A stochastic overbooking model for outpatient clinical scheduling with no-shows

In this paper a stochastic overbooking model is formulated and an appointment scheduling policy is developed for outpatient clinics. The schedule is constructed for a single service period partitioned into time slots of equal length. A clinic scheduler assigns patients to slots through a sequential patient call-in process where the scheduler must provide each calling patient with an appointment time before the patient's call terminates. Once an appointment is added to the schedule, it cannot be changed. Each calling patient has a no-show probability, and overbooking is used to compensate for patient no-shows. The scheduling objective captures patient waiting time, staff overtime and patient revenue. Conditions under which the objective evolution is unimodal are derived and the behavior of the scheduling policy is investigated under a variety of conditions. Practical observations on the performance of the policy are presented.