The Analytics of Bed Shortages: Coherent Metric, Prediction, and Optimization

Bed shortages in hospitals usually have a negative impact on patient satisfaction and medical outcomes. In practice, healthcare managers often use bed occupancy rates (BORs) as a metric to understand bed utilization, which is insufficient in capturing the risk of bed shortages. We propose the bed shortage index (BSI) to capture more facets of bed shortage risk than traditional metrics such as the occupancy rate, the probability of shortages, and expected shortages. The BSI is based on the riskiness index by Aumann and Serrano, and it is calibrated to coincide with BORs when the daily arrivals in the hospital unit are Poisson distributed. Our metric can be tractably computed and does not require additional assumptions or approximations. As such, it can be consistently used across the descriptive, predictive, and prescriptive analytical approaches. We also propose optimization models to plan for bed capacity via this metric. These models can be efficiently solved on a large scale via a sequence of linear optimization problems. The first maximizes total elective throughput while managing the metric under a specified threshold. The second determines the optimal scheduling policy by lexicographically minimizing the steady-state daily BSI for a given number of scheduled admissions. We validate these models using real data from a hospital and test them against data-driven simulations. We apply these models to study the real-world problem of long stayers to predict the impact of transferring them to community hospitals as a result of an aging population.