An integer programming and decomposition approach to general chance-constrained mathematical programs

Abstract

We present a new approach for exactly solving general chance constrained mathematical programs having discrete distributions. Such problems have been notoriously difficult to solve due to nonconvexity of the feasible region, and currently available methods are only able to find provably good solutions in certain very special cases. Our approach uses both decomposition, to enable processing subproblems corresponding to one possible outcome at a time, and integer programming techniques, to combine the results of these subproblems to yield strong valid inequalities. Computational results on a chance-constrained two-stage problem arising in call center staffing indicate the approach works significantly better than both an existing mixed-integer programming formulation and a simple decomposition approach that does not use strong valid inequalities. Thus, the strength of this approach results from the successful merger of stochastic programming decomposition techniques with integer programming techniques for finding strong valid inequalities. © 2010 Springer-Verlag.