MGT 3110: Exam 3 Study Guide

Discussion questions1. What is the purpose of safety stock in the ROP model?2. Define aggregate production plan? What is the objective and what are the requirements for

developing one? 3. What are demand options for aggregate planning? Give examples and discuss the effects of each.4. Describe “Chase” strategy for aggregate planning and discuss the advantages and disadvantages this

approach. 5. Describe “Level” strategy for aggregate planning and discuss the advantages and disadvantages this

approach. 6. Describe “Mixed” strategy for aggregate planning and discuss the advantages and disadvantages this

approach. 7. Define independent and dependent demand items. 8. What is Master Production Schedule? 9. What is Bill of Materials? 10. What is Low-Level coding and what how is it used?11. What are the benefits of MRP? 12. What are the inputs required for MRP? 13. What is “Lot Sizing” in MRP? 14. What are the reasons for using a lot sizing method other than Lot-for-lot?

Problems1. The Winfield Distributing Company has maintained an 80% service level policy for

inventory of string trimmers. Mean demand during the reorder period is 130 trimmers, and the standard deviation is 80 trimmers. What is the value of ROP and SS?

2. The new office supply discounter, Paper Clips, Etc. (PCE), sells a certain type of ergonomically correct office chair which costs $300. The annual holding cost rate is 40%, annual demand is 600, and the order cost is $20 per order. The store is open 300 days per year and PCE has decided to establish a customer service level of 90%.a. Suppose that the lead time is a constant 4 days and the demand is variable with a

standard deviation of 2.4 chairs per day. What is the safety stock and reorder point?b. Suppose that the lead time is a variable with an average of 4 days and standard

deviation of 3 days. Further suppose that the demand is constant. What is the safety stock and reorder point?

c. Suppose that the lead time is a variable with an average of 4 days and standard deviation of 3 days. Further suppose that the demand is also variable with a standard deviation of 2.4 chairs per day. What is the safety stock and reorder point?

3. A warehouse store sells laser printer cartridges in bulk. The company places restocking orders 1000 boxes at a time. The annual demand is 7000 boxes. The demand during lead time is given below. The average demand during lead time is 60 boxes. Assume holding cost of $5 per box per year and a stock out cost of $50 per box.

Demand during lead time Probability40 0.150 0.260 0.270 0.280 0.290 0.1

Determine the least cost safety stock and the corresponding ROP.

4. An oyster bar buys fresh oysters for $3 per pound and sells them for $10 per pound. Unsold oyster at the end of the day is sold to a grocery store for $1.20 per pound. The daily demand is estimated to be 150 pounds with a standard deviation of 12 pounds. How many pounds of oysters must be ordered each day?

5. Leisure Travels, Inc. manufactures and sells Recreation Vehicles. The demand for the next four quarters is forecasted as 160, 180, 220, and 200. The labor required to produce one unit is 100 hours. Each worker works 8 hours per day for 65 days per quarter. Regular wages is $15 per hour and O.T. wages is $20 per hour. O.T. is limited to 20% regular hours. Limited subcontracting is available at the rate of $2500 per unit. Holding cost per unit per quarter is $100. Cost of hiring a worker is $350 and firing worker will cost $500. The company currently has 30 employees.a. Determine the production rate per worker per day and per quarter.b. Determine the regular time wage per worker per day and per quarter.c. Determine the O.T. cost per unit.d. Develop a “Chase” plan and the corresponding cost summary.e. Develop a “Level” plan and the corresponding cost summary.f. Develop a “Mixed” plan with a constant work force of 31 workers, but produce only

what the net demand is each month, i.e. not accumulate any inventory in excess of the safety stock. If regular time capacity is not sufficient, use O.T. production first and use subcontracting only of O.T. capacity is not enough to make up the shortage.

