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

TL;DR

This paper develops a framework combining machine learning and optimization to improve surgical scheduling for cardiovascular patients with highly variable and long post-surgical stays, highlighting the challenges of modeling long-tailed data.

Contribution

It introduces a stochastic optimization approach tailored for long-tailed LOS distributions, outperforming traditional methods and manual scheduling in reducing congestion.

Findings

Conservative stochastic optimization outperforms manual scheduling.

Machine learning models achieved modest LOS prediction accuracy.

Handling long-tailed distributions is crucial for effective scheduling.

Abstract

Using data from cardiovascular surgery patients with long and highly variable post-surgical lengths of stay (LOS), we develop a modeling framework to reduce recovery unit congestion. We estimate the LOS and its probability distribution using machine learning models, schedule procedures on a rolling basis using a variety of 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 and other stochastic and robust optimization approaches. These results highlight the perils of using oversimplified distributional models of LOS for scheduling procedures and the importance of using optimization methods well-suited to dealing with long-tailed behavior.