Simple approximations for the reorder point in periodic and continuous review (s, S) inventory systems with service level constraints

In this paper we consider a general class of (s, S) inventory systems including periodic review and continuous review systems. We allow for stochastic lead times for replenishment orders provided that the probability of orders crossing in time is negligible for the relevant (s, S) control rules. In accordance with common practice we emphasize on service level constraints rather than assuming given stockout costs. In particular we consider the service measure requiring that a specified fraction of the demand is met directly from stock on hand. The purpose of this paper is to present practically useful approximations for the recorder point s such that the required service level is achieved. By a simple and direct approach, a unifying treatment of the general class of (s, S) inventory systems considered is given. We obtain for the first time tractable approximations for the continuous review (s, S) inventory system with undershoots of the reorder point. Also, we discuss 2-moments approximations obtained by fitting normal respectively gamma distributions to the empirical demand distributions. Extensive numerical experience with the approximations is reported, including results about the sensitivity of the reorder point to the higher moments of the demand distributions.