Data-driven distributionally robust surgery planning in flexible operating rooms over a Wasserstein ambiguity

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