solution of outsourcing problem for filatoi riuniti
TRANSCRIPT
Background introduction
• Filatoi Riuniti (F.R) is an Italian spinning mill.
• F.R has limited machine capacity and have
to outsource spinning product from six local
mills, cost too much.
• Milan Consulting Group Inc. was hired by
the new CEO of F.R to solve the problem.
Background introduction
Minimize the cost
Product bought from each supplier (Kg/month)
Size Size
Supplier Extrafine Fine Medium Coarse
Ambrosi - - - -
Bresciani - - - -
Castri - - - -
De Blasi - - - -
Estensi - - - -
Filatoi R. - - - -
Giuliani - - - -
DEMAND TO MEET
(Kg/month)
Extrafine Fine Medium Coarse
25,000 26,000 28,000 28,000
Meet the demand
Formula to set up the model
•Total cost=
Cost of production+Cost of transportation
(Input 28 decision variables)
•Cost of production= Output X Unit price
•Cost of transportation= Output X Transport unit price
•Prodcution time= Machine hours required X Output
Model(FILATOIR.XLS)
DECISION VARIABLES MACHINE HOURS REQUIRED FOR PRODUCTION
Yarn produced by each factory (Kg/month) (Hours/Kg)
Size Size
Supplier Extrafine Fine Medium Coarse Supplier Extrafine Fine Medium Coarse
Ambrosi Ambrosi 0.400 0.375 0.250
Bresciani Bresciani 0.700 0.500 0.350 0.250
Castri Castri 0.675 0.450 0.400 0.250
De Blasi De Blasi 0.450 0.350 0.200
Estensi Estensi 0.650 0.450 0.400 0.250
Filatoi R. Filatoi R. 0.625 0.500 0.425 0.425
Giuliani Giuliani 0.700 0.450 0.350 0.400
COST OF PRODUCTION COST OF TRANSPORTATION
($/Kg) ($/Kg)
Size Size
Supplier Extrafine Fine Medium Coarse Supplier Extrafine Fine Medium Coarse
Ambrosi 13.00 10.65 9.60 Ambrosi 0.30 0.30 0.45 0.45
Bresciani 17.40 14.10 11.20 9.45 Bresciani 0.40 0.40 0.60 0.60
Castri 17.40 14.22 11.00 9.50 Castri 0.80 0.80 1.20 1.20
De Blasi 14.30 11.25 9.60 De Blasi 0.70 0.70 1.05 1.05
Estensi 17.50 13.80 11.40 9.60 Estensi 0.70 0.70 1.05 1.05
Filatoi R. 18.25 13.90 11.40 8.90 Filatoi R. - - - -
Giuliani 19.75 13.90 10.75 9.40 Giuliani 0.50 0.50 0.75 0.75
($/Kg/Km) 0.010 0.010 0.015 0.015
DEMAND TO MEET
(Kg/month)
Extrafine Fine Medium Coarse
25,000 26,000 28,000 28,000
Xi,j
Constraints
CONSTRAINTS Actual Sign RHS
Extrafine 25,000 = 25,000
Fine 26,000 = 26,000
Medium 28,000 = 28,000
Coarse 28,000 = 28,000
Ambrosi ex - = -
De Blasi ex - = -
Ambrosi 2,500 <= 2,500
Bresciani 3,000 <= 3,000
Castri 2,500 <= 2,500
De Blasi 714 <= 2,600
Estensi 2,500 <= 2,500
Filatoi R. 38,000 <= 38,000
Giuliani 2,500 <= 2,500
Demand
Special
Capacity
Total Cost
Total cost (production+transportation) ($)
1,382,544
Cost of production ($)
1,365,801
Cost of transportation ($)
16,743
Result
DECISION VARIABLES
Product bought from each supplier (Kg/month)
Size
Supplier Extrafine Fine Medium Coarse
Ambrosi - 6,250 - -
Bresciani 4,286 - - -
Castri 3,704 - - -
De Blasi - - 2,040 -
Estensi 3,846 - - -
Filatoi R. 13,164 19,750 18,817 28,000
Giuliani - - 7,143 -
Upgrade with extra capacity 600H/M for Factory F, but
cost $1500/M, is it worthy?