6. Consider the following data for an Aggregate Planning problemCost data Demand forecastWage/hour $8.50 Month Demand DaysOT pay rate $10.00 January 1000 20Subcontracting cost/unit $25.00 February 800 18Carrying cost $10.00 March 1100 22Hiring cost/unit $200.00 April 1200 20Firing cost/unit $400.00 May 1300 22

Other data Initial conditionLabor-hours/unit 2 Workers on roll 8

Hours/day 8Current production rate 50

OT Limit 15% Current inventory 50

Safety stock 10

a. Determine the production rate per worker per day.b. Determine the regular time wage per worker per day.c. Determine the O.T. cost per unit.d. Develop a “Chase” plan and the corresponding cost summary.e. Develop a “Level” plan and the corresponding cost summary. (Round up the production

rate per day)f. Develop a “Mixed” plan with a constant work force of 12 workers, but produce only what

the net demand is each month, i.e. not accumulate any inventory in excess of the safety stock. If regular time capacity is not sufficient, use O.T. production. Consider any shortage over and above OT capacity is subcontracted.

7. Consider the following Solver model for an aggregate planning problem givebn in the next page.Determine the excel formula for the following cells:

B18B19B20B23E23F23B24B31C31F31G31H31B32B37B38B39B40B41B42B43

a. What is the Solver Target cell?b. What are the Solver changing cells?c. What are the Solver constraints?d. What options of Solver must be checked?

a.

8. A Bill of Materials is desired for a bracket (A) that is made up of a base (B), two springs (C) and four clamps (D). The base is assembled from one clamp (D) and two housings (E). Each clamp has one handle (F) and one casting (G). Each housing has two bearings (H) and one shaft (I). a. Develop a product structure tree.b. The lead time for the parts are given below. Develop a time-phased product structure.c. The available inventory for each part is given in the table below. Determine the net

requirement quantities of all parts required to assemble 50 units of bracket A.

Item Lead time AvailableA 1 5B 2 5C 3 10D 2 20E 1 50F 2 150G 1 50H 1 5I 2 0

9. A product (A) consists of a base (B) and a casting (C). The base consists of a plate (P) and three fasteners (F). The lead time, current on-hand inventory and scheduled receipts are given below. All components are lot for lot. The MPS requires start of production of 100 units of product A in week 4 and 150 in week 6. Produce the MRP for the upcoming six weeks. Produce a list of all planned order releases.

Part Lead time On-hand Scheduled receiptsB 1 100 50 in week 1C 3 30 20 in week 1, 30 in week 2P 2 0 50 in week 1F 4 0 30 in week 1, 40 in week 3

10. For the following item the inventory holding cost is $0.80 per week and the setup cost is $300. Determine the lot sizes and total cost for this item under (i) Lot-for-Lot, (ii) EOQ, and (iii) PPB methods

Item LT = 1Week: 1 2 3 4 5 6 7 8Gross requirement 100 250 200 150 250 200 200 150Scheduled receiptsProjected on-hand 100Net RequirementPlanned receiptsPlanned order releases

Answers to discussion questions

1. What is the purpose of safety stock in the ROP model?The purpose of safety stock is to decrease the probability of stock out during lead time of a replenishment order, which increases the probability of meeting demand, aka service level.

2. Define aggregate production plan? What is the objective and what are the requirements for developing one?Aggregate production plan is a plan of overall production level, prepared over a rolling horizon of 12 to 18 monthly periods, or 4 to 6 quarterly periods. The objective is to minimize cost by adjusting production rates, labor levels, inventory levels, overtime work, subcontracting rates.The requirements for developing an aggregate production plan include:

a logical overall unit for measuring sales and output a forecast of demand for the planning horizon in these aggregate terms standard hours to produce one unit of the product in these aggregate term cost data such as wages (regular time, overtime, and subcontracting), inventory carrying cost,

and hiring/firing costs

3. What are demand options for aggregate planning? Give examples and discuss the effects of each.Demand options are techniques used to even out fluctuations in demand. Following are some examples.

