Scheduling Operating Rooms with Elective and Emergency Surgeries

The issue of allocating capacity to accommodate emergent surgery cases while scheduling elective patients has major policy implications for Level-1 trauma centers including most large academic medical centers. This is because operating rooms (ORs) are the greatest source of revenues for hospitals, while also being the largest cost centers. However, scheduling ORs, especially at level-1 trauma hospitals, is challenging due to significant uncertainty in the arrivals of patients requiring emergent surgery. When scheduling surgeries, hospitals face a trade-off between the need to be responsive to emergency cases and the need to conduct scheduled elective surgeries as planned. We develop a model that allocates the OR capacity to elective patients so that the emergency patients who arrive randomly can be accommodated without incurring any excessive delays. The objective is to develop a framework for aggregate weekly schedules and generate detailed daily schedules that minimize a weighted sum of the ORs' operating time, idle time, and overtime. Optimization procedures are developed to devise effective block schedules while a rescheduling procedure schedules elective patients who are affected by an emergency arrival. Initially, the procedures are based on deterministic surgery times for the elective patients and then they are extended to stochastic surgery times. We illustrate our methodology on specialized ORs for trauma cases related to neurosurgery. We show that for a given arrival rate of emergency patients, the total expected cost is convex in the weekly load of the elective surgeries scheduled. Numerical experiments are devised to obtain the total expected cost curves for various arrival rates of emergency patients. Using these cost curves the optimal capacity allocation of ORs to elective patients can be determined as a function of the arrival rate of emergency patients