Tolerance sensitivity and optimality bounds in linear programming

Tolerance sensitivity and optimality bounds in linear programming

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Article ID: iaor20073862
Country: United States
Volume: 50
Issue: 6
Start Page Number: 797
End Page Number: 803
Publication Date: Jun 2004
Journal: Management Science
Authors:
Abstract:

Traditional sensitivity analysis in linear programming usually focuses on variations of one coefficient or term at a time. The tolerance approach was proposed to provide a decision maker with an effective and easy-to-use method to summarize the effects of simultaneous and independent changes in selected parameters. In particular, for variations of the objective function coefficients, the approach gives a maximum-tolerance percentage within which selected coefficients may vary from their estimated values (within a priori limits) while still retaining the same optimal basic feasible solution. Although an optimal solution may cease being optimal for variations beyond the maximum-tolerance percentage, it may still be close to optimal. Herein we characterize the potential loss of optimality for variations beyond the maximum-tolerance percentage as a maximum-regret function. We consider theoretical properties of this function and propose a method to compute a relevant portion of it.

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