• Solution 1
① Compare the saving cost with extra rental cost
② Reassign the total capacity of Factory F by 38,600
③ Total cost = $ 1,381,274
compare with previous $ 1,382,544
④ The extra saving $1,270 /M < extra cost $1,500/M
• So do not rent the upgrade
Rent for extra capacity Cont’— Solution 2
• Extra 600H allocation for factory F to produce Medium production
=> 600/0.425=1,412 kg
• Cost Saving = ($12.3/kg-$11.4kg)*1,412 kg
= $1,271 < extra cost $1,500 monthly
• So do not rent the upgrade
• Compare the saving cost with
extra rental cost
• Total cost = C production + C transportation
TOTAL COST
($/Kg)
Size
Supplier Extrafine Fine Medium Coarse
Ambrosi 13.30 11.10 10.05
Bresciani 17.80 14.50 11.80 10.05
Castri 18.20 15.02 12.20 10.70
De Blasi 15.00 12.30 10.65
Estensi 18.20 14.50 12.45 10.65
Filatoi R. 18.25 13.90 11.40 8.90
Giuliani 20.25 14.40 11.50 10.15
Allocation of Extra Production PowerCOST OF PRODUCTION COST OF TRANSPORTATION
($/Kg) ($/Kg)
Size SizeRound trip
distance
Supplier Extrafine Fine Medium Coarse Supplier Extrafine Fine Medium Coarse (Km)
Ambrosi 13.00 10.65 9.60 Ambrosi 0.30 0.30 0.45 0.45 30
Bresciani 17.40 14.10 11.20 9.45 Bresciani 0.40 0.40 0.60 0.60 40
Castri 17.40 14.22 11.00 9.50 Castri 0.80 0.80 1.20 1.20 80
De Blasi 14.30 11.25 9.60 De Blasi 0.70 0.70 1.05 1.05 70
Estensi 17.50 13.80 11.40 9.60 Estensi 0.70 0.70 1.05 1.05 70
Filatoi R. 18.25 13.90 11.40 8.90 Filatoi R. - - - - -
Giuliani 19.75 13.90 10.75 9.40 Giuliani 0.50 0.50 0.75 0.75 50
($/Kg/Km) 0.010 0.010 0.015 0.015
DECISION
VARIABLES
Product bought from each supplier (Kg/month)
Size
Supplier Extrafine Fine Medium Coarse
Ambrosi - 6,250 - -
Bresciani 4,286 - - -
Castri 3,704 - - -
De Blasi - - 2,040 -
Estensi 3,846 - - -
Filatoi R. 13,164 19,750 18,817 28,000
Giuliani - - 7,143 -
TOTAL COST
($/Kg)
Size difference for each size
Supplier Extrafine Fine Medium Coarse Extrafine Fine Medium Coarse
Ambrosi 13.30 11.10 10.05 0.600
Bresciani 17.80 14.50 11.80 10.05 0.45
Castri 18.20 15.02 12.20 10.70 0.05
De Blasi 15.00 12.30 10.65 (0.900)
Estensi 18.20 14.50 12.45 10.65 0.05
Filatoi R. 18.25 13.90 11.40 8.90 - - - -
Giuliani 20.25 14.40 11.50 10.15 (0.100)
Rent for extra 300H/M only to produce M in F with same productivity,
production cost is $5.7/kg, but cost $3000/M, is it worthy?
Extra Saving will be :
($11.4/kg-$5.7kg)*706kg = $4,024 >
extra cost $3,000 /M
Extra 300H allocation for F to produce M
→ extra productivity: 300/0.425=706 kg
COST OF PRODUCTION
($/Kg)
Size
Supplier Extrafine Fine Medium Coarse
F 18.25 13.90 11.40 8.90
F-EX - - 5.70 -
MACHINE HOURS REQUIRED FOR
PRODUCTION
(Hours/Kg)
Size
Supplier Extrafine Fine Medium Coarse
F 0.625 0.500 0.425 0.425
Compare the saving cost with extra rental cost
So rent the machine
A new client is interested in purchasing 6,000 kg/month.
