Single-Period Models

Abstract

The models and environments discussed in the preceeding chapters have all been based on the premise that the demand process is deterministic. In most real situations, this assumption is violated. Our goal in this, and in subsequent chapters, is to consider uncertainty directly in the decision models. In this chapter we will study the most basic models in which demand is described by a random variable. These models pertain to situations in which only a single procurement decision is made, and the effect of that decision is felt over a single period of finite duration. These models are often called one-shot or newsvendor models.

The newsvendor name for this type of model arises for the following reason. Suppose a newsvendor operates a corner newstand. Each day the newsvendor places an order for newspapers which will be delivered to the newstand the following morning. Only one order can be placed for the papers. Suppose there is a cost to purchase each newspaper and that there is a selling price as well. Demand for the newspapers occurs throughout the day. If this demand exceeds the quantity ordered, there are lost sales. There may be long-term consequences of lost sales since unsatisfied customers may look elsewhere for papers in the future. On the other hand, if the demand is less than the supply of papers, the newsvendor will incur the cost of disposing of the unsold papers. Day old papers have no value. The decision faced by the newsvendor is therefore how many papers should be purchased.