A note on optimal policies for a periodic inventory system with emergency orders

Abstract

In this article, we develop a dynamic programming model for a periodic review inventory system in which emergency orders can be placed at the start of each period, while regular orders are placed at the beginning of an order cycle (which consists of a number of periods). We assume that the regular and emergency supply lead times differ by one period. We devise a simple algorithm of computing the optimal policy parameters. Thus, the ordering policy developed is easy to implement. Scope and purpose Alternative resupply modes are commonly used in inventory systems. For example, a materials manager could choose to replenish the inventory of an item by air if its inventory position gets dangerously low. In this article, we study a periodic review inventory system in which there is an emergency supply mode in addition to a regular supply mode. We develop optimal ordering policies that minimize the total expected discounted cost of procurement, holding, and shortage over a finite planning horizon. These optimal policies are next shown to converge as the planning horizon is extended, if some conditions that are easy to hold are satisfied. Finally, we derive an algorithm which involves solving only a one-order-cycle dynamic program for the optimal policy parameters.