Clinic Scheduling Models with Overbooking for Patients

10 Clinical overbooking is intended to reduce the negative impact of patient no-shows on clinic op11 erations and performance. In this paper, we study the clinical scheduling problem with overbooking 12 for heterogeneous patients, i.e. patients who have different no-show probabilities. We consider the 13 objective of maximizing expected profit, which includes revenue from patients and costs associated 14 with patient waiting times and physician overtime. We show that the objective function with ho15 mogeneous patients, i.e. patients with the same no-show probability, is multimodular. We also 16 show that this property does not hold when patients are heterogeneous. We identify properties of 17 an optimal schedule with heterogeneous patients and propose a local search algorithm to find local 18 optimal schedules. Then, we extend our results to sequential scheduling and propose two sequential 19 scheduling procedures. Finally, we perform a set of numerical experiments and provide managerial 20 insights for health care practitioners. 21 Key Wordsclinical scheduling, overbooking, patient no-show, multimodularity 22