Emergency department staffing policy: An integrated probabilistic forecasting and newsvendor solution
Abstract
Emergency department (ED) staffing plans rely on accurate forecasts of patient admissions for each shift. However, conventional forecasting approaches often provide point forecasts that do not directly align with the staff-to-patient policies often used in planning. This gap hinders the efficient coordination and organisation of staff planning and scheduling tasks, which may result in situations of inadequate or excessive staffing with negative consequences for the quality of patient care, the well-being of staff, and the financial performance of the hospital. We first discretise the number of admissions in each shift into categories based on the staffing ratio. We develop a LASSO ordinal regression model to produce probabilistic forecasts of admission categories in each shift. We then integrate the probabilistic forecasts with a newsvendor model to optimise the level of staffing in each shift. Using a data set from a UK ED spanning four and a half years of admissions, we compare the results using both statistical error measures and utility measures such as the newsvendor cost resulting from over- and under-staffing. The proposed approach generates more accurate probabilistic forecasts when compared to benchmarks using the Brier Score and Ranked Probability Score. Our proposed method also has a lower cost when compared to relevant benchmarks. We propose a direct and accurate approach to producing staffing forecasts by using a staff-to-patient ratio policy in EDs. In addition, we combine a newsvendor model with probabilistic forecasts of admission categories in each shift to create a useful and reliable input for ED staffing. We provide information on the costs related to the staffing policy, a specific forecasting approach, and a specific staff-to-patient ratio, although our approach is easily generalised to other settings. In addition, we explore the rationale for ED managers’ need to not only track the accuracy of their forecasts but also evaluate the implications of their actions, specifically in terms of staff costs.