For the most part, the optimization problems covered in this book are deterministic. In other words, parameters are assumed known, and nothing about the problem is subject to uncertainty. In practice, problems may come to us with uncertain elements, but we often suppress the randomness when we build an optimization model. Quite often, this simplification is justified because the random elements in the model are not as critical as the main optimization structure. However, it is important to know that the techniques we develop are not limited to deterministic applications. Here, we show how to extend the concepts of linear programming to decision problems that are inherently probabilistic. This class of problems is generally called stochastic programming.
A4.1. ONE-STAGE DECISIONS WITH UNCERTAINTY
We can think of stochastic programming models as generalizations of the deterministic case. To demonstrate the relevant concepts, we examine probabilistic variations of a simple allocation problem.
EXAMPLE A4.1 General Appliance Company
General Appliance Company (GAC) manufactures two refrigerator models. Each refrigerator requires a specified amount of work to be done in three departments, and each department has limited capacity. The Standard refrigerator model is sold nationwide to several retailers who place their orders each month. In a given month, demand for the Standard model is subject to random variation. Demand for the Deluxe model comes from ...