Background Concepts: An Introduction to the (s − 1, s) Policy under Poisson Demand

Abstract

In the previous chapter we studied order-up-to policies when time was divided into periods. We will now discuss the implications of following a similar policy, called an (s–1, s) inventory policy. In this chapter we assume inventories are reviewed continuously in time. Recall that the stock level, s, measures the amount of inventory on hand plus on order minus backorders, that is, the stock level represents the inventory position for a particular location. In certain situations, we will refer to the on-order quantity as the “in resupply” quantity. This “in resupply” terminology is often used in military and aviation applications in which items fail and are repaired or are procured from an external source. When an (s–1, s) policy is followed in continuous review environments, an order is placed immediately whenever a demand occurs for one or more units of an item. The order quantity matches the size of the demand exactly. Hence, the inventory position is constant in the case where the demand process and costs are stationary over an infinite planning horizon, which is the one we will examine in some detail in this chapter.