This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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...
View
Full
Document
 Fall '09

Click to edit the document details