Determining the reorder point and order-up-to-level in a periodic review system so as to achieve a desired fill rate and a desired average time between replenishments

In this paper we consider a periodic review, reorder point, order-up-to-level system, a type commonly used in practice. Motivated by a specific practical context, we present a novel approach to determining the reorder point and order-up-to-level (for a given review interval) so as to target desired values of i) customer fill rate and ii) average time between consecutive replenishments. Specifically, by using a diffusion model (producing normally distributed demand) we convert a periodic review, constant lead time setting into one having continuous review and a random lead time. The method is simple to implement and produces quite reasonable results.