Distributionally robust master surgery scheduling with duration uncertainty and specialty parallelism

This study investigates master surgery scheduling at the tactical decision-making level of operating room (OR) management, addressing uncertainty in surgeons’ surgery durations and parallelism in surgical specialties. The goal is to optimize OR time block types within the scheduling cycle, allocate them efficiently to surgical specialties and surgeons, and determine the appropriate number of surgeries to schedule. Given the limited historical data on surgery durations, we employ a distributionally robust optimization (DRO) approach to address the uncertainty in the distribution. To address the needs of different OR managers, we develop a distributionally robust chance-constrained model to manage overtime that extends beyond the designated OR time blocks. Meanwhile, we construct a distributionally robust bi-objective optimization model with the goals of minimizing the expected total duration of overtime and maximizing the number of surgeries scheduled. These optimization models are reformulated into computationally tractable forms using dual theory. We validate the proposed methods with real hospital data, finding that the DRO approach offers greater stability in scheduling solutions compared to the sample average approximation approach.