An Introductory Tutorial on Stochastic Linear Programming Models

Linear programming is a fundamental planning tool. It is often difficult to precisely estimate or forecast certain critical data elements of the linear program. In such cases, it is necessary to address the impact of uncertainty during the planning process. We discuss a variety of LP-based models that can be used for planning under uncertainty. In all cases, we begin with a de-terministic LP model and show how it can be adapted to include the impact of uncertainty. We present models that range from simple recourse policies to more general two-stage and multistage SLP formulations. We also include a discussion of probabilistic constraints. We illustrate the various models using examples taken from the literature. The examples involve models developed for airline yield management, telecommunications , flood control, and production planning. O ver the past several decades, linear programming (LP) has become a fundamental planning tool. It is routinely applied in engineering, business, economics , environmental studies, and other disciplines. This widespread acceptance may be due to (1) good algorithms, (2) practi-tioners' understanding of the power and scope of LP, and (3) widely available and reliable software. Furthermore, research on specialized problems, such as assignment , transportation, and network problems , has made LP methodology indispensable in many industries, including