Inference-Based Sensitivity Analysis for Mixed Integer/Linear Programming

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 perturbation that satis es a certain system of linear inequalities will reduce the optimal value no more than a prespeci ed 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