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

Abstract

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.

Managing waiting times to predict no-shows and cancelations at a children’s hospital

“…Research on how to manage waiting lists has mainly focused on mathematical models that help hospitals better manage resources. Queuing theory has been the most common methodology applied, and the possibility of missed appointments has been taken into account in these models (Cayirli, Yang & Quek, 2012;Green, 2010;Green & Yankovic 2011;Liu, 2016).…”

Organizing integrated processes in cancer care

“…Liu [184] recently explored the idea of limiting the maximum scheduling interval instead of the panel size. Using this scheduling window, one can control the waiting list as well, and thus the number of no-shows and cancellations.…”

“…However, rejecting all patients that require an appointment outside the scheduling window, might result in patient loss and under-utilization of the system [321]. Therefore, Liu [184] developed an M/M/1/K queuing model, which penalizes the patient loss, and considered a small revenue for empty slots, both due to under-utilization and no-shows.…”

“…After the data analysis, which serves as input for the scheduling approach, we build on the scheduling approach of Liu [184] to answer the research question. This approach allows for implementation in outpatient clinical practice, and includes the time-dependency of no-shows and cancellations.…”

“…This approach allows for implementation in outpatient clinical practice, and includes the time-dependency of no-shows and cancellations. We use an M/M/1/K queue, similar to the work of Liu [184] and Green and Savin [116]. However, our work differs from these studies as they do not consider cancellations, for they are excluded [184] or included as no-shows [116].…”