Allocating spares to maximize the window fill rate in a periodic review inventory system

Abstract

We study the spares allocation problem in a multiple-item, multiple-location inventory system with periodic review. The system allocates spares with the objective of maximizing the window fill rate, which is the probability that a random customer is served within a given time window. The advantage of the window fill rate as a service performance measure is that it takes into account that customers may tolerate a certain wait before they are served. We develop the window fill rate formula and show that, depending on the tolerable wait, it is either a constant, concave or convex-concave with the number of spares. We use this result to develop an efficient algorithm to find the optimal spares allocation for a given budget or for a given target window fill rate. We show that when the tolerable wait or the budget are small, spares will be clustered in a subgroup of the locations (or item-types), while the other locations (or item-types) do not receive any spares. In addition, we numerically illustrate the spares allocation problem using two different synthetic large-scale examples. In particular, we use these examples to demonstrate the cost (in terms of additional spares) of a periodic review compared to a continuous review. The numerical illustration also highlights the complexity of the window fill rate and the savings gained by using it as an optimality criterion.