The (R, Q) inventory policy subject to a compound Poisson demand pattern

Most inventory management models are based upon rather restrictive assumptions, e.g. unit sized demands and the normal distribution for total demand during replenishment time. In a majority of inventory management systems, circumstances seem to allow these simplifications, and inventory policies based upon these assumptions yield satisfying results. However, in some particular cases, these simplifications differ fundamentally from the actual conditions and particle. Therefore, applications of the models mentioned above can result in an overinvestment in inventory or in an unacceptable low service level. One of the situations in which we cannot rely on these simplified inventory models is studied in this paper. We consider an inventory subject to a probabilistic non-unit sized demand pattern, and we propose an exact and an approximate reorder point calculation method for the (R, Q) inventory policy. The exact algorithm involves formulas for the discrete distributions of the total demand during replenishment time and the undershoot. The approximate method is based on the use of continuous distributions, and will be more appropriate when historical data are sparse. Results of both approaches are compared. The algorithms proposed in this study are simple, fast and easy to implement in a variety of (existing) inventory management systems.