What is the minimum quoting price?
• Change the demand for medium size yarn
• Calculate the minimum price using the variation of the total cost
Minimum quoting price /kg
= (1,457,238 - 1,382,544) / 6,000 = 74,694 / 6,000 = $ 12.45 / kg
DEMAND TO MEET
(Kg/month)
Extrafine Fine Medium Coarse
25,000 26,000 28,000 28,000
DEMAND TO MEET
(Kg/month)
Extrafine Fine Medium Coarse
25,000 26,000 34,000 28,000
Total Cost ($)
1,382,544
Total Cost ($)
1,457,238
A new client is interested in purchasing 6,000 kg/month.
The minimum quoting price is fixed per kg?
• Would $ 12.45 be a fixed price per kg?
No.
We still need to find out how many quantity the order
is and how long the contract will be from the client.
What additional questions might be asked to this client?
What is the exact order quantity in the contract?
• > 6,000
• = 6,000 ($ 12.45 /kg)
• < 6,000 ($ 12.30 /kg)
What is the contract time for the order?
• Long term
• Short term
Sensitivity Analysis
• In case of the internal production costs of
Filatoi Riuniti could vary within a 5% range.
• In case of the production capacity of De
Blasi could vary within a 20% range.
Internal Production Costs
• Analysis:
– The change of internal production costs may cause the change of the available lowest which could cause the change of production allocation.
• Vertical Scenario:
– The scenario changed between the costs of F. and those of other factories.
• Horizontal Scenario:
– The scenario changed between the costs of different Size of F. and those of other factories.
Analysis the Key Factors
Vertical Scenario
—— Absolute Lower
Horizontal Scenario
—— Comparative Lower
Size
Supplier Extrafine Fine Medium Coarse
Ambrosi -100.00% -6.47% -6.58% 7.87%
Bresciani -4.66% 1.44% -1.75% 6.18%
Castri -4.66% 2.30% -3.51% 6.74%
De Blasi -100.00% 2.88% -1.32% 7.87%
Estensi -4.11% -0.72% 0.00% 7.87%
Filatoi R. 0.00% 0.00% 0.00% 0.00%
Giuliani 8.22% 0.00% -5.70% 5.62%
Size
Supplier Extrafine Fine Medium Coarse
Ambrosi -100.00% 0.00% -18.08% -26.15%
Bresciani 23.40% 0.00% -20.57% -32.98%
Castri 22.36% 0.00% -22.64% -33.19%
De Blasi -100.00% 0.00% -21.33% -32.87%
Estensi 26.81% 0.00% -17.39% -30.43%
Filatoi R. 31.29% 0.00% -17.99% -35.97%
Giuliani 42.09% 0.00% -22.66% -32.37%
All Increased by 5% All Decreased by 5%
Just Increase Extrafine by 5% Just decrease Extrafine by 5%
Just Increase Fine by 5% Just decrease Fine by 5%
Just Increase Medium by 5% Just decrease Medium by 5%
Just Increase Coarse by 5% Just decrease Coarse by 5%
Affected Production 13,876
Total Production 107,000
Percentage 13%
Maximum Error 5%
Range of Result 0.65%
Results of Simulation
Scenario of the change of production
All Increased by 5% No Change All Decreased by 5% No Change
Just Increase Extrafine by 5% Change Just decrease Extrafine by 5% Change
Just Increase Fine by 5% Change Just decrease Fine by 5% Change
Just Increase Medium by 5% Change Just decrease Medium by 5% Change
Just Increase Coarse by 5% No Change Just decrease Coarse by 5% No Change
For Example:Product of Supplier Origin
Size
Supplier Extrafine Fine Medium Coarse
Ambrosi - 6,250 - -
Bresciani 4,286 - - -
Castri 3,704 - - -
De Blasi - - 2,040 -
Estensi 3,846 - - -
Filatoi R. 13,164 19,750 18,817 28,000
