Lecture13 - Introduction to Mathematical Programming IE406...

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Introduction to Mathematical Programming IE406 Lecture 13 Dr. Ted Ralphs
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IE406 Lecture 13 1 Reading for This Lecture Bertsimas Chapter 5
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IE406 Lecture 13 2 Sensitivity Analysis In many real-world problems, the following can occur: The input data is not very accurate . We don’t know all of the constraints ahead of time . We don’t know all of the variables ahead of time . Because of this, we want to analyze the dependence of the model on the input data, i.e., the matrix A , the right-hand side vector b , and the cost vector c . We would also like to know the effect of additional variables and constraints. This is done using sensitivity analysis . Sensitivity analysis requires nothing more than straightforward application of techniques we’ve already developed.
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IE406 Lecture 13 3 The Fundamental Idea Using the simplex algorithm to solve a standard form problem, we know that if B is an optimal basis , then two conditions are satisfied : B - 1 b 0 c - c B B - 1 A 0 When the problem is changed, we can check to see how these conditions are affected . This is the simplest kind of analysis—we have already seen several examples. When using the simplex method, we always have B - 1 available, so we can easily recompute appropriate quantities .
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