Stochastic model for physician staffing and scheduling in emergency departments with multiple treatment stages

We propose a new solution for the Emergency Department (ED) staffing and scheduling problem, considering uncertainty in patient arrival patterns, multiple treatment stages, and resource capacity. A two-stage stochastic mathematical programming model was developed. We employed a Sample Average Approximation (SAA) method to generate scenarios and a discrete event simulation to evaluate the results. The model was applied in a large hospital, with 72,988 medical encounters and 85 physicians in a ten-month period. Compared to the hospital’s actual scheduling, we obtained an overall average waiting time reduction from 54.6 (54.0–55.1) to 16.8 (16.7–17.0) minutes and an average Length of Stay reduction from 102.1 (101.7–102.4) to 64.3 (64.2–64.5) minutes. Therefore, this study offers a stochastic model that effectively addresses uncertainties in EDs, aligning physician schedules with patient arrivals and potentially improving the quality of service by reducing waiting times.