Robust Elective Hospital Admissions With Contextual Information

Increasing demand for hospitalization requires hospitals to optimize the admission schedules of elective patients to minimize operation cost and improve service quality. In this study, we propose a robust predict-then-optimize methodology to address the elective patient admission scheduling problem under uncertainty. The objective is to minimize total cost associated with postponement and daily bed over-utilization considering uncertain patients’ length of stay (LOS). Starting from prediction models, we first predict patients’ LOS using elaborate clusterwise regression methods. Considering the distributions of the regression residuals, we propose two-stage stochastic programming (SP) and distributionally robust optimization (DRO) approaches to model and solve the elective patient admission scheduling problem. We reformulate the proposed DRO model and construct a column-and-constraint generation algorithm to solve it efficiently. Finally, using real-world data, we conduct extensive numerical experiments comparing the performance of our proposed DRO model with benchmark methods, and discuss insights and implications for elective patient admission scheduling. The results show that our proposed DRO model can help hospitals manage high quality care, i.e., proper bed occupancy rates, at a reduced cost.
Note to Practitioners
—This article is motivated by our collaborations with a tertiary hospital in Beijing, China. From the perspective of hospital admission centers, we consider an elective patient admission scheduling problem that must decide the admission time for elective patients within a specified planning horizon. However, this is a challenging optimization problem due to patients’ uncertain LOS. Additionally, it is difficult to accurately describe the probability distribution of patients’ LOS. The managers find it difficult to give high-quality admission schedules to patients when they are registered which may reduce patients’ satisfaction. Therefore, we propose a predict-then-optimize framework to solve this problem. In particular, a two-phase approach that consists of LOS prediction and a two-stage optimization model is designed. We show that the methods presented in this article can be used as a practical tool to help hospital managers obtain more reasonable elective patient admission scheduling solutions that can improve service quality.