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

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 .