We study the spares allocation problem in a multiple location inventory system with stochastic lead times under a periodic review policy. The system’s performance measure is the window fill rate, which is defined as the probability that a random customer is served within a given time window. The appeal of using the window fill rate is that it incorporates the fact that customers usually tolerate a certain wait either due to patience or as a result of contractual agreement. We develop the window fill rate formula for a single location and argue that, depending on the tolerable wait, the window fill rate is either concave or convex-concave with the number of spares. When the inventory system comprises multiple locations, the system’s window fill rate is the average of the locations’ window fill rates weighted by the rate of arrivals and therefore, it is generally a separable sum of convex-concave functions. We use these observations to develop an efficient algorithm that solves the spares allocation problem. In addition, we define the a priori and a posteriori distances from optimum of the algorithm and show that they decrease with the number of locations in the system.