Physician Staffing for Emergency Departments with Time-Varying Demand

Fluctuations in emergency department (ED) patient arrivals during the day are one of the main causes of the long waiting times that are frequently encountered, and ED staffing is one of the key drivers of ED service quality improvement. This paper first proposes discrete-time models for approximating the patient waiting times for any given ED staffing. The waiting time approximation is based on three simple ideas: the separation of patients served in a period and patients overflowed, the combination of M/M/c approximation for patients served and waiting time analysis of overflow patients, and the transformation of the performance evaluation into an optimization problem with the number of overflow patients as decision variables. The resulting waiting time approximations are then integrated into ED staffing optimization models, and variable neighborhood search algorithms are developed to solve the ED staffing models. Numerical experiments with real-life data from Chinese hospitals are performed to validate the proposed models and algorithms. The results show that the proposed methodology is able to significantly reduce the total waiting time of patients without increasing staff capacity.