An Intersection Cutting Plane Algorithm for Chance-Constrained Programs with Finite Support

Abstract

Standard Big-M mixed-integer programming reformulations of chance-constrained programs (CCPs) with finite support often yield weak linear relaxations and scale poorly as the number of scenarios increases. To address this limitation, we derive two families of intersection cuts from problem-specific S-free sets and develop decomposition-based branch-and-cut frameworks. The first one exploits the submodular structure of the scenario requirement function, while the second one uses probability covers. We propose hybrid separation strategies that combine classical mixing inequalities and quantile cuts with the proposed intersection cuts. Computational experiments on integrated production-distribution planning instances show that the proposed hybrid methods reduce computational time compared to pure methods.