IEOR150F10_hw07 - IEOR 150, Fall 2010 Homework 7 1. (30...

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Unformatted text preview: IEOR 150, Fall 2010 Homework 7 1. (30 points) In this problem, we discuss the newsvendor problem in a supply chain and the effect of double marginalization . Consider a manufacturer who produces a product with a unit cost c = $1. The daily demand D for this product is uniformly distributed between 0 and 1. The retail price is fixed to be r = $2 in all cases. Products not sold in a day become useless on the next day. (a) (10 points) Suppose the manufacturer adopts direct sales and sell the product by itself. In this case, the manufacturer faces a simple newsvendor problem. i. (5 points) Solve the newsvendor problem and determine the optimal daily production quantity q D ( D stands for direct). ii. (5 points) Find the expected profit of the manufacturer M D = r E min { D,q D } - cq D . Hint. For this problem, the expected sales quantity under an inventory level q [0 , 1] is E min { D,q } = Z q xf ( x ) dx + Z 1 q qf ( x ) dx, where f is the pdf of the random demand D . (b) (15 points) Suppose the manufacturer adopts indirect sales and sell the product to a retailer, who then sells the product to end consumers. In this case, the manufacturer first announces a wholesale price w and then the retailer decides the order quantity...
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IEOR150F10_hw07 - IEOR 150, Fall 2010 Homework 7 1. (30...

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