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hwk3 - ORIE 321/521 Optimization II Summer 2006 Homework 3...

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ORIE 321/521 Optimization II Summer 2006 Homework # 3 Due: Wednesday, August 2, in class. Please print your name clearly on the first page of your homework. 1. #6, BHM Chapter 8. 2. #13, BHM Chapter 8 – formulate only. 3. #26, BHM Chapter 8. 4. Given below is the utility data for a 5 × 5 assignment model ( max total utility). 3 5 6 2 2 2 3 5 3 2 3 0 4 2 2 3 0 3 2 2 0 3 0 1 0 (a) What is the size of a basis for this problem? How many degenerate variables must each basic solution have? Answer the previous two questions for a general n × n assignment model. (b) How do you expect the considerations of part (a) to affect the algorithms discussed in class for the transportation model, when applied to assignment problems? (c) For this model, starting with a basis determined by the greedy procedure, perform three full iterations (i.e., proceed through three additional bases, stopping if you demonstrate optimality) of the primal-dual transportation algorithm studied in OR 320.
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