A stochastic programming approach to the physician staffing and scheduling problem

Abstract

A challenging problem for Emergency Department (ED) managers is determining the best allocation of the medical staff that is required to promptly attend patients in the face of increasing demand for emergency care, and the ensuing long patient waiting times. We propose a solution framework that supports physician staffing and scheduling in the ED, considering uncertainties related to patient arrivals. For this, we introduce a two-stage stochastic programming model with fixed recourse that solves in an integrated manner the staffing and scheduling problems and aligns physician scheduling with patient arrivals while minimizing the total number of patients waiting and accounting for all scheduling requirements and contractual agreements. We create possible realization scenarios to consider demand uncertainty using Sample Average Approximation (SAA). In addition, we use discrete-event simulation to estimate the benefits derived from the schedule generated by our model. We validate our methodology with two case studies using real data from hospital EDs. The proposed method enhances alignment between service capacity and demand, significantly improving all queue and wait time indicators. In our first case study, the frequency of queue and average time door-to-doctor were reduced by 73% and 92%, respectively, compared to the current manually-defined ED schedule, and in the second case study, the frequency of queue decreased about 22%, and the average time door-to-doctor decreased 48%. Finally, sensitivity analysis showed that our model-generated optimal schedule is robust to variations in both demand and service rates, indicating that, under small perturbations of current operating conditions, hospital managers would not need to rerun the model.