Joint Panel Sizing and Appointment Scheduling in Outpatient Care

Patients nationwide experience difficulties in accessing medical care in a timely manner due to long backlogs of appointments. Medical practices aim to utilize their valuable resources efficiently, deliver timely access to care, and at the same time they strive to provide short waiting times for patients present at the medical facility. We address 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 time scales involved in accessing medical care: appointment delay (order of days, weeks) and clinic delay (order of minutes, hours). Closed-form expressions are derived for the performance measures of interest based on diffusion approximations. Our model captures many features of the complex reality of outpatient care, including patient no-shows, balking behavior, and random service times. Our analysis provides theoretical and numerical support for the optimality of an open access policy in outpatient scheduling when we account for both types of delay, and it demonstrates the importance of considering panel sizing and scheduling decisions in a joint framework.