Decomposition Algorithms for Two‐Stage Recourse Problems

Abstract

In this article, decomposition methods for two‐stage linear recourse problems with a finite discrete distribution are discussed. First, we cover the L‐shaped decomposition method which represents a breakthrough concerning numerically efficient methods for solving two‐stage recourse problems. This algorithm was the basis for the development of several other decomposition methods. After giving an overview of these algorithms, we present regularized decomposition and stochastic decomposition in a more detailed fashion. Variance for recourse‐constrained problems and special cases including simple recourse with a random technology matrix are also considered. With reference to stochastic decomposition, the scope of which is not restricted to finite discrete distributions, algorithms for the continuous‐distribution case are discussed briefly with references to the literature.