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