HW12 - If so find a formula that describes a general...

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IOE 510 – Fall 2008 Homework 12 Due December 8, 2008 1) An oil company imports crude from three foreign sources and refines it at five refineries. This question is concerned with minimizing the cost of transporting the crude from the sources to the refineries. Sources 1, 2, 3 can ship 20, 50, 20 units of crude respectively each week. Refineries 1 to 5 need 10, 24, 6, 20, 30 units of crude respectively every week. c ij is the cost ($/unit) of shipping crude from source i to refinery j , and the matrix c=(c ij ) is given below. 30 30 10 27 15 c = 15 15 8 13 5 25 21 5 15 21 Solve this problem beginning with the basic set of cells {(1,3), (1,5), (2,1), (2,2), (2,5), (3,1), (3,4)}. Does this problem have alternate optimum solutions?
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Unformatted text preview: If so, find a formula that describes a general optimum solution. A company called PSC headquartered in the same city as our company operates the shipping route from source 3 to refinery 1. Discuss how much our company would lose per unit of business given to PSC if our company wanted to patronize them. Do cost ranging for cost coefficient c 13 . From the present optimum solution, obtain an optimum solution for the problem if c 13 becomes 14. Consider the original problem again (i.e., c 13 = 10). If the weekly supply at source 3, and the weekly demand at refinery 1 change to 20 +δ, 10 +δ respectively; find an optimum solution as a function of δ and its optimality range....
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