A Granular Approach to Optimal and Fair Patient Placement in Hospital Emergency Departments

Prolonged emergency department (ED) length of stay (LOS) is associated with detrimental effects on patient care quality and outcomes. There is evidence that certain groups of patients experience longer LOS based on their gender or race, especially with regard to the part of LOS that is attributable to waiting to be seen by a clinician. This work tackles the patient prioritization and placement aspects of ED operations with the goal of improving throughput and wait time in a fair, equitable way. We present a novel Mixed Integer Linear Programming (MILP) predictive-prescriptive formulation that incorporates a breakdown of predicted patient ED LOS into actionable pieces. We incorporate considerations for fairness and reformulate the MILP formulation into a compact and computationally tractable formulation that can be solved efficiently in real time. To deal with uncertainty, we propose a sampling-based solution, and provide provable guarantees regarding its convergence, stability and sample complexity. The proposed solution increases the throughput of the ED by 50 - 100 % and decreases the average wait time by 50 - 75 % compared to current hospital practice. In addition, the method is near-optimal in terms of throughput, and produces high-quality solutions in terms of average wait time compared to a clairvoyant oracle. Our proposed approach demonstrates desirable properties when it comes to fairness in patient prioritization, illustrating a path for addressing hidden biases in patient ED wait times and hospital operations as a whole. This work was conducted in collaboration with a large US academic medical center. Data from more than 40,000 patient visits were used to shape and evaluate the predictive-prescriptive models. An important practical contribution is translating a complex algorithm's output into recommendations that can be operationalized in the context of existing processes in the ED. Specifically, we develop an interpretable metamodel that is trained to mimic the predictive-prescriptive algorithm's decisions and provides a transparent set of rules for patient placement. The method will be used by the hospital to improve patient flow and quality of care as well as to support more fair and consistent bed allocation decisions.