Preprocessing in two-stage stochastic linear programming with simple recourse

Abstract

In the setting of two-stage stochastic linear programs, properties of different types of recourse and theoretical properties of the recourse function are reviewed. Such properties are applied during the preprocessing phase to derive the so-called deterministic equivalent, which is a solvable and interpretable reformulation of the underlying stochastic program. Special structure of stochastic programming problems plays an important role in preprocessing and in computations that follow. The most common structure that allows for further efficiencies is in the case of simple recourse. The simple recourse model has been studied for various applications, many of which are understood as production or allocation problems where only the demand is stochastic. The purpose of this dissertation is to investigate the preprocessing technique required in simple recourse problems for the case of uniformly distributed demand. A special case, namely the simple recourse problem with piece-wise uniformly distributed demand, is also analysed. This analysis is originated by the author. The theoretical achievements are supported by a detailed case study of a stochastic programming application, which is based on the real-world production process of marble tiles. The application of stochastic programming to such a production process is also unprecedented. Computational results that follow are analysed and interpreted.