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On Solving General Two-Stage Stochastic Programs

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

Abstract: We study general two-stage stochastic programs and present conditions under which the second stage programs can be convexified. This allows us to relax the restrictions, such as integrality, binary, semi-continuity, and many others, on the second stage variables in certain situations. Next, we introduce two-stage stochastic disjunctive programs (TSS-DPs) and extend Balas's linear programming equivalent for deterministic disjunctive programs to TSS-DPs. In addition, we develop a finitely convergent algorithm, which utilizes the sequential convexification approach of Balas within L-shaped method, to solve various classes of TSS-DPs. We formulate a semi-continuous program (SCP) as a DP and use our results for TSS-DPs to solve two-stage stochastic SCPs (TSS-SCPs). In particular, we provide linear programming equivalent for the second stage of the TSS-SCPs and showcase how our convexification approach can be utilized to solve a TSS-SCP having semi-continuous inflow set in the second stage.

Keywords: two-stage stochastic program; tight formulations; disjunctive programs; sequential convexification; semi-continuous programs; lift-and-project; cutting planes; convex hull

Category 1: Stochastic Programming

Category 2: Integer Programming (Cutting Plane Approaches )

Citation: Technical Report MBSM1, Department of Industrial Engineering & Management Sciences, Northwestern University, October 2015

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Entry Submitted: 10/15/2015
Entry Accepted: 10/15/2015
Entry Last Modified: 02/15/2016

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