Chance Constrained Mixed Integer Program: Bilinear and Linear Formulations, and Benders Decomposition

TL;DR

This paper introduces novel bilinear and linear formulations for chance constrained mixed integer programs, along with an enhanced Benders decomposition method that significantly improves computational efficiency over existing solvers.

Contribution

It develops stronger linear formulations from a bilinear model, extends Jensen's inequality for stochastic programs, and proposes an effective Benders decomposition approach with enhancements.

Findings

The new formulations outperform existing ones in strength.

The Benders decomposition method is an order of magnitude faster than commercial solvers.

Enhanced strategies improve solution detection and computational efficiency.

Abstract

In this paper, we study chance constrained mixed integer program with consideration of recourse decisions and their incurred cost, developed on a finite discrete scenario set. Through studying a non-traditional bilinear mixed integer formulation, we derive its linear counterparts and show that they could be stronger than existing linear formulations. We also develop a variant of Jensen's inequality that extends the one for stochastic program. To solve this challenging problem, we present a variant of Benders decomposition method in bilinear form, which actually provides an easy-to-use algorithm framework for further improvements, along with a few enhancement strategies based on structural properties or Jensen's inequality. Computational study shows that the presented Benders decomposition method, jointly with appropriate enhancement techniques, outperforms a commercial solver by an order of magnitude on solving chance constrained program or detecting its infeasibility.