Scheduling Elective Surgeries with Emergency Patients at Shared Operating Rooms

Operating rooms (ORs) are the greatest source of revenues for hospitals and also their largest cost centers. When scheduling surgeries, hospitals face a trade‐off between the need to conduct planned elective surgeries and the need to be responsive to emergency cases. However, scheduling ORs, especially at Level‐1 trauma hospitals, is challenging due to significant uncertainties in the arrivals of patients requiring emergent surgery. The issue of allocating limited capacity to emergent surgery cases while scheduling elective patients has major policy implications. We develop a model for allocating the OR capacity to elective patients in such a way that the emergency patients who arrive randomly can be accommodated without incurring excessive delays. The objective is to develop a framework for aggregate weekly schedules and generate detailed daily schedules that minimize the total cost of the ORs’ expected operating time, idle time, and overtime. We present optimization procedures for generating effective schedules and rescheduling procedures that adjust the schedules of elective patients affected by emergency arrivals. Initially, the procedures assume deterministic surgery times for elective patients; the procedures are then extended to include stochastic surgery times. We show that for a given arrival rate of emergency patients, the total expected cost is convex in the weekly load of elective surgeries being scheduled. Numerical experiments are devised to obtain total expected cost curves for various emergency arrival rates. Using these curves, the optimal capacity allocation of ORs to elective patients can be determined as a function of the emergency arrival rate.