cost (KD/day) 74.18327
Page | 538
The best layout developed by CRAFT was using the 3-way followed by 2-way
exchange method. This layout alternative was massaged and compared with the
layout developed by the RDM method.
8.6 Comparison of Method 1 and Method 2: Massaged Layouts
A: CRAFT Alternative
10 2 2 2 1 1 1 12
10 2 5 5 1 1 1
10 13 4 5 6 1 1 8
3 4 4 4 6 1 1 8 8
3 4 4 4 6 6 11 8 8
3 7 7 7 6 6 14 8 8
7 7 7 7 9 9
Figure 8.36: Grid Blocks representing the CRAFT Alternative Layout.
\
Page | 539
B: RDM Alternative
2 2 9 9 6 7 7
2 2 3 5 6 7 7 8
1 1 3 5 6 7 7 8 8
1 1 3 5 6 7 8 8
1 1 4 4 6 10 8 8
1 1 4 4 6 10
1 1 4 4 13 10 12 14 11
Figure 8.37: Grid Blocks representing the RDM Alternative Layout.
After massaging both alternatives, the layouts were input into CRAFT to display the
actual MH cost associated with our massaged layouts.
Page | 540
A: CRAFT Layout
Figure 8.38: CRAFT Alternative Layout.
CRAFT Layout MH Cost 50.52348
B: RDM Layout
Figure 8.39: RDM Alternative Layout.
RDM Layout MH Cost 79.45359
Page | 541
Prioritization Matrix
The following evaluation criteria were selected to be used in comparing both layout
alternatives in order to determine which is better. Each criterion was then compared
to the other and a score was given based on how important each criterion was with
respect to the other.
Table 8.76: Weights used to compare the importance of each pair.
Weight Meaning
1 Equally Important
5 Significantly more important
10 Extremely more important
1/5 Significantly less important
1/10 Extremely less important
Evaluation Criteria:
A. Minimize the cost of distance traveled.
B. Smooth intradepartmental flow.
C. Improve the overall aesthetics of the layout.
D. Space utilization.
NB. Relative Weight = Row Totals/Total.
Table 8.77: Prioritization Matrix.
A B C D Row Totals
Relative Weight
A 1 5 10 5 21 0.57
B 1/5 1 5 1 7.2 0.20
C 1/10 1/5 1 1/5 1.5 0.04
D 1/5 1 5 1 7.2 0.20
Column Total
1.5 7.2 21 7.2 36.9 1.00
Page | 542
A: Minimize Cost of Distance Traveled
Table 8.78: Criterion A.
A CRAFT RDM Row Totals
Relative Weight
CRAFT 1 5 6 0.83
RDM 1/5 1 1 1/5 0.17
Column Totals
1.2 6 7.2 1
A lower MH cost was associated with the CRAFT alternative.
B: Smooth Intradepartmental Flow
Table 8.79: Criterion B.
B CRAFT RDM Row Totals
Relative Weight
CRAFT 1 10 11 1.53
RDM 1/10 1 1 1/10 0.15
Column Totals
1.1 11 12.1 1.68
Based on the study of the flow between the departments, the alternative developed
by CRAFT had a smooth flow, resulting in fewer overlapping flows.
Page | 543
C: Improve Overall Aesthetics of the Layout
Table 8.80: Criterion C.
C CRAFT RDM Row Totals
Relative Weight
CRAFT 1 1/5 1.2 0.17
RDM 5 1 6 0.83
Column Totals
6 1 1/5 7.2 1
The alternative developed by the RDM had more regular shaped departments than
the alternative developed by CRAFT, therefore it was deemed to look better than the
alternative developed by CRAFT.
D: Space Utilization
Table 8.81: Criterion D.
D CRAFT RDM Row Totals
Relative Weight
CRAFT 1 1/5 1.2 0.17
RDM 5 1 6 0.83
Column Totals
6 1 1/5 7.2 1
The RDM layout gathered all the originally wasted space into one area which the
factory could then use parts of as storage instead of having to randomly store items
throughout the factory.
Page | 544
Ranking Alternatives Based on Scores
Table 8.82: Final Ranking of Alternatives.
A B C D Row Totals
Relative Weight
CRAFT 0.47 0.30 0.01 0.03 0.81 0.72
RDM 0.09 0.03 0.03 0.16 0.32 0.28
Column Totals
0.57 0.33 0.04 0.20 1.13 1.00
Table 8.83: Alternative Scores.
