Solution of Outsourcing Problem for Filatoi Riuniti

Solution of Outsourcing

Problem for Filatoi Riuniti

Case Study of DMD

Presentation by Group 4

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


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)


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


Size


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


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


Size


Ambrosi - 6,250 - -


Castri 3,704 - - -

De Blasi - - 2,040 -

Estensi 3,846 - - -

Filatoi R. 13,164 19,750 18,817 28,000


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


F 18.25 13.90 11.40 8.90

F-EX - - 5.70 -

MACHINE HOURS REQUIRED FOR

PRODUCTION

(Hours/Kg)

Size


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)


25,000 26,000 28,000 28,000

DEMAND TO MEET

(Kg/month)


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


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


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


Ambrosi - 6,250 - -


Castri 3,704 - - -

De Blasi - - 2,040 -

Estensi 3,846 - - -

Filatoi R. 13,164 19,750 18,817 28,000


Just Increase Fine by 5% Changed

Size


Ambrosi - 6,250 - -


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


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


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


New mill 21.03 14.80 11.45 10.01

Giuliani double capacity—New mill with capacity of 2500

DECISION VARIABLES


Size


Ambrosi - 6,250 - -


Castri 3,704 - - -

De Blasi - - 2,040 -

Estensi 3,846 - - -

Filatoi R. 13,164 19,750 18,817 28,000


Total Cost: 1,382,544

Total Cost: 1,382,338

FILATOIR-twinkle.xls

DECISION VARIABLES


Size


Ambrosi - 6,250 - -


Castri 3,704 - - -

De Blasi - - - -

Estensi 3,846 - - -

Filatoi R. 13,164 19,750 18,817 28,000


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

Thank you

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Solution of Outsourcing Problem for Filatoi Riuniti

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