Disjunctive Decomposition for Two-Stage Stochastic Mixed-Binary Programs with Generalized Upper Bound Constraints

Abstract

The disjunctive decomposition (D2) algorithm has emerged as a powerful tool to solve stochastic integer programs. In this paper, we consider two-stage stochastic integer programs with binary first-stage and mixed-binary second-stage decisions and present several computational enhancements to D2. First, we explore the use of a cut generation problem restricted to a subspace of the variables, which yields significant computational savings. Then, we examine problems with generalized upper bound constraints in the second stage and exploit this structure to generate cuts. We establish convergence of D2 variants. We present computational results on a new stochastic scheduling problem with an uncertain number of jobs motivated by companies in industries such as consulting and defense contracting, where these companies bid on future contracts but may or may not win the bid. The enhancements reduced computation time on average by 45% on a set of test problems.