lect14 - ISE 536Fall03: Linear Programming and Extensions...

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ISE 536–Fall03: Linear Programming and Extensions October 22, 2003 Lecture 14: Sensitivity Analysis Lecturer: Fernando Ord´o˜nez 1 Re-optimizing a problem In this section we will consider that we solve a problem ( P ) min c t x s . t . Ax = b x 0 to optimality. We assume that we have access to the optimal basis B , which satisfies 1. B - 1 b 0 (primal feasibility) 2. c - c B B - 1 A 0 (dual feasibility) 1.1 Change in b Modify only the i -th coordinate of b , from b i to b i + ε , with ε 6 = 0. Is B still optimal after the change? How large can the change be for B to remain optimal? How do we reoptimize? 1
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Change in c Modify only the j -th coordinate of c , from c j to c j + ε , with ε 6 = 0. Is B still optimal after the change? How large can the change be for B to remain optimal? if j is non-basic if j is basic How do we reoptimize? 1.3 A new variable x n +1 is added Add variable x n +1 with column A n +1 to matrix A and cost c n +1 . The new problem becomes ( P
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lect14 - ISE 536Fall03: Linear Programming and Extensions...

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