A distribution-aware optimization model for improving operating room utilization and out-patient flow

Operating rooms (OR) are responsible for the majority of total hospital revenues and costs, making OR scheduling a critical component of hospital operations as it controls the patient flow in and out of the system. A major challenge in determining effective OR schedules is the uncertainty surrounding new (types of) cases related to, e.g., surgery duration and the post-surgical lengths of stay (LOS). We propose a distribution-aware learning method that estimates the distributions of surgery duration and LOS for each type using historical data. For types with insufficient historical data, we develop a transfer learning method that calculates Wasserstein barycenters to estimate the distributions from similar types with sufficient data points. Using the estimated distributions, we formulate a mixed-integer program that maximizes OR utilization, minimizes OR overtime, and controls the variability in daily discharges. We validate the proposed optimization and distribution-aware learning model in three surgery departments at the University Health System (UHS). The results show that the OR schedules created by the proposed method significantly outperform their human scheduler counterparts and two algorithmic baselines, a greedy algorithm and an optimization model using machine learning predictions. Equally important, the model parameters transfer across time and healthcare sites for the same surgery department, showing robustness of our approach to distribution shifts.