A partially flexible routing strategy for assigning emergency department patients to inpatient wards

Abstract

Increasing flexibility in assigning emergency department patients to inpatient wards shortens the boarding time, which is known as an important driver for emergency department overcrowding crisis, whereas high levels of flexibility damages quality of care, adversely affects staff satisfaction, and complicates the implementation. We propose a partially flexible routing strategy to balance the trade-offs between positive and negative aspects of flexibility. We consider a partially flexible two-class queue with two heterogeneous server pools as our base model and analyze it by adopting a Matrix Analytic approach and derive a closed-form expression for the performance measures of this system by utilizing probability-generating functions. Using the base model, we develop a partially flexible routing algorithm that forms a bipartite graph that is both connected and cyclic. Connectivity and cyclicity alongside other properties of this algorithm offer comparable boarding times, a high level of quality of care, simplicity in practice, and staff satisfaction. By considering a fully flexible structure, where all patients can be assigned to all inpatient wards, as a benchmark, our simulation study results show that the performance of our proposed policy is similar to a fully flexible design in reducing boarding time under various system settings.