Optimal stationary appointment schedules

A prevalent operations research problem concerns the generation of appointment schedules that effectively deal with variation in e.g. service times. In this paper we focus on the situation in which there is a large number of statistically identical customers, leading to an essentially equidistant ('stationary') schedule. We develop a powerful approach that minimizes an objective function incorporating the service provider's idle times and the customers' waiting times. Our main results concern easily computable, or even closed-form, approximations to the optimal schedule with a near-perfect fit. In addition, accurate explicit heavy-traffic approximations are provided, which, as we argue, can be considered as robust.