Constant Job-Allowance Policies for Appointment Scheduling: Asymptotic Optimality and Numerical Analysis

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We consider the appointment scheduling problem, which determines the job allowance over the planning horizon. In particular, we study a simple but effective scheduling policy -- the so-called plateau policy, which allocates a constant job allowance for each appointment. Prior studies on appointment scheduling suggests a dome shape structure for the optimal job allowance over the planning horizon. This implies that job allowance does not vary significantly in the middle of the schedule sequence, but varies at the beginning and also at the end of the optimal schedule. Using a dynamic programming formulation, we derive an explicit performance gap between the plateau policy and the optimal schedule, and examine how this gap behaves as the number of appointments increases. We show that a plateau policy is asymptotically optimal when the number of appointments increases. We extend this result to a more general setting with multiple service types. Numerical experiments show that the plateau policy is near optimal even for a small number of appointments, which complements the theoretical results that we derived. Our result provides a justification and strong support for the plateau policy, which is commonly used in practice. Moreover, with minor modifications, the plateau policy can be adapted to more general scenarios with patient no-shows or heterogeneous appointment types.