Joint Panel Sizing and Appointment Scheduling in Outpatient Care

Patients nationwide experience difficulties in accessing medical appointments in a timely manner due to long backlogs. Meanwhile, patients do not always show up for their scheduled services, with significant no-show rates. Unattended appointments result in under-utilization of a clinic’s valuable resources, and limit the access for other patients who could have filled the missed slots. Medical practices aim to utilize their valuable resources efficiently, provide timely access to care, and at the same time they strive to provide short waits for patients present at the medical facility. We study the joint problem of determining the panel size of a medical practice and the number of offered appointment slots per day, so that patients do not face long backlogs and the clinic is not overcrowded. We explicitly model the two separate time scales involved in accessing medical care: appointment delay (order of days, weeks) and clinic delay (order of minutes, hours). We analyze the two queueing systems associated with each type of delay, and provide explicit expressions for the performance measures of interest based on diffusion approximations. In our analysis we capture many features of the complex reality of outpatient care, including patients’ non-punctuality, no-shows, balking behavior, and stochastic service times. Two additional distinctive characteristics of this study are the balking behavior of the patients who face long appointment backlogs, and the transient-state analysis of the clinic delay, which allow the study of a system with traffic intensity greater than one. Concerning the panel sizing and appointment scheduling decisions, our analysis provides theoretical and numerical support that the two-variable optimization problem reduces to a single variable-one, and either an “Open Access” policy is optimal, or supply and demand are perfectly matched and are both very small (“Limited Access” regime). Under our Open Access regime, the clinic offers as many appointment slots as possible per day, and the optimal panel size depends on the clinic’s characteristics. A solution within the Limited Access regime arises when the service times are long, and the patients are very sensitive to the appointment delay.