Determining the reorder point and order‐up‐to level to satisfy two constraints in a periodic review system under negative binomial demand

In this paper we consider an inventory management problem motivated by a specific practical context that concerns the commonly used periodic review, reorder point, order‐up‐to‐level control system. In particular, the reorder point and order‐up‐to level have to be selected so as to satisfy two management‐specified constraints. First, from a marketing (or, more generally, a business) perspective, the actual fill rate achieved must be no lower than a prescribed value. Second, for production or supply purposes, the average time between consecutive replenishments must be as close as possible to a target value. The demand distribution considered is the negative binomial. An efficient procedure is developed with illustrations.