Back ordering during high- demand periods (Effective if substitute products are not available, but may result in loss of customer orders to competition and lost customer good will)

Counter-seasonal product mix (effective in reducing huge ups and downs in demand , but may lead to products or services outside the company’s areas of expertise

Economic incentives such as discounts (loss of profit)

4. Describe “Chase” strategy for aggregate planning and discuss the advantages and disadvantages this approach.Chase strategy matches output rates to demand forecast for each period by varying the workforce levels or vary production rate.Advantage: Very low inventoriesDisadvantage: Requires frequent hiring and firing of workers

5. Describe “Level” strategy for aggregate planning and discuss the advantages and disadvantages this approach.Level strategy uses uniform production rate. Fluctuations in demand is managed through accumulation of inventory during lean demand periods.Advantage: Stable production leads to better quality and productivity Disadvantage: High levels of inventory

6. Describe “Mixed” strategy for aggregate planning and discuss the advantages and disadvantages this approach.Mixed strategy maintains uniform production rate, but does not build inventory. Overtime and subcontracting is used to meet demand.Advantage: Stable production leads to better quality and productivity and low levels of inventoryDisadvantage: Use of overtime and/or subcontracting may increase cost and may lead to quality related problems

7. Define independent and dependent demand items.Finished products whose demand is independent of production decisions are called “Independent demand” items. Items for which demand can be directly calculated from production decisions are called “Dependent demand” items. These are raw-materials and parts required for the production of the finished goods.

8. What is Master Production Schedule?Master Production Schedule specifies production quantities of each Independent Demand item for a planning horizon of 12 to 15 weeks. Total of MPS quantities must be in accordance with the aggregate production plan.

9. What is Bill of Materials?Bill of materials is structured list of components, ingredients, and materials needed to make an end product. Items needed to produce a given part are called components or “children”. The part into which the components go us called “Parent”. The BOM also gives the number of units of a child item needed to produce one unit of the parent item.

10. What is Low-Level coding and what how is it used?A level code starting from zero at the top of the BOM tree and incremented by 1 going down each level of the BOM tree is assigned. Then, the lowest level at which an item appears is called Low-Level code. The MRP computations are processed one level at a time, starting from level zero.

11. What are the benefits of MRP? Better response to customer orders Faster response to market changes Improved utilization of facilities and labor Reduced inventory levels

12. What are the inputs required for MRP? Master Production Schedule Bill of Materials Inventory status

13. What is “Lot Sizing” in MRP?The process of combining net requirements into production lots is called lot sizing.

14. What are the reasons for using a lot sizing method other than Lot-for-lot? Lot-for-lot often requires too many lots that may not be economically justifiable Sometime lot-for-lot generates absurdly small lots

Answers to problems

1. Given dL = 130, dLT = 80, and for 80% service level, Z = 0.84ROP = 130 + 0.84 x 80 = 197.2, or round up to 198 for at least 80% service level

2. d = D/No. of days per year = 600/300 = 2 per dayZ for 90% service level = 1.285

a. Given: L = 4 days Constant, d = 2.4 per day, therefore dLT = 2.4 √4 = 4.8Safety stock = Z dLT = 1.285 x 4.8 = 6.2 or 7 (round up for at least 90% service level)ROP = dL + SS = (2 chairs/day * 4) + 7 = 15

b. Given: L = 4 days with L = 3 and demand is constant, dLT = 2 (3) = 6Safety stock = Z dLT = 1.285 x 6 = 7.7 or 8 (round up for at least 90% service level)ROP = dL + SS = (2 chairs/day * 4) + 8 = 16

c. Given: L = 4 days with L = 3 , and d = 2.4 per day, therefore dLT = √4 (2.4)2+2232 = 7.684Safety stock = Z dLT = 1.285 x 7.684 = 9.9 or 10 (round up for at least 90% service level)ROP = dL + SS = (2 chairs/day * 4) + 10 = 18

3. Number of orders per year = 7, H = $5, S = $50

ROPSafety stock Carrying cost Expected stock out

Stock out cost/order

Stock out cost/year

Total cost

60 0 0 (10x.2 + 20x.2 + 30x.1) = 9 9 x $50 = $450 $3,150 $3,15070 10 10 x $5 = $50 (10x.2 + 20x.1) = 4 4 x $50 = $200 $1,400 $1,45080 20 20 x $5 = $100 (10x.1) = 1 1 x $50 = $50 $350 $45090 30 30 x $5 = $150 0 0 $0 $150

