The Timing of Staffing Decisions in Hospital Operating Rooms: Incorporating Workload Heterogeneity into the Newsvendor Problem

We study the problem of setting nurse staffing levels in hospital operating rooms when there is uncertainty about daily workload. The workload is the number of operating room hours used by a medical specialty on a given day to perform surgical procedures. Variable costs consist of wages at a regular (scheduled) rate and at an overtime rate when the realized workload exceeds the scheduled time. Using a newsvendor framework, we consider the problem of determining optimal staffing levels with different information sets available at the time of decision: no information, information on number of cases, and information on number and types of cases. We develop empirical models for the daily workload distribution in which the mean and variance change with the information available. We use these models to derive optimal staffing rules based on historical data from a U.S. teaching hospital and prospectively test the performance of these rules. Our numerical results suggest that hospitals could potentially reduce their staffing costs by up to 39%-49% by deferring staffing decisions until procedure type information is available. The results demonstrate how data availability can affect a newsvendor's performance. The systematic approach of empirical modeling presented in the paper can be applied to other newsvendor problems with heterogeneous sources of demand.