Sequencing and Scheduling Appointments with Potential Call-In Patients

This paper considers an appointment scheduling system that accommodates routine patients who book well in advance as well as same-day patients with acute needs who call in the morning for an appointment later that day. In addition to determining the appointment times that are assigned up-front to the routine patients, our model is the first to determine when and how to slot in those last-minute same-day patients throughout the day. By formulating the problem as a stochastic linear program, our model includes patient no-shows, random service times, ancillary physician tasks, and appointment delays for same-day patients who prefer to see the doctor as soon as possible. We also develop two heuristic rules for the combinatorial problem of sequencing similar routine and same-day patients.