Mitigating overtime risk in tactical surgical scheduling

Overtime is a common phenomenon in surgery departments, causing stress to physicians, dissatisfaction to patients, and financial loss to hospitals. We help risk-averse managers of operating rooms (ORs) to mitigate overtime in tactical surgery scheduling, which determines the assignment of elective patients to available ORs in upcoming time periods. We model the uncertain surgical durations via partial, full, or empirical distributions. To mitigate overtime, our model maximizes the risk aversion level of the OR manager (and thus the risk-hedging ability of the solution) while ensuring that the certainty equivalent of surgery duration in each OR at each time period does not exceed the stipulated working hours. The corresponding decision criterion, termed the maximized risk aversion level, is demonstrated in theory and in numerical experiments to be able to mitigate both the overtime probability and the expected overtime duration. To solve the problem, we develop an exact hill-climbing algorithm and demonstrate its convergence and correctness. Numerical experiments based on real-life surgery data show that our method outperforms the existing methods in several indicators that of concern to OR managers. In particular, this method is computationally amiable and hence is applicable to larger-scale instances.