Bed shortages in hospitals usually have a negative impact on patient satisfaction and medical outcomes. In practice, healthcare managers often use bed occupancy rates (BOR) as a metric to understand bed utilization, which is insufficient in capturing the risk of bed shortages. Based on the riskiness index of Aumann and Serrano (2008), we propose the entropic bed shortage metric, which captures more facets of bed shortage risk than traditional metrics such as the occupancy rate, the probability of shortages and expected shortages. Building upon this, we propose the entropic BOR, which represents the risk-corrected BOR and thus can be intuitively understood by practitioners. Our metric has the ability to incorporate high-fidelity statistical information without compromising its computability, and can be consistently used across the descriptive, predictive and prescriptive analytical approaches. We also propose optimization models to control the risk of bed shortages and plan for bed capacity via this metric. These models have linear program re-formulations which can be solved efficiently on a large scale. Our first model determines the optimal scheduling policy by lexicographically minimizing the daily entropic bed shortage metric in a week in the steady state for a given number of scheduled elective admissions. The second maximizes total elective throughput while managing the shortage metric under a specified threshold. We validate these models using real data from a hospital and test them against data-driven simulations. Finally, we apply these models to study the real-world problem of long stayers. This enables us to predict the impact of having fewer long stayers in acute hospitals after transferring them to community hospitals, and its impact as a result of an aging population.
*Light refreshments will be served at 12pm