On solving two-stage distributionally robust disjunctive programs with a general ambiguity set

Manish Bansal and Sanjay Mehrotra

European Journal of Operational Research, 2019, vol. 279, issue 2, 296-307

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; Semi-continuous program; Reverse convex program (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0377221719304631
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:279:y:2019:i:2:p:296-307

DOI: 10.1016/j.ejor.2019.05.033

Access Statistics for this article

European Journal of Operational Research is currently edited by Roman Slowinski, Jesus Artalejo, Jean-Charles. Billaut, Robert Dyson and Lorenzo Peccati

More articles in European Journal of Operational Research from Elsevier
Bibliographic data for series maintained by Catherine Liu ().