Least cost safety stock = 30, ROP = 90

4.Cs = Lost profit = Selling price per unit – Cost per unit = 10 – 3 = $7Co = Cost/unit – salvage value/unit = 3 – 1.20 = $1.80

Optimum service level = 7/(7 + 1.80) = 0.795 = 79.5%From normal table, for 79.5% service level, Z = 0.83Order quantity = + Z = 150 + 0.825 (12) = 159.9 or 160

5.Hiring cost/worker = 350 Worker hours/quarter = 520Firing cost/worker = 500 Standard hours/unit = 100RT Wage/hour = 15 Holding cost = 100OT wage rate/hour = 20Sub-contracting cost/unit = 2500

a. Production rate/worker/day = 8 hours per day/100 hours per unit = 0.08 per worker/dayProduction rate/worker/quarter = 0.08/worker/day x 65 days/quarter = 5.2/worker/ quarter

b. Wage rate per worker per day = $15/hour x 8 hours/day = $120Wage rate per worker per quarter = $15/hour x 8 hours/day x 65 days/quarter = $7800

c. OT cost/unit = $20/hour x 100 hours/unit = $2000

d. Chase plan

Period DemandProduction required

Workers needed

Workers needed (Rounded)

Hired workers

Fired workers

30

1 160160–(0–0) =

160 160/5.2=30.77 31 1 02 180 180 180/5.2=34.62 35 4 03 220 220 220/5.2=42.31 43 8 04 200 200 200/5.2=38.46 39 0 4

148 13 4Cost summaryRegular wages 148 workers-quarters x $7800 = 1,154,400O.T. cost =S.C. costHiring cost 13 workers x $350 = 4,550Firing cost 4 workers x $500 = 2,000Carrying costTotal cost $1,160,950

d. Level PlanSum of demand = 760Average demand = 760/4 = 190 i.e. = production per quarter

Period Demand RT Production E.I.0

1 160 190 302 180 190 403 220 190 104 200 190 0

Average demand = 190 760 80Workers needed/quarter = 36.54

Workers rounded up = 37Cost summaryRegular wages 37 workers x 4 quarters x $7800 = 1,154,400O.T. cost =S.C. costHiring cost (37 workers – 30 workers) x $ 350 = 2,450Firing cost -Carrying cost 80 x $100 = 8,000Total cost $1,164,850

f. Mixed planPlan CNo. of workers = 31Production per quarter with 31 workers = 31 x 5.2 = 161.2 or 161O.T. capacity/quarter = 161 x 20% = 32

Period DemandProduction

capacity RT ProductionShortage O.T

CapacityO.T.

Production S.C.1 160 161 Min(160,161) =160 160 – 160=0 32 0 02 180 161 Min(180,161) =161 180-161=19 32 Min(19,32)=19 03 220 161 Min(220,161) =161 220-161=59 32 Min(59,32)=32 59-32=274 200 161 Min(200,161) =161 200-161=39 32 Min(39,32)=32 39-32=7

643 83 34

Cost summaryRegular wages 31 workers x 4 quarters x $7800 = 967,200O.T. cost = 83 units x $2000 166,000S.C. cost 34 units x $2500 = 85,000Hiring cost (31 – 30) x $350 = 350Firing cost -Carrying cost -Total cost $1,218,550

6.a. Production rate/worker/day = 8 hours per day/2 hours per unit = 4 per worker/dayb. Wage rate per worker per day = $8.50/hour x 8 hours/day = $68c. OT cost/unit = 2 hours/unit x $10/hour = $20/unitd. Chase plan:

Month Demand Production Days Production rate Hire Fire50

Jan 1000 960 20 960/20 = 48 0 2Feb 800 800 18 800/18 = 44 0 4March 1100 1100 22 1100/22 = 50 6 0April 1200 1200 20 1200/20 = 60 10 0May 1300 1300 22 1300/22 = 59 0 1

16 7

Production rate WorkersWorkers

(Rounded) Wages5048 48/4 = 12 12 $16,32044 44/4 = 11 11 $13,46450 50/4 = 12.5 13 $19,44860 60/4 = 15 15 $20,40059 59/4 = 14.75 15 $22,440

