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prelim4 - PRELIM 4 Closed book exam Justify all work 1 ORIE...

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PRELIM 4 ORIE 3310/5310 April 28, 2009 Closed book exam. Justify all work. 1. a. (25 points) You work as an OR analyst for a manufacturing corporation which has production sites i = 1 , . . . , m and distribution (sales) centers j = 1 , . . . , n . The (internal) unit shipping cost is currently set at c ij from production site i to distribution center j ; this cost is passed on to consumers by the distribution centers. As an incentive to increase sales, the company is considering the following change in shipping cost allocation: for each distribution center, shipping cost for up to 100 items would be billed at 1/2-price, while items after the 100th would be shipped at full price. Suppose product availability at the i th production site is a i , that demand at the j th distribution center is d j , and that i a i = j d j . You have been assigned the task of determining a shipping model which allocates available pro- duction capacity to meet the demand at minimum shipping cost. You have devised a simple transportation model which accomplishes this. What is your model? I.e., give the mathematical
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