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Homework7 - ENGRI 1101 Engineering Applications of OR Fall...

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ENGRI 1101 Engineering Applications of OR Fall 2008 Homework 7 The Transportation and Assignment Problems Due date: 4:00pm on Monday, October 20, 2008 in the ENGRI 1101 box at the west end of the corridor on the second floor of Rhodes Hall, where it connects to Upson. Reading assignment: Handout 7 and Chapter 3 of Winston (included in coursepack), at least through section 3.5. Make sure to put your name on the first page and staple the problems in order. 1. (40 points) Consider the assignment problem that corresponds to the following cost matrix. 5 7 11 14 6 2 9 3 4 7 12 6 8 5 9 5 (a) (15 points) Suppose that we subtract now 15 from all the entries in the first row of the matrix. Explain carefully, why the resulted problem defined on the new cost matrix, is equivalent to the original one. (b) (25 points) Apply the Hungarian algorithm to solve the given (original) assignment problem. 2. (30 points) (Adapted from Winston) A shoe company forecasts the following demands for pairs of shoes during the next three months: month 1, 180; month 2, 260; month 3, 240. It costs $7 to produce a pair
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