### Consider a buyer at bloomingdale''s responsible for purchase

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Question 1: Consider a buyer at Bloomingdale's responsible for purchasing dinnerware with Christmas patterns. The dinnerware only sells over the Christmas season and the buyer places an order for delivery in early November. Each dinnerware set cost \$100 and sells for a retail price of \$250. Any sets unsold by Christmas are heavily discounted in the post-Christmas sales and sold for a salvage value of \$80. The buyer has estimated that demand is normally distributed with a mean of µ=350. Historically, forecast errors have had a standard deviation of s =150. The buyer has decided to conduct additional market research to get a better forecast. Evaluate the impact of improved forecast accuracy on profitability as the buyer reduces s from 150 to 0. Question 2: A large fraction of Benetton's sales are from knit garments in solid colors. Starting with thread, there are two steps to completing the garment - dying and knitting. Traditionally, thread was dyed and then the garment was knitted (Option 1). Benetton, however, has developed a procedure where dying was postponed until after the garment was knitted (Option 2). Benetton sells each garment at a retail price p=\$50. Option 1 results in a manufacturing cost of \$20, whereas option 2 results in a manufacturing cost of \$22 per garment. Benetton disposes of any unsold garments at the end of the season in a clearance for \$10 each. The knitting or manufacturing process takes a total of 20 weeks. Assume now that Benetton sells garments in four colors. Twenty weeks in advance, Benetton forecasts demand for each color to be normally distributed with a mean of µ=1000 and a standard deviation of s =500. Demand for each color is independent. With Option 1, Benetton makes the buying decision for each color 20 weeks before the sale period and holds separate inventories for each color. With Option 2, Benetton only forecasts the aggregate uncolored thread to purchase 20 weeks in advance. The inventory held is based on the aggregate demand across all four colors; they decide the quantity for individual colors after demand is known. a) Evaluate the profitability of both Options for Benetton. b) Assume now that demand for red sweaters at Benetton is forecast to be normally distributed with a mean µred=1000 and a standard deviation of sred =800. Demand for the other three colors is forecast to be normally distributed with a mean µ =300 and a standard deviation of s =200. Evaluate the profitability of both Options for Benetton, and explain how and why the results differ from those obtained in part a). Would it be possible to tailor Option 2 to better take advantage of postponement under this scenario? If so, briefly explain, how (qualitatively)

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