Lecture14 - Advanced Operations Research Techniques IE316...

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Unformatted text preview: Advanced Operations Research Techniques IE316 Lecture 14 Dr. Ted Ralphs IE316 Lecture 14 1 Reading for This Lecture • Bertsimas Chapter 5 IE316 Lecture 14 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. IE316 Lecture 14 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 ≥ – c T- c T B B- 1 A ≥ • 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....
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This note was uploaded on 08/06/2008 for the course IE 316 taught by Professor Ralphs during the Fall '08 term at Lehigh University .

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Lecture14 - Advanced Operations Research Techniques IE316...

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