Lecture24

Lecture24 - Advanced Operations Research Techniques IE316...

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Unformatted text preview: Advanced Operations Research Techniques IE316 Lecture 24 Dr. Ted Ralphs IE316 Lecture 24 1 Reading for This Lecture Bertsimas Sections 10.2, 10.3, 11.1, 11.2 IE316 Lecture 24 2 Preprocessing Often, it is possible to simplify a model using logical arguments. Most commercial LP solvers do preprocessing automatically, but if you are developing a model that will be solved repeatedly, it may be worthwhile. The constraint a 1 x b 1 dominates the constraint a 2 x b 2 if a 1 i a 2 i i, and b 1 b 2 In this case, the dominated inequality could be deleted. We can also derive implied bounds for variables from each constraint ax b . If a > , then x 1 ( b- X j : a j > a j l j- X j : a j < a j u j ) /a IE316 Lecture 24 3 More Preprocessing The constraint ax b is redundant if X j : a j > a j u j + X j : a j < a j l j b. The LP is infeasible if X j : a j > a j l j + X j : a j < a j u j > b. For an LP of the form min { c T x | Ax b,l x b } , If a ij i [1 ..m ] and c j < , then x j = u j in any optimal solution....
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Lecture24 - Advanced Operations Research Techniques IE316...

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