Data-Driven Patient Scheduling in Emergency Departments: A Hybrid Robust–Stochastic Approach

Emergency care necessitates adequate and timely treatment, