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On Solving Two-Stage Distributionally Robust Disjunctive Programs with a General Ambiguity Set

Manish Bansal (bansal***at***vt.edu)
Sanjay Mehrotra (mehrotra***at***northwestern.edu)

Abstract: We introduce two-stage distributionally robust disjunctive programs (TSDR-DPs) with disjunctive constraints in both stages and a general ambiguity set for the probability distributions. The TSDR-DPs subsume various classes of two-stage distributionally robust programs where the second stage problems are non-convex programs (such as mixed binary programs, semi-continuous program, nonconvex quadratic programs, separable non-linear programs, etc.). TSDR-DP is an optimization model in which the degree of risk aversion can be chosen by decision makers. It generalizes two-stage stochastic disjunctive program (risk-neutral) and two-stage robust disjunctive program (most-conservative). To our knowledge, the foregoing special cases of TSDR-DPs have not been studied until now. In this paper, we develop decomposition algorithms, which utilize Balas’ linear programming equivalent for deterministic disjunctive programs or his sequential convexification approach within L-shaped method, to solve TSDR-DPs. We present sufficient conditions under which our algorithms are finitely convergent. These algorithms generalize the distributionally robust integer L-shaped algorithm of Bansal et al. (SIAM J. on Optimization 28: 2360-2388, 2018) for TSDR mixed binary programs, a subclass of TSDR-DPs. Furthermore, we formulate a semi-continuous program (SCP) as a disjunctive program and use our results for TSDR-DPs to solve general two-stage distributionally robust SCPs (TSDR-SCPs) and TSDR-SCP having semi-continuous inflow set in the second stage.

Keywords: Stochastic Programming; Distributionally robust disjunctive programs; decomposition algorithms; sequential convexification; parametric cutting planes

Category 1: Stochastic Programming

Category 2: Integer Programming (0-1 Programming )

Citation: European Journal of Operational Research, Volume 279, Issue 2, 1 December 2019, Pages 296-307

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Entry Submitted: 08/07/2018
Entry Accepted: 08/08/2018
Entry Last Modified: 07/18/2019

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