Time-Varying Physician Productivity and Implications for Emergency Department Modeling and Staffing

Problem definition: Physician productivity (measured by new patients seen per hour) in emergency departments (EDs) exhibits a distinct time-varying pattern. We examine the factors contributing to this phenomenon empirically and analytically, and investigate the implications of incorporating time-varying service rates into ED modeling and physician staffing. Methodology/results: Using data from a Canadian ED, we provide empirical evidence that the "shift hour" (time elapsed since the shift started) is the most significant predictor of physician productivity. We then model the new patient pickup decisions using an optimal control framework. Assuming physicians' objective is to maximize throughput while avoiding handoffs or overtime, the optimal policy implies adjusting pickup rates throughout a shift is a rational decision. We then investigate the impact of incorporating the time-varying physician productivity in ED modeling and staffing. Validated using data from two Canadian EDs, our simulation results demonstrate that a multi-server queueing model with shift-hour-dependent service rates, despite its lower dimensionality, can accurately capture time-of-day-dependent patient waiting times, whereas models assuming constant service rates deviate significantly from observed data. Furthermore, a case study reveals that staffing plans optimized for time-varying rates outperform current practices, leading to substantial cost savings. Managerial implications: Our findings underscore the necessity of accounting for the time-varying nature of physician productivity. Hospital administrators and schedulers should incorporate this shift-hour dependency into staffing decisions to enhance resource allocation and ED operational efficiency.