Postoptimality Analysis for Integer Programming Using Binary Decision Diagrams

Abstract

We show how binary decision diagrams (BDDs) can be used to solve and obtain postoptimality analysis for linear and nonlinear integer programming problems with binary or general integer variables. The constraint set corresponds to a unique reduced BDD that represents all feasible or near-optimal solutions, and in which optimal solutions correspond to certain shortest paths. The BDD can be queried in real time for in-depth postoptimality reasoning. The approach is equally effective for linear and nonlinear problems. There are currently no other methods for obtaining such an analysis, short of repeatedly re-solving the problem. We illustrate the analysis on capital budgeting and network reliability problems.