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 deterministic 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 stochastic LP formulations. We also include a discussion of probabilistic constraints. We illustate the various models using examples taken from the literature. The examples involve models developed for airline yield management, telecommunications, flood control, and production planning.