Wasserstein distributionally robust surgery scheduling with elective and emergency patients

Abstract

We study a surgery scheduling problem with regard to both elective and emergency patients, where surgery durations are uncertain and emergency patients arrive dynamically. The problem determines, at the beginning of a day, how many operating rooms to open and how to allocate elective and (possibly dummy) emergency patients into them to minimize the operating room opening and expected overtime costs. Incorporating (possibly dummy) emergency patients provides a novel approach for reserving emergency capacity. We propose a robust data-driven model that allows for distributional ambiguity via the Wasserstein metric. We derive its mixed-integer conic reformulation and develop an exact branch-and-cut algorithm. We also uncover our model’s connections to its sample average approximation counterpart. Since emergency patients necessitate adequate and timely treatments, we formalize a rolling horizon scheme to dynamically reschedule and prioritize the emergency patients upon their arrivals. Our scheme handles practical features such as dynamic emergency arrivals and uncertain service duration. We perform simulation studies based on real data and numerical experiments show that our method outperforms the benchmark ones in a variety of performance indicators.