A Scenario Tree-Based Decomposition of Multistage Stochastic Mixed-Integer Problems

Abstract

Based on our problem formulation of Section 3.2, we are interested in solving optimization problems where a set of parameters is uncertain. Modeling uncertainty via a set of scenarios and describing their relationship by the corresponding scenario tree, we obtain a multistage stochastic mixed-integer program (SMIP). As nonanticipativity constraints have to be respected, the deterministic problems associated with one scenario cannot be solved separately. Additionally, we want to consider problems where integer restrictions can appear in any stage of the problem, which may even make the solution of a one-scenario subproblem difficult. Furthermore, the size of problems normally grows very quickly with increasing number of time stages and scenarios considered in the model. In this chapter, we present a decomposition approach in order to solve the S-OPGen problem which shows the potential of solving a wide range of related problems.