Stochastic Appointment Scheduling in a Team Primary Care Practice with Two Flexible Nurses and Two Dedicated Providers

AbstractWaiting is common in appointment-based outpatient care: patients experience delays before seeing a nurse and then in the examination room before seeing the doctor. Given that service times are uncertain, the challenge for outpatient practices is to control the spacing between successive appointments to minimize waiting time while ensuring the doctor is not idle for too long. Whereas scheduling in single-doctor practices is well studied, team practice, in which one of two nurses can flexibly see the patient before the patient consults with one of two assigned doctors, is not. Optimal scheduling in a team practice is far more challenging from a computational viewpoint because the order in which patient appointments are scheduled need not be the order in which they see their doctors (i.e., patients may be allowed to crossover). In this article the authors propose a model that can solve realistic instances of this problem optimally. On the basis of analyses, the results show that (1) empty slots (which function as slack to alleviate waiting) alternate in the two doctors’ schedules and do not occur simultaneously, and (2) allowing nurse flexibility and patient crossovers produces greater benefits when service time variation is high.We consider the team primary care practice scheduling problem in which each patient is seen by one of two available nurses before seeing her provider. In other words, the nurse step is flexible, whereas the provider step is dedicated. Both steps have uncertain durations. The patients can also cross over in schedule, so the order of patients seen by the nurse might not be the same as the order in which the provider sees patients. We develop a two-stage stochastic integer programming model to solve the challenging scheduling problem of determining patient appointment times, given in 15-minute time intervals, so as to minimize a weighted combination of patient wait and provider idle times for the team practice. To overcome the computational complexity associated with solving the problem under the large set of scenarios required to accurately capture uncertainty in this setting, our approach relies on a lower bounding technique based on solving an exhaustive and mutually exclusive group of scenario subsets. Our computational results identify the structure of optimal schedules and quantify the impact of nurse flexibility, patient crossovers, and no-shows. We conclude with practical scheduling guidelines for team primary care practices.The e-companion is available at https://doi.org/10.1287/serv.2018.0219.