Alternative Score
A 72%
B 28%
Based on the final score, the CRAFT alternative was considered to be the better
choice as the new layout.
Page | 545
8.7 Proposed Layout
#7 Labeling and
Packaging
#6 Can Sterilizing
#9 Labels
inventory
#2 Empty
Cans
Storage
#5 Can Filling
and
Coding
#3 storage
and Mixing
Tanks
#13
Water
Treat-
ment
Room
#8 Filled
Cans
Inventor
y
Storage
#10 Cold
Storage Area #12
Main
t.
#11
Offic.
#1
4 V
ine
ga
r
Lin
e
#4 Raw Material
Prep.
#1 Can Production
Figure 8.40: Proposed Factory Layout.
Page | 546
8.8 Savings in Cost
Table 8.84: Summary of Costs and Savings.
Material handling cost in initial condition 124.1587 KD/day
Material handling cost in proposed layout 50.52348 KD/day
Savings 59.3 %
Annual Savings 22,975 KD
Average Annual profit = 775911.15 KD.
Average Daily profit = 2487 KD (assuming 12 months, 26 working days).
Therefore, the average daily loss in production, for every day the factory has to stop
working in order to change the layout will equal the average daily profit. Assuming it
would take approximately 14 – 21 days to change the factory layout, it would cause a
34,818 - 52,227 KD loss in production, on average. Also, assuming productive labor
are hired to do the job at an average cost of 2000 KD to change the layout, the total
cost is between 37,000 – 55,000 KD.
Figure 8.41: Cash Flow Diagram.
0 1 2 3 4 5 6 7
P= 37,000~55,000 KD
22,975 KD 22,975 KD 22,975 KD 22,975 KD 22,975 KD 22,975 KD 22,975 KD
Page | 547
Taken P = 37,000 KD
• P = P + A(P/A, i=12%, n=2) = - 37,000 + 22,975(1.69) = 1,827 KD.
Taken P = 55,000 KD
• P = P + A(P/A, i=12%, n=3) = - 55,000 + 22,975(2.40) = 140 KD.
This change in layout is profitable in almost 2 years if 37,000 KD was invested in
changing the layout and is profitable in almost 3 years if 55,000 KD was invested.
Page | 548
8.9 Conclusion
Facilities planning techniques were used throughout this study in order to
propose a new layout that would minimize material handling costs, improve space
utilization, allow a smoother interdepartmental flow, and improve the overall
aesthetics of the layout. The factory was split into 14 departments while keeping in
mind that every department contained a part of the production line that was
inseparable.
Two methods were used to propose new, better layouts. To apply those two
methods it was necessary to develop a relationship chart, which explains the
importance of the existence of every department with respect to the other, to be used
in the relationship diagramming method. The flow and cost of the flow between
departments and the material handling modes, was also collected and used in
CRAFT software.
The layouts developed by both methods were compared based on selected
criteria and the best layout was chosen and massaged. The costs of changing the
layout were justified showing it would be profitable in a couple of years.
Page | 549
9. Conclusion
Page | 550
Page | 551
General Conclusion
By applying IMSE tools on the problems faced at the factory, many improvements
were achieved. To start off, the over filling of cans was eliminated. Proper quality
control procedures including adequate documentation and statistically reliable raw
material sampling plans were also introduced.
Also, a safer, more ergonomic work environment was provided for the
employees, in order to avoid significant injuries in the workplace and thereby
minimize any compensation or repair costs associated with major accidents.
By breaking down and analyzing all the costs of the company, areas of waste
such as over filling of cans and disparately high transportation costs for some
markets, were highlighted and minimized.
Furthermore, after studying the current maintenance policies, new plans were
proposed. By using Arena simulation software, it was proven that these new plans
minimize the maintenance costs whilst increasing daily production.
In addition, specialized inventory models, including the EOQ and EPQ, were
introduced to optimize the company’s production plans and help meet the demand
forecasted for the near future.
Having noticed that the transportation costs were high, and that the company
is struggling to meet demand, burdened by excessive overtime, distribution plans
were developed in order to reduce transportation costs and increase production
capacity.
Finally, a new proposed layout was introduced to minimize material handling
costs, utilize space more efficiently, and improve the overall aesthetics of the factory.