A study on the impact of prioritising emergency department arrivals on the patient waiting time

In the past decade, the crowding of the emergency department has gained considerable attention of researchers as the number of medical service providers is typically insufficient to fulfil the demand for emergency care. In this paper, we solve the stochastic emergency department workforce planning problem and consider the planning of nurses and physicians simultaneously for a real-life case study in Belgium. We study the patient arrival pattern of the emergency department in depth and consider different patient acuity classes by disaggregating the arrival pattern. We determine the personnel staffing requirements and the design of the shifts based on the patient arrival rates per acuity class such that the resource staffing cost and the weighted patient waiting time are minimised. In order to solve this multi-objective optimisation problem, we construct a Pareto set of optimal solutions via the 𝜖-constraints method. For a particular staffing composition, the proposed model minimises the patient waiting time subject to upper bounds on the staffing size using the Sample Average Approximation Method. In our computational experiments, we discern the impact of prioritising the emergency department arrivals. Triaging results in lower patient waiting times for higher priority acuity classes and to a higher waiting time for the lowest priority class, which does not require immediate care. Moreover, we perform a sensitivity analysis to verify the impact of the arrival and service pattern characteristics, the prioritisation weights between different acuity classes and the incorporated shift flexibility in the model.