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Homework6 - ENGRI 1101 Engineering Applications of OR Fall...

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ENGRI 1101 Engineering Applications of OR Fall ’09 Homework 6 The Transportation Problem Due date: 4:00pm on Friday, October 16, 2009 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: Pages 1-4 in Handout 7 on the transportation problem. Make sure to put your name, netid, and lab section on the first page and staple the problems in order. 1. (50 points) Consider the following problem: there are m warehouses, where warehouse i has supply s i , for each i = 1 , . . . , m ; there are n stores, where store j has demand d j , for each j = 1 , . . . , n ; however, for the first n i units(where n i s i ) shipped from warehouse i , there is a per-unit shipping charge from warehouse i to store j of c ij dollars, for each i = 1 , . . . , m , j = 1 , . . . , n , whereas for the remaining s i - n i units there is a surcharge of p i > 0 dollars per unit shipped. Our aim is to find the shipments that incur the least total cost (that is, the sum of both shipping and shortfall costs).
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