GT ISYE 6230 - Supply Chain (3 pages)

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Supply Chain



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Supply Chain

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Pages:
3
School:
Georgia Institute of Technology
Course:
Isye 6230 - Economic Decision Analy
Economic Decision Analy Documents

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HW 3 Supply Chain Stocking People magazine l l p 3 95 w 1 50 c 0 50 g 2 00 Uniform demand 1000 2000 F x x a b a f x 1 b a What is q profit for M and S with no coordination Expected overstock l l l cu 3 95 2 00 1 50 co 1 50 We know optimal q satisfies F q cu cu co 4 45 4 45 1 5 0 7479 F q q 1000 2000 1000 q 1748 Decentralized Supply Chain Seller s Profit l l l l p sales wq g lost sales Sales q 1 F q sq1000 xf x dx qF q sq1000 F x dx Lost sales sq2000 x q f x dx 3 95 1468 25 1 50 1748 2 00 31 75 3114 08 Manufacturer q w c 1748 Leftover Inventory sq1000 q x f x dx 279 75 Total SC profit 3115 08 1748 4862 08 1 Centralized Supply Chain Order quantity l l cu 3 95 2 00 0 50 co 0 50 F q cu cu co 5 45 5 45 0 50 0 9159 q 1916 Profit l l Same as seller s profit function but with different cost values p sales cq g lost sales 4946 01 Buyback If there is a buyback price b 0 75 does this coordinate l l l In coordinating contract b p 1 and wb p 1 c b 0 75 0 81013 To coordinate we need wb 3 95 10 81 0 81 0 50 1 155 Here buyback without a changed w will not coordinate 2 Buyback Seller s q l l Seller s profit is same as before but now b leftover inventory l cu 3 95 2 00 1 50 co 1 50 0 75 F q 0 8558 q 1856 p q 1 F q sq1000 xf x dx wq g sq2000 x q f x dx b sq1000 q x f x dx 3354 Manufacturer q w c b sq1000 qx f x dx 1581 SC Profit 4935 Supplier is better off and Manufacturer is worse off but total SC is better off Buyback with Capacity What if limited to capacity of 1748 l l l Since q 1748 the seller will stock as much as possible until that point so q 1748 Seller q 1748 b 0 75 3323 Manufacturer q 1748 b 0 75 1538 Buyback is still a good idea for the supplier although the M still loses some compared to the 1st case 3



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