$92,072

Cost summaryRegular wages $92,072OT costSubcontractingHiring cost $3,200.00Firing cost $2,800.00Carrying cost $500.00Total cost $98,572

e. Level planNet total demand = 5400 – (50 – 10) = 5360Average demand rate /day = 5360/102 days = 52.5Production rate/day – rounded up 53No. of workers needed = 53/4 = 13.25Rounded number of workers = 14

Month Demand Days Production E.I.50

Jan 1000 20 53 x 20 = 1060 110Feb 800 18 53 x 18 =- 954 264March 1100 22 53 x 22 = 1166 330April 1200 20 53 x 20 = 1060 190May 1300 22 53 x 22 = 1166 56

5400 102 950Cost summaryRegular wages $97,104OT costSubcontractingHiring cost $600Firing cost $0Carrying cost $9,500Total cost $107,204

f. Mixed plan Workers 12Production rate/day = 12 x 4 unit/day = 48

Month Requirement Days Capacity Production Shortage

Jan 960-(0-0)=960 20 20x48=960 Min(960,960)=960 0Feb 800 18 18x48=864 Min(800,864)=800 0March 1100 22 22x48=1056 Min(1100,1056)=1056 1100-1056=44April 1200 20 20x48=960 Min(1200,960)=960 1200-960=240May 1300 22 22x48=1056 Min(1300,1056)=1056 1300-1056=244

102

Shortage OT Capacity OT SC

0 00 01100-1056=44 1056x0.15=158 44 44-44 = 01200-960=240 960x0.15=144 144 240 – 144 = 961300-1056=244 1056x0.15=158 158 244 – 158 = 86

346 182

Cost summaryRegular wages = 12 workers x $68/day x 102 days = $83,232OT wages = 346 units x $20 per unit = $6,920SC = 182 x $20 = $4,550Hiring cost $0Firing cost (50 – 48) x $400 $800Carrying cost = 10 units x 5 months x $10 = $500Total cost $96,002

7.

B18 =B14/B13b. B43

c. C23:D26, D31:E34

d. D31:D34 <= H31:H34G31:G34 >= E15C23:D26 = Integer (if needed)D31:E34 = Integer (if needed)

e. Assume linear modelAssume non-negative

B19 =B14*B5B20 =B13*B6B23 =E13E23 =B23+C23-D23F23 =E23*F6*$B$18B24 =E23B31 =E14C31 =F23F31 =E6G31 =B31+SUM(C31:E31)-F31H31 =C31*$B$15B32 =G31B37 =SUMPRODUCT(E23:E26,F6:F9)*B19B38 =D35*B20B39 =E35*B7B40 =C27*B9B41 =D27*B10B42 =G35*B8B43 =SUM(B37:B42)

A

B C2

D4

F

E2

H2 I

D1

GF G

8.

F

D

G

B

H

E

I

C A

F

D

G

1 2 3 4 5 6 7

Lead time = 7 weeks

Part Gross Available Net

A 50 5 50 – 5 = 45B 1 x A = 45 5 45 – 5 = 40C 2 x A = 2 x 45 = 90 10 90 – 10 = 80D 4 x A + 1 x B = 4 x 45 + 40 = 220 20 220 – 20 = 200E 2 x B = 80 50 80 – 50 = 30F 1 x D = 200 150 200 – 150 = 50G 1 x D = 200 50 200 – 50 = 150H 2 x E = 2 x 30 = 60 5 60 – 5 = 55I 1 x E = 30 0 30 – 0 = 30

9.1 2 3 4 5 6

MPS start for A 100 150

Item B Lead time = 1Week: 1 2 3 4 5 6Gross requirement 0 0 0 100 0 150Scheduled receipts 50Projected on-hand 100 100 150 150 150 50 50Net requirement 100Planned receipts 0 0 0 0 0 100Planned order releases 0 0 0 0 100 0

