Some insights regarding the optimal reorder period in periodic review inventory systems

The periodic review inventory system is not only pervasive, but also has an extensive literature dealing with various aspects, from its theoretical underpinnings through to its performance. However, the selection of the best review period and its behaviour with respect to basic inventory parameters such as demand and supply variability appears to be poorly understood. In this paper we treat the normal and gamma distributions which are probably the two most commonly used distributions of demand over the key (protection) time interval in a periodic review system. We show that the total cost function is not necessarily well behaved as a function of the review period; in particular, it can be non-convex, which complicates the determination of the best value of the review interval. Also we demonstrate and explain how the best review period changes as the values of various parameters are modified. Some of these changes are initially counterintuitive in nature. Managerially oriented interpretations should also be helpful to organisations seeking improvement in inventory system performance.