Customer waiting times in an (R, S) inventory system with compound Poisson demand

Besides service level and mean physical stock, customer waiting time is an important performance characteristic for an inventory system. In this paper we discuss the calculation of this waiting time in case a periodic review control policy with order-up-to-level S is used and customers arrive according to a Poisson process. For the case of Gamma distributed demand per customer, we obtain (approximate) expressions for the waiting time characteristics. The approach clearly differs from the traditional approaches. It can also be used to obtain other performance characteristics such as the mean physical stock and the service level.