Physician Scheduling for Emergency Departments Under Time-Varying Demand and Patient Return

Emergency departments (EDs) are facing increasing overcrowding and long patient waiting time, which is mainly caused by the time-varying demand of new and returning patients. In this paper, we focus on scheduling ED physicians to reduce the patient waiting time and the physician working hours. We consider the ED network as a time-varying queuing system with returns and provide an analytical methodology to approximate the system state and patient waiting time of this system. The computation of the system state is based on the pointwise stationary fluid flow approximation method, while we compute the patient waiting time by classifying the patients into groups and individually calculating the waiting time of each group. Because of the nonlinearity of the approximation methods, we propose a linearization technique to formulate the physician scheduling problem as a mixed-integer programming (MIP) model. Since the MIP model is hard to be solved by an optimization solver, a tabu search algorithm is designed. Numerical experiments show that our proposed methods can reasonably approximate the system state and patient waiting time of this complex queueing model. The scheduling computed by the heuristic algorithm can improve the physician schedule without increasing the number of physicians.