Data-Driven Distributionally Robust Surgery Planning in Flexible Operating Rooms Over a Wasserstein Ambiguity

Abstract: We study elective surgery planning in flexible operating rooms (ORs) where emergency patients are accommodated in the existing elective surgery schedule. Specifically, elective surgeries can be scheduled weeks or months in advance. In contrast, an emergency surgery arrives randomly and must be performed on the day of arrival. Probability distributions of the actual durations of elective and emergency surgeries are unknown, and only a possibly small set of historical realizations may be available. To address distributional uncertainty, we first construct an ambiguity set that encompasses all possible distributions of surgery durations within a 1-Wasserstein distance from the empirical distribution. We then define a distributionally robust surgery assignment (DSA) problem to determine optimal elective surgery assignment decisions to available surgical blocks in multiple ORs, considering the capacity needed for emergency cases. The objective is to minimize the total cost consisting of the fixed cost related to scheduling or rejecting elective surgery plus the maximum expected cost associated with OR overtime and idle time over all distributions defined in the ambiguity set. Using the DSA model's structural properties, we derive an equivalent mixed-integer linear programming (MILP) reformulation that can be implemented and solved efficiently using off-the-shelf optimization software. In addition, we extend the proposed model to determine the number of ORs needed to serve the two competing surgery classes and derive a MILP reformulation of this extension. We conduct extensive numerical experiments based on real-world surgery data, demonstrating our proposed model's computational efficiency and superior out-of-sample operational performance over two state-of-the-art approaches. In addition, we derive insights into surgery scheduling in flexible ORs.