Sequential Clinical Scheduling with Patient No-shows and General Service Time Distributions

We develop a sequential clinical scheduling method for patients with general service time distributions. Patients are scheduled during a call-in period that precedes the scheduled consultation session. The session is divided into a set of time intervals called “slots”. When a patient calls, the scheduler assigns the patient to a suitable slot if one exists. Each scheduled patient has a probability of not showing up for the appointment, and the scheduler can compensate through overbooking. We show that the proposed scheduling policy always yields a unimodal objective evolution, which provides an optimal stopping criteria for scheduling and is thus critical. We further analytically explore the special case in which service times have a gamma distribution and show how the computational complexity of the scheduling algorithm can be significantly reduced. Finally, we provide exhaustive computational results accompanied by discussion providing insights into the practical aspects of the scheduling approach.