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