Quantitative Practice Problems on GAP's Supply Chain Management

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SUPPLY CHAIN MANAGEMENT CASE 2 Quantitative Practice Problems MSc12, 11 May 2004 Question 1. a) Which of the two products should the GAP carry at the stores and which at the central warehouse for the online channel? Khaki pants Information given : The mean μ 800 Standard deviation σ100 Cost$30,- Holding cost 25% Lead time 4 weeks Target cycle service level95% z-value 1,645 Safety stock Khaki pants Service level * σ * √( Lead time) 1,645 * 100 * √(4) Safety stock for Khaki pants = 329 Cost Khaki pants Holding cost * safety stock 0,25 * $30,- * 329 Total holding cost of Khaki pants is $2.467,50 Cashmere sweaters Information given : The mean μ 50 Standard deviation σ50 Cost$100,- Holding cost 25% Lead time 4 weeks Target cycle service…show more content…
The stockout rate is lower than in the old situation, and that is a very positive thing for the retailer! Question 4 Suppose there are two firms in a supply chain, supplier and a retailer. The following events occur in this simple supply chain: (i) the supplier chooses a wholesale price W (ii)the retailer orders Q units from the supplier (iii)Supplier produces Q units at a cost of $ 80 per unit and ship these units to the retailer (iv)Retailer sells these Q units at a price P where P = 400 - Q. a) Design a quantity discount contract that will maximize the supply chain's profit and that will lead to win-win situation to both manufacturer and retailer (Note: your contract should indicate the range of discount that will lead to win-win situation) . Indicate the maximum supply chain profit and the extra profit that could be earned by both manufacturer and retailer due to your designed contract P = 400-Q so Q = 400-P Manufacturer profit:M = (W-80)*Q Retailer profit:R = (P-W)*Q Decentralized situation: Retailer profit:R = (P-W)*(400-P) =400P -400W -P2 + WP dR/dP = 400 -2P +W = 0 P = 200 + ½*W Fill this in for Q:Q = 200 - ½*W Manufacturer profit:M = (W-80)*(200-1/2*W) =240W - 16000 -1/2*W2 dM/dw = 240 - W = 0 W = 240 Retail price:P = 200 + ½*W = 320 Retail order quantity: Q = 400 - 320 = 80 Now retailer profit is (320-240)*80 = 6400 Now manufacturer profit is (240-80)*80 = 9600 Total supply chain profit in decentralized chain is 6400 + 9600 =16000.
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