Optimal Choice for Appointment Scheduling Window under Patient No-Show Behavior

Observing that patients with longer appointment delays tend to have higher no-show rates, many providers place a limit on how far into the future that an appointment can be scheduled. This article studies how the choice of appointment scheduling window affects a provider's operational efficiency. We use a single server queue to model the registered appointments in a provider's work schedule, and the capacity of the queue serves as a proxy of the size of the appointment window. The provider chooses a common appointment window for all patients to maximize her long-run average net reward, which depends on the rewards collected from patients served and the penalty paid for those who cannot be scheduled. Using a stylized M/M/1/K queueing model, we provide an analytical characterization for the optimal appointment queue capacity K, and study how it should be adjusted in response to changes in other model parameters. In particular, we find that simply increasing appointment window could be counterproductive when patients become more likely to show up. Patient sensitivity to incremental delays, rather than the magnitudes of no-show probabilities, plays a more important role in determining the optimal appointment window. Via extensive numerical experiments, we confirm that our analytical results obtained under the M/M/1/K model continue to hold in more realistic settings. Our numerical study also reveals substantial efficiency gains resulted from adopting an optimal appointment scheduling window when the provider has no other operational levers available to deal with patient no-shows. However, when the provider can adjust panel size and overbooking level, limiting the appointment window serves more as a substitute strategy, rather than a complement.