A Decomposition Method for Distributionally-Robust Two-stage Stochastic Mixed-integer Cone Programs

TL;DR

This paper introduces a decomposition algorithm for distributionally-robust two-stage stochastic mixed-integer convex cone programs, enabling efficient solutions and significant computational improvements over traditional methods.

Contribution

It generalizes existing algorithms to a broader class of problems and proves finite convergence under certain conditions, with practical computational benefits demonstrated.

Findings

Significant reduction in solution time for complex models

Ability to solve previously intractable models

Distributionally-robust models have comparable solution times

Abstract

We develop a decomposition algorithm for distributionally-robust two-stage stochastic mixed-integer convex cone programs, and its important special case of distributionally-robust two-stage stochastic mixed-integer second order cone programs. This generalizes the algorithm proposed by Sen and Sherali~[Mathematical Programming 106(2): 203-223, 2006]. We show that the proposed algorithm is finitely convergent if the second-stage problems are solved to optimality at incumbent first stage solutions, and solution to an optimization problem to identify worst-case probability distribution is available. The second stage problems can be solved using a branch-and-cut algorithm. The decomposition algorithm is illustrated with an example. Computational results on a stochastic programming generalization of a facility location problem show significant solution time improvements from the proposed approach. Solutions for many models that are intractable for an extensive form formulation become possible. Computational results suggest that solution time requirement does not increase significantly when considering distributional robust counterparts to the stochastic programming models.