Surgical Scheduling via Optimization and Machine Learning with Long-Tailed Data

Using data from cardiovascular surgery patients with long and highly variable post-surgical lengths of stay (LOS), we develop a model to reduce recovery unit congestion. We estimate LOS using a variety of machine learning models, schedule procedures with a variety of online optimization models, and estimate performance with simulation. The machine learning models achieved only modest LOS prediction accuracy, despite access to a very rich set of patient characteristics. Compared to the current paper-based system used in the hospital, most optimization models failed to reduce congestion without increasing wait times for surgery. A conservative stochastic optimization with sufficient sampling to capture the long tail of the LOS distribution outperformed the current manual process. These results highlight the perils of using oversimplified distributional models of patient length of stay for scheduling procedures and the importance of using stochastic optimization well-suited to dealing with long-tailed behavior.