Appointment Scheduling Under Patient No-Shows and Service Interruptions

We consider an appointment-based service system (for example, an outpatient clinic) for which appointments need to be scheduled before the service session starts. Patients with scheduled appointments may or may not show-up for their appointments. The service of scheduled patients can be interrupted by emergency requests that have a higher priority. We develop a framework which can be utilized in determining the optimal appointment policies under different assumptions regarding rewards, costs, and the decision variables. We propose two methods that can be used in evaluating the objective function for a given appointment schedule. We specifically consider two different formulations both of which aim to balance the trade-off between the patient waiting times and server utilization and carry out a numerical study to provide insights into optimal policies. We find that policies that ignore interruptions perform quite badly, especially when the number of appointments to be scheduled is also a decision variable. We also find that policies that require equally-spaced appointments perform reasonably well when the interruption rate is constant. However, their performance worsens significantly when the interruption rate is time-dependent.