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 ÃÂ¼ 800 Standard deviation ÃÂ100 Cost$30,- Holding cost 25% Lead time 4 weeks Target cycle service level95% z-value 1,645 Safety stock Khaki pants Service level * ÃÂ * Ã¢ÂÂ( Lead time) 1,645 * 100 * Ã¢ÂÂ(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 ÃÂ¼ 50 Standard deviation ÃÂ50 Cost$100,- Holding cost 25% Lead time 4 weeks Target cycle service level95% z-value1.645 Safety stock Cashmere sweaters Service level * ÃÂ * Ã¢ÂÂ( Lead time) 1,645 * 50 * Ã¢ÂÂ(4) Safety stock for Cashmere sweaters = 164,50 Cost Cashmere sweaters Holding cost * safety stock 0,25 * $100,- * 164,5 Total holding cost of Cashmere sweaters is $ 4.112,50

If one compares the total holding cost of the Khaki pants ($2.467,50) and the Cashmere sweaters ($ 4.112,50), one can conclude that the holding cost for the Cashmere sweaters are higher than the holding cost for the Khaki pants. For the reason that the inventory cost of Cashmere sweaters are high it is important to distribute those sweaters by the online channel and distribute the pants by the retail stores.

b)How much Safety Inventory reduction can The Gap expect on moving each of the two products from the stores to the online channel? According to the case, we assume that the demand from one week to the next week is independent Khaki pants Standard deviation ÃÂ Ã¢ÂÂ(1002* 900) = 3.000 Safety stock Service level * ÃÂ * Ã¢ÂÂ( Lead time) 1,645 * 3000 * Ã¢ÂÂ(4) Safety stock is 9.870 Cost Holding cost * safety stock 0,25 * $30,- * 9.870 Holding costs are $ 74.025,- The holding costs for retail distribution are: $2.467,50 * 900 = $ 2.200.750,- Cashmere sweaters Standard deviation ÃÂ Ã¢ÂÂ(502* 900) = 1.500 Safety stock Service level * ÃÂ * Ã¢ÂÂ( Lead time) 1,645 * 1500 * Ã¢ÂÂ(4) Safety stock is 4.935 Cost Holding cost * safety stock 0,25 * $100,- * 4.935 Holding costs are $ 123.375,- The holding costs for retail distribution are: $4.112,50 * 900 = $3.701.250,- One can conclude the following: The total cost for safety stock for the 900 stores is $ 2.200.750,- + $3.701.250,- = $ 5.922.000,- Safety stock for distribution by the internet (centralized) is: $ 74.025,- + $ 123.375,- = $197.400,- The reduction in inventory cost is: $ 5.922.000 - $197.400 = $5.724.600,- Question 3AThe demand is normally distributed with a mean of 20,000 and a standard deviation of 10,000. The retailer sells the jackets at $60 and buys them at a price of $30. Total manufacturing costs are $25. If there are any leftovers they will be sold for $25 each at the end-year sale.

(i): How many units should a retailer order to optimize his performance? And what would be the out of stock rate? = 0.85 is the optimum order quantity = 30,700 Stock out rate = = 1- 0.85 = 0.15 (ii:) How many units should a retailer order to optimize SC performance? = 1.00 is the out of stock rate = 120,000 (which should actually be infinity in real life) Stock out rate = = 1- 1.00 = 0 This means that to achieve the optimum SC performance you would have to buy an infinite amount of products, or a very very large number of jackets, if done there are no leftover cost. Another option would be if a cooperation in the supply chain would lead to this kind of volume.

3BShipping the left over jackets to America at an additional cost of $8 but with a selling price of $35. Would you recommend this option and what will be the affect on the ordering decision? If you do this, the costs for the left over jackets are 30+8 = 38. You can sell the jackets for $35, so a loss of $3 for each overstocked unit compared to $5 in the earlier situation.

Under stocking costs are 30 Over stocking costs are 3 = 0.909 = 33,400 Stock out rate = = 1- 0.909 = 0.091 This is very small, so it is a very good idea to sell the jackets that are left over to South America! 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 + ÃÂ½*W Fill this in for Q:Q = 200 - ÃÂ½*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 + ÃÂ½*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.

Centralized situation: For the maximize supply chain profit means that (P-80)*Q is maximum.

Q = 400-P (P-80)*(400-P) = 480*P -32000 -P2 should be at maximum.

Now find the derivative of this function: 480 -2P and this one is at its maximum where 480 - 2P = 0 P = 240 So Q = 400-240 = 160. Maximum SC profit = 25600.

Manufacturer profit:M = (W-80)*160 = 160*W -12800 Retailer profit:R=(240-W)*160 = 38400 - 160*W T = SC profit = 25600 Profit for retailer is 0 when W = 240 Profit for manufacturer is 0 when W = 80.

Win-Win situation means that it is somewhere in between where both the manufacturer and the retailer gain as much profit as possible.

In case of powerful manufacturer: Wholesale price is $240.- because the manufacturer is powerful, he will give the retailer the old profit of 6400 and keeps extra profit for himself.

Minimum purchase of 160 units Offer quantity discount of 6400/160 = 40 per unit In case of a powerful retailer: The retailer accepts the wholesale price of $240.- but he gives the manufacturer only a profit of 9600 and takes 25600 - 6400 =19200 as a profit for himself.

Minimum purchase of 160 units Demand quantity discount of 19200/160 is 120 per unit.

So range of discount is between 40 and 120 per unit for the retailer, depending which party is most powerful.

Than supply chain profit of 25600 instead of 16000 for decentralized situation.

b) Design a Fixed-fee contract that will give the same effect ( result ) of quantity discount contract that you designed in the question (a) [ Note: "same effect" with respect to manufacturer's profit, retailer's profit and total supply chain profit as obtained in the previous question ] Set W = C = 80 Supply chain profit has to be 25600 again.

In case of powerful manufacturer: The manufacturer will give the retailer a profit of 6400.

Now profit per unit for retailer without lump sum is 240-80 is 160.

They will sell 160 units, so lump sum is 160*160 is 19200.

In case of powerful retailer: The retailer will give manufacturer a profit of 9600.

So the lump sum will be 9600 This means that the lump sum is between 9600 and 19200.

## WTF?

Its difficult to understand, if it were readable i would gladly give it a C.

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