Inventory control using a service constraint on the expected customer order waiting time

In this paper an analytical model is presented which permits the determination of the minimal inventory reorder point subject to (a) a maximum specified expected customer order waiting time or (b) a maximum specified probability of a customer order waiting more than a predetermined time span. The probability distribution of the customer order waiting time is determined for an arbitrary demand distribution (e.g. normal, gamma or exponential) and under stochastic replenishment lead time conditions by use of arguments from renewal theory. The results established can be used for the customer-oriented control of inventory policy as well as for the analysis of multi-echelon inventory systems.