On Service Level Measures in Stochastic Inventory Control

We consider the issue of modeling service level measures in stochastic decision making via chance constraints. More specifically we focus on service level measures in production/inventory control under stochastic demand and α service level constraints, which are constraints enforcing a prescribed non-stockout probability for the system. We introduce multiple ways of expressing these chance constraints by using conditional probability. Then we demonstrate that, when these constraints are formulated by using expressions that do not involve a conditional probability, a base stock policy is optimal for this problem only under a number of assumptions. To demonstrate this, we discuss a number of examples for simple cases in which it is possible to find better policies and we also present some analytical results. In contrast, when our novel measure involving a conditional probability is used, a base stock policy is optimal under much less restrictive assumptions, although the cost performance of the system tends to deteriorate.