Sequential clinical scheduling with patient no-show: The impact of pre-defined slot structures

Abstract

This paper develops a sequential scheduling algorithm for consultation periods not divided into slots. Patients call a scheduler and request appointments with a specified provider. The scheduler provides the patient with an appointment time before the call terminates. In making the appointment, the scheduler cannot alter the appointments of previously scheduled patients. Service times are random and each scheduled patient has a probability of “no-showing” for the appointment. Each arriving patient generates a given amount of revenue, and costs are incurred from patient waiting and provider overtime. The scheduling method selects the calling patient's appointment time by minimizing the total expected cost. We prove that total expected cost is a convex function of appointment times and that the expected profit of the schedule is unimodal, which provides a unique stopping criterion for the scheduling algorithm. Computational studies compare this approach with no-show based sequential scheduling methods for out-patient clinics where a predefined slot structure is assumed. The new method yields higher expected profit and less overtime than when service periods are pre-divided into slots. Because slot scheduling is ingrained in healthcare, we use the model to design slot structures that account for no-show and service time variation.