Item C Lead time = 3Week: 1 2 3 4 5 6Gross requirement 0 0 0 100 0 150Scheduled receipts 20 30Projected on-hand 30 30 50 80 80 0 0Net requirement 20 150Planned receipts 0 0 0 20 0 150Planned order releases 20 0 150 0 0 0

Item P Lead time = 2Week: 1 2 3 4 5 6Gross requirement 0 0 0 0 100 0Scheduled receipts 50Projected on-hand 0 0 50 50 50 50 0Net requirement 50Planned receipts 0 0 0 0 50 0Planned order releases 0 0 50 0 0 0

Item F Lead time = 4Week 1 2 3 4 5 6Gross requirement 0 0 0 0 300 0

Scheduled receipts 30 40Projected on-hand 0 0 30 30 70 70 0Net requirement 230Planned receipts 0 0 0 0 230 0Planned order releases 230 0 0 0 0 0

Planned order releases:A has releases of 100 in week 4, 150 in week 7B has a release of 100 in week 5C has releases of 20 in week 1, 150 in week 3P has a release of 50 in week 3F has a release of 230 in week 1

10. (i) L-4-LItem LT = 1Week: 1 2 3 4 5 6 7 8Gross requirement 100 250 200 150 250 200 200 150Scheduled receiptsProjected on-hand 100 100 0 0 0 0 0 0 0Net Requirement 0 250 200 150 250 200 200 150Planned receipts 0 250 200 150 250 200 200 150Planned order releases 250 200 150 250 200 200 150 0

No. of setup = 7Carrying cost = 0Setup cost = 7 x $300 = 2100Total cost = 2100

(ii) EOQ:Total demand for 8 weeks = 1500D (1 year) = (1500/8) x 52 weeks/year = 9750H (for 52 weeks) = $0.80/week x 52 weeks = $41.60S = 300

Q = √ 2 (9750 )30041.6

= 375

Item LT = 1Week: 1 2 3 4 5 6 7 8Gross requirement 100 250 200 150 250 200 200 150Scheduled receipts 0 0 0 0 0 0 0 0Projected on-hand 100 100 0 125 300 150 275 75 250Net Requirement 0 250 75 0 100 0 125 0Planned receipts 0 375 375 0 375 0 375 0Planned order releases 375 375 0 375 0 375 0 0

Annual setup cost = (D/Q) S = (9750/375) x 300 = 7800Annual holding cost = (Q/2)H per year = (375/2) x 41.60 = 7800

Annual cost = Annual setup cost + Annual holding cost = 7800 + 7800 = 15600Weekly cost = Annual cost/52 = 15600/52 = 300Cost for 8 weeks = Cost per week x 8 weeks = 300 x 8 = 2400

(iii) PPB

EPP = 300/0.80 = 375Item LT = 1Week: 1 2 3 4 5 6 7 8Gross requirement 100 250 200 150 250 200 200 150Scheduled receipts 0 0 0 0 0 0 0 0Projected on-hand 100 100 0 350 150 0 200 0 150Net Requirement 0 250 250 200Planned receipts 0 600 450 350Planned order releases 600 450 350

Periods combined

Quantities combined

Periods brought forward for the last quantity

New Part-periods

Total combined part-periods

Lot #1 with planned receipt in week #2

2 250 0 0 0

2, 3 250 + 200 = 450 1 200x1 = 200 200

2, 3, 4 450 + 150 = 600 2 150 x 2 = 300 200 + 300 = 500(500 is closer to EPP of 375)

Lot #2 with planned receipt in week #5

5 250 0 0 0

5, 6 250 + 200 = 450 1 200 x 1 = 200 200(200 is closer to EPP of 375)

5, 6, 7 450 + 200 = 650 2 200 x 2 = 400 200 + 400 = 600

Lot #1 with planned receipt in week #2

7 200 0 0 0

7, 8 200 + 150 = 350 1 1x 150 = 150 150

Summary:Lot # Planned order release in Week Weeks covered Lot size Lot PP

1 Week 1 2, 3, 4 600 500

2 Week 4 5, 6 450 200

3 Week 6 7, 8 350 150

850

Total cost = 3 Setups x 300 + 850 x 0.8 = $1,580