Generating cluster submodels from two-stage stochastic mixed integer optimization models

Abstract

Stochastic optimization problems of practical applications lead, in general, to some large models. The size of those models is linked to the number of scenarios that defines the scenario tree. This number of scenarios can be so large that decomposition strategies are required for problem solving in reasonable computing time. Methodologies such as Branch-and-Fix Coordination and Lagrangean Relaxation make use of these decomposition approaches, where independent scenario clusters are given. In this work, we present a technique to generate cluster submodel structures from the decomposition of a general two-stage stochastic mixed integer optimization model. Scenario cluster submodels are generated from the original stochastic problem by combining the compact and splitting variable representations in some of the variables related to the nodes that belong to the first stage. We consider a two-stage stochastic capacity expansion problem as illustrative example where several decompositions are provided.