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

Abstract

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.

Keywords:

• inventory
• inventory control
• negative binomial
• supply chain management

Acknowledgements

We thank Daniel Costa, Head of Demand and Supply Planning, Supply Chain Management at Nestlé Suisse, for describing a practical situation that motivated the topic studied. The research leading to this paper was supported by the Natural Sciences and Engineering Research Council of Canada under grant 239153-05.