Inference-based sensitivity analysis for mixed integer/linear programming

Inference-based sensitivity analysis for mixed integer/linear programming

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Article ID: iaor20021993
Country: United States
Volume: 48
Issue: 4
Start Page Number: 623
End Page Number: 634
Publication Date: Jul 2000
Journal: Operations Research
Authors: ,
Keywords: programming: linear
Abstract:

A new method of sensitivity analysis for mixed integer/linear programming (MILP) is derived from the idea of inference duality. The inference dual of an optimization problem asks how the optimal value can be deduced from the constraints. In MILP, a deduction based on the resolution method of theorem proving can be obtained from the branch-and-cut tree that solves the primal problem. One can then investigate which perturbations of the problem leave this proof intact. On this basis it is shown that, in a minimization problem, any pertubation that satisfies a certain system of linear inequalities will reduce the optimal value no more than a prespecified amount. One can also give an upper bound on the increase in the optimal value that results from a given perturbation. The method is illustrated on two realistic problems.

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