Next-Day Operating Room Scheduling with Time-Dependent Stochastic Surgery Durations

Operating rooms (ORs) are the most costly part of hospitals, thus a priority for hospital administrations. In this paper, we consider the next-day OR scheduling problem for multiple operating rooms. We assume that surgeries have uncertain durations, and distributions of surgery durations are time-dependent. Our aim is to find the assignment of surgeries to the available ORs, the sequence, and the planned starting times of surgeries in order to minimize the weighted sum of expected waiting time of patients, idle time of ORs, and overtime of the hospital staff. In order to find solutions to the problem, we propose an L-Shaped method, customized to our problem formulation. We quantify the penalty of ignoring the time-dependency of surgery durations within a numerical study. We find that the penalty of ignoring the time-dependency increases with the overtime cost, average surgery durations, and decreases with surgery variability.