Giuliani - - 7,143 -
Just Increase Fine by 5% Changed
Size
Supplier Extrafine Fine Medium Coarse
Ambrosi - 6,250 - -
Bresciani 4,286 - - -
Castri 3,704 - - -
De Blasi - 1,502 - -
Estensi - 5,556 - -
Filatoi R. 17,011 7,137 28,000 28,000
Giuliani - 5,556 - -
Analysis the Results
The Typical Scenario With Change
The Costs Change Caused by production Allocation
Cost Senario of Production Allocation of F
Filatoi R. Extrafine Fine Medium Coarse
Origin 13,164 19,750 18,817 28,000
Increase_Fine 17,011 7,137 28,000 28,000
Increase_Medium 17,450 26,000 5,162 28,000
Dedrease_Extra 19,202 14,194 16,474 28,000
Decrease_Fine 13,164 26,000 11,464 28,000
Decrease_Medium 13,164 11,944 28,000 28,000
Cost Senario of Difference of Cost of Production
Filatoi R. Unit Cost By Cost Total By Allocate
Origin
Increase_Fine 0.695 4,960 10,365 5,405
Increase_Medium 0.570 2,942 8,625 5,683
Dedrease_Extra (0.913) (17,522) (13,093) 4,429
Decrease_Fine (0.695) (18,070) (15,702) 2,368
Decrease_Medium (0.570) (15,960) (13,258) 2,702
The 5% range of estimation of internal production could cause the change of production allocation,
however the typical monthly costs variance caused by the change of production allocation are less than 6k.
It is unnecessary to change our linear programming model.
Production Capacity of D.
• Analysis:
– The change of production capacity of De Blasi
will change the constraints which may cause
the change of production allocation.
• Compare:
– (2600 * 20%) and the tolerance of capacity in
Sesnsitivity Report.
Insight of Sensitivity Report
终 阴影 约束 允许的 允许的
单元格 名称 值 价格 限制值 增量 减量$C$45 Extrafine Actual 25000 19.57352941 25000 3664.143264 1387.285307
$C$46 Fine Actual 26000 14.95882353 26000 4580.17908 1734.106634
$C$47 Medium Actual 28000 12.3 28000 5388.445977 2040.125452
$C$48 Coarse Actual 28000 9.8 28000 5388.445977 2040.125452
$C$50 Extrafine Actual 0 -19.27352941 0 1387.285307 0
$C$51 Extrafine Actual 0 -18.87352941 0 1387.285307 0
$C$54 Ambrosi Actual 2500 -4.147058824 2500 693.6426536 1832.071632
$C$55 Bresciani Actual 3000 -2.533613445 3000 971.0997151 2564.900285
$C$56 Castri Actual 2500 -2.034858388 2500 936.4175824 2473.296703
$C$57 De Blasi Actual 714.0439082 0 2600 1E+30 1885.956092
$C$58 Estensi Actual 2500 -2.113122172 2500 901.7354497 2381.693122
$C$59 Filatoi R. Actual 38000 -2.117647059 38000 867.0533171 2290.08954
$C$60 Giuliani Actual 2500 -2.285714286 2500 714.0439082 1885.956092
The production allocation will not change within a 20% range of
production capacity of D.
•Ambrosi mill presently can only produce medium and coarse size yarn, and they would incur substantial one-time set-up costs to ramp up for the production of fine size yarn.
•The optimal solution of the model indicates that it would be in Filatoi’sinterests for the Ambrosi mill to produce fine size yarn.
•The owners want to maintain good business relations with Filatoi, but they do not want to bear the full cost of ramping up for production of fine yarn.
•The contracts that Filatoi currently has with its customers will not expire for at least another 12 months.
Up to what amount would Filatoi be willing to share the one-time set-up costs for production of fine yarn with the owners of the Ambrosi mill?
