Chance Constrained Mixed Integer Program: Bilinear and Linear Formulations, and Benders Decomposition
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.
Cite
@article{arxiv.1403.7875,
title = {Chance Constrained Mixed Integer Program: Bilinear and Linear Formulations, and Benders Decomposition},
author = {Bo Zeng and Yu An and Ludwig Kuznia},
journal= {arXiv preprint arXiv:1403.7875},
year = {2016}
}