The Optimal Reorder Policy in an Inventory System with Spares and Periodic Review

We analyze the window fill rate in an inventory system with constant lead times under a periodic review policy. The window fill rate is the probability that a random customer gets serviced within a predefined time window. It is an extension of the traditional fill rate that takes into account that customers generally tolerate a certain waiting time. We analyze the impact of the reorder-cycle on the window fill rate and present an inventory model that finds the optimal spares allocation and the optimal reorder cycle with the objective of minimizing the total costs. Furthermore, we present a numerical example and find that the number of spares increase almost linearly when the reorder-cycle time increases. Finally, we show how managers can find the optimal spares allocation and the optimal reorder-cycle time and show how they can estimate the cost of changing the required window fill rate and the reorder-cycle time.