What amount would Filatoi be willing to share the one-time set-up costs
Ambrosi can produce fine size yarn Ambrosi cannot produce fine size yarnDECISION VARIABLES DECISION VARIABLES
Product bought from each supplier (Kg/month) Product bought from each supplier (Kg/month)
Size Size
Supplier Extrafine Fine Medium Coarse Supplier Extrafine Fine Medium Coarse
Ambrosi - 6,250 - - Ambrosi - 0 6,667 -
Bresciani 4,286 - - - Bresciani 4,286 - - -
Castri 3,704 - - - Castri 3,704 - - -
De Blasi - - 2,040 - De Blasi - - 2,726 -
Estensi 3,846 - - - Estensi 3,846 - - -
Filatoi R. 13,164 19,750 18,817 28,000 Filatoi R. 13,164 26,000 11,464 28,000
Giuliani - - 7,143 - Giuliani - - 7,143 -
TOTAL COST TOTAL COST
($/Kg) ($/Kg)
Size Size
Supplier Extrafine Fine Medium Coarse Supplier Extrafine Fine Medium Coarse
Ambrosi 13.30 11.10 10.05 Ambrosi 13.30 11.10 10.05
Bresciani 17.80 14.50 11.80 10.05 Bresciani 17.80 14.50 11.80 10.05
Castri 18.20 15.02 12.20 10.70 Castri 18.20 15.02 12.20 10.70
De Blasi 15.00 12.30 10.65 De Blasi 15.00 12.30 10.65
Estensi 18.20 14.50 12.45 10.65 Estensi 18.20 14.50 12.45 10.65
Filatoi R. 18.25 13.90 11.40 8.90 Filatoi R. 18.25 13.90 11.40 8.90
Giuliani 20.25 14.40 11.50 10.15 Giuliani 20.25 14.40 11.50 10.15
DEMAND TO MEET DEMAND TO MEET
(Kg/month) (Kg/month)
Extrafine Fine Medium Coarse Extrafine Fine Medium Coarse
25,000 26,000 28,000 28,000 25,000 26,000 28,000 28,000
OBJECTIVE FUNCTION OBJECTIVE FUNCTION
Total cost (production+transportation) ($) 1,382,544 Total cost (production+transportation) ($) 1,384,912
Filatoi is willing to share the one-time set-up cost :
1,384,912 - 1,382,544 = 2,368
What amount would Filatoi be willing to share the one-time set-up costs
Capacity: 25005000(Overtime shift)
Workers’ salary increase 13%
Workers’ salary / Production cost ≈50%
New mill capacity: 2500
New mill production cost: $19.75/KG $21.03/KG
Production cost ×50% ×(1+13%)+ Production cost ×50%
COST OF PRODUCTION
($/Kg)
Size
Supplier Extrafine Fine Medium Coarse
New mill 21.03 14.80 11.45 10.01
Giuliani double capacity—New mill with capacity of 2500
DECISION VARIABLES
Product bought from each supplier (Kg/month)
Size
Supplier Extrafine Fine Medium Coarse
Ambrosi - 6,250 - -
Bresciani 4,286 - - -
Castri 3,704 - - -
De Blasi - - 2,040 -
Estensi 3,846 - - -
Filatoi R. 13,164 19,750 18,817 28,000
Giuliani - - 7,143 -
Total Cost: 1,382,544
Total Cost: 1,382,338
FILATOIR-twinkle.xls
DECISION VARIABLES
Product bought from each supplier (Kg/month)
Size
Supplier Extrafine Fine Medium Coarse
Ambrosi - 6,250 - -
Bresciani 4,286 - - -
Castri 3,704 - - -
De Blasi - - - -
Estensi 3,846 - - -
Filatoi R. 13,164 19,750 18,817 28,000
Giuliani - - 7,143 -
New mill - - 2,040 -
Giuliani double capacity—New mill with capacity of 2500
Conclusion
• Process: Understand problems and identify object function List the constraints Construct and launch the model Sensitivity Analysis
• Linear optimization helps to find the best solution to reach the goal under constrained conditions
• Do your best with your capacity