Optimal Sequencing of Unpunctual Patients : Provider's Wait-Preempt Dilemma

Even though it is well known that patients often arrive early and out of turn for scheduled appointments in outpatient clinics, no research has been undertaken to establish whether an idle provider should see an early patient right away (preempt) or wait for the patient scheduled next. In practice, this problem is typically resolved using a first-come-first-served policy, which consists of seeing the early patient. By contrast, we analytically determine the time intervals where it is optimal to preempt and those where it is optimal to wait. Our analysis indicates that the first-come-first-served policy is never optimal, although it is a good heuristic under certain circumstances, e.g. when overtime charges are high, appointment lengths are short, or if patients are likely to arrive very late. Compared to the first-come-first-served policy, our method dramatically reduces patient waiting times at the cost of a modest increase in overtime. Our results are obtained analytically and validated with simulated and empirical data. A software program is provided that clinics can readily use to solve the wait-preempt dilemma