Disjunctive Benders Decomposition

Abstract

We propose an enhancement to Benders decomposition (BD) that generates valid inequalities for the convex hull of the Benders reformulation, addressing the limitation that classical BD cuts are typically tight only for the continuous relaxation. Our method integrates disjunctive programming with BD and introduces a routine that leverages existing cut-generating oracles as-is to construct convex hull inequalities. For mixed-binary linear programs, the approach removes the need to solve the master problem as a mixed-integer program, even with separable subproblems. It builds on a unified normalization framework for cut-generating programs, encompassing norm-based, reverse polar, and right-hand-side normalization, and enabling the design of new normalization schemes with streamlined analysis of supporting cuts. Computational results on large-scale instances show substantial reductions in branch-and-bound nodes often by orders of magnitude, while consistently outperforming commercial solvers on selected problem classes.