Scheduling of Physicians with Time-Varying Productivity Levels in Emergency Departments

Emergency department (ED) overcrowding and long patient wait times have become a worldwide problem. We propose a novel approach to assigning physicians to shifts such that ED wait times are reduced without adding new physicians. In particular, we extend the physician rostering problem (PRP) by including heterogeneity among emergency physicians in terms of their productivity (measured by the number of new patients seen in 1 hour) and by considering the stochastic nature of patient arrivals and physician productivity. We formulate the PRP as a two-stage stochastic program and solve it with a sample average approximation and the L-shaped method. To formulate the problem, we perform a data analysis to investigate the major drivers of physician productivity using patient visit data from our partner ED, and we find that the individual physician, shift hour, and shift type (e.g., day or night) are the determining factors of ED productivity. A simulation study calibrated using real data shows that the new scheduling method can reduce patient wait times by as much as 13% compared to the current scheduling system at our study ED. We also demonstrate how to incorporate physician preference in scheduling through physician clustering based on productivity. Our simulation results show that EDs can receive almost the full benefit of the new scheduling method even when the number of clusters is small.