In this chapter, we consider a setting similar to the economic order quantity (EOQ) model (Section 3.2) but with stochastic demand. The mean demand per year is . The inventory position is monitored continuously, and orders may be placed at any time. There is a deterministic lead time L ( ). Unmet demands are backordered.
If the demand has a continuous distribution, then the inventory level decreases smoothly but randomly over time, with rate , as in Figure 5.1. (Think of liquid draining out of a tank at a fluctuating rate.) This is the interpretation used in most of this chapter. Or demands may occur at discrete points in time (as customers arrive), for example, if the demand follows a Poisson process, as in Section 5.5.
We'll assume the firm follows an policy: When the inventory position reaches a certain ...