lect18 - Supply Contracts Yossi Sheffi ESD.260 Logistics...

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Supply Contracts Yossi Sheffi ESD.260 Logistics Systems November 9 th , 2006
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(c) Yossi Sheffi, MIT 2 Outline ± Supply contracts ± Wholesale contracts ± Buyback contracts ± Revenue sharing contracts ± Option contracts
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(c) Yossi Sheffi, MIT 3 The Scenario: ± A contract is negotiated ± The retailer places order (a single period) ± The supplier makes and sends the stuff ± The selling season takes place ± Accounting (sales, salvage, etc.) Supplier Retailer
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(c) Yossi Sheffi, MIT 4 Consumer Demand Demand Density at Retail Level 0 2 4 6 8 10 12 14 16 400 500 600 700 800 900 1,000 1,100 1,200 1,300 Actual Demand Probability Bin Freq. 400 0 500 2 600 5 700 11 800 15 900 10 1,000 5 1,100 3 1,200 1 1,300 0 Average: 811.54 Std Dev: 154.23
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(c) Yossi Sheffi, MIT 5 Demand Distribution Normal Approximation 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 300 400 500 600 700 800 900 1,000 1,100 1,200 1,300 Actual Demand Probability Frac. Norm P Average: 811.54 Std Dev: 154.23
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(c) Yossi Sheffi, MIT 6 Notations: Retail Price R Wholesale Price W Supplier’s Cost C Salvage Value S Quantity Ordered Q Actual Retail Demand d Retail Demand Density f(D) Retail Cum. Demand Distribution F(D)
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(c) Yossi Sheffi, MIT 7 Wholesale Contracts ± Prices and costs: ² Supplier has a cost to make/purchase ( C =$50) ² Supplier is selling and retail is buying at a wholesale price ( W =$135) ² Retailer is selling for a retail price ( R =$200) ² Retailer can salvage ( S =$10) ± How do we optimize the retailer’s expected profit? ² Retailer is facing a Newsboy problem and supplier’s profit is trivial ± How do we optimize the supplier’s expected profit?
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(c) Yossi Sheffi, MIT 8 Wholesale Price Contract Retailer: Order: 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 Demand Prob 400 0.00 $13,000 $19,500 $26,000 $13,500 $1,000 -$11,500 -$24,000 -$36,500 -$49,000 -$61,500 -$74,000 -$86,500 -$99,000 -$111,500 -$124,000 500 0.04 $13,000 $19,500 $26,000 $32,500 $20,000 $7,500 -$5,000 -$17,500 -$30,000 -$42,500 -$55,000 -$67,500 -$80,000 -$92,500 -$105,000 600 0.10 $13,000 $19,500 $26,000 $32,500 $39,000 $26,500 $14,000 $1,500 -$11,000 -$23,500 -$36,000 -$48,500 -$61,000 -$73,500 -$86,000 700 0.21 $13,000 $19,500 $26,000 $32,500 $39,000 $45,500 $33,000 $20,500 $8,000 -$4,500 -$17,000 -$29,500 -$42,000 -$54,500 -$67,000 800 0.29 $13,000 $19,500 $26,000 $32,500 $39,000 $45,500 $52,000 $39,500 $27,000 $14,500 $2,000 -$10,500 -$23,000 -$35,500 -$48,000 900 0.19 $13,000 $19,500 $26,000 $32,500 $39,000 $45,500 $52,000 $58,500 $46,000 $33,500 $21,000 $8,500 -$4,000 -$16,500 -$29,000 1,000 0.10 $13,000 $19,500 $26,000 $32,500 $39,000 $45,500 $52,000 $58,500 $65,000 $52,500 $40,000 $27,500 $15,000 $2,500 -$10,000 1,100 0.06 $13,000 $19,500 $26,000 $32,500 $39,000 $45,500 $52,000 $58,500 $65,000 $71,500 $59,000 $46,500 $34,000 $21,500 $9,000 1,200 0.02 $13,000 $19,500 $26,000 $32,500 $39,000 $45,500 $52,000 $58,500 $65,000 $71,500 $78,000 $65,500 $53,000 $40,500 $28,000 1,300 0.00 $13,000 $19,500 $26,000 $32,500 $39,000 $45,500 $52,000 $58,500 $65,000 $71,500 $78,000 $84,500 $72,000 $59,500 $47,000 Expected Profit: $13,000 $19,500 $26,000 $32,500 $38,269 $42,212 $42,135 $36,577 $27,365 $16,327 $4,192 -$8,308 -$20,808 -$33,308 -$45,808 Maximum Profit: 1 Supplier: Order: 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 Demand Prob 400 0.00 $17,000 $25,500 $34,000 $42,500 $51,000 $59,500 $68,000 $76,500 $85,000 $93,500 $102,000 $110,500 $119,000 $127,500 $136,000 500 0.04 $17,000 $25,500 $34,000 $42,500 $51,000 $59,500 $68,000 $76,500 $85,000 $93,500 $102,000 $110,500 $119,000 $127,500 $136,000 600 0.10 $17,000 $25,500 $34,000 $42,500 $51,000 $59,500 $68,000 $76,500 $85,000 $93,500 $102,000 $110,500 $119,000 $127,500 $136,000 700 0.21 $17,000 $25,500 $34,000 $42,500 $51,000 $59,500 $68,000 $76,500 $85,000 $93,500 $102,000 $110,500 $119,000 $127,500 $136,000 800 0.29 $17,000 $25,500 $34,000 $42,500 $51,000 $59,500 $68,000 $76,500 $85,000 $93,500 $102,000 $110,500 $119,000 $127,500 $136,000 900 0.19 $17,000 $25,500 $34,000 $42,500 $51,000 $59,500 $68,000 $76,500 $85,000 $93,500 $102,000 $110,500 $119,000 $127,500 $136,000 1,000 0.10 $17,000 $25,500 $34,000 $42,500 $51,000 $59,500 $68,000 $76,500 $85,000 $93,500 $102,000 $110,500 $119,000 $127,500 $136,000 1,100 0.06 $17,000 $25,500 $34,000 $42,500 $51,000 $59,500 $68,000 $76,500 $85,000 $93,500 $102,000 $110,500 $119,000 $127,500 $136,000 1,200 0.02 $17,000 $25,500 $34,000 $42,500 $51,000 $59,500 $68,000 $76,500 $85,000 $93,500 $102,000 $110,500 $119,000 $127,500 $136,000 1,300 0.00 $17,000 $25,500 $34,000 $42,500 $51,000 $59,500 $68,000 $76,500 $85,000 $93,500 $102,000 $110,500 $119,000 $127,500 $136,000 Expected Profit: $17,000 $25,500 $34,000 $42,500 $51,000 $59,500 $68,000 $76,500 $85,000 $93,500 $102,000 $110,500 $119,000 $127,500 $136,000 Maximum Profit: !!! Total Profit: $30,000 $45,000 $60,000 $75,000 $89,269 $101,712 $110,135 $113,077 $112,365 $109,827 $106,192 $102,192 $98,192 $94,192 $90,192 Maximum Profit !!! R=$200 W=$135 C=$50 S=$10
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(c) Yossi Sheffi, MIT 9 Wholesale Price Contract Expected Profits -$60,000 -$40,000 -$20,000 $0 $20,000 $40,000 $60,000 $80,000 $100,000 $120,000 $140,000 $160,000 200 400 600 800 1000 1200 1400 1600 Order Expected Profi Retailer Profit Supplier Profit Total Profit R=$200 W=$135 C=$50 S=$10
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(c) Yossi Sheffi, MIT 10 Wholesale Price Contract Exp Profits (Normal Approx) -$60,000 -$40,000 -$20,000 $0 $20,000 $40,000 $60,000 $80,000 $100,000 $120,000 $140,000 $160,000 200 400 600 800 1000 1200 1400 1600 Order Expected Profit Retailer Supplier Total R=$200 W=$135 C=$50 S=$10 Optimal Retailer order= 1 200 135 ,811,154 746 200 10 RW FN O R M I N V RS −− ⎛⎞ == ⎜⎟ ⎝⎠ Optimal channel order= 1 200 50 936 200 10 RC O R M I N V
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lect18 - Supply Contracts Yossi Sheffi ESD.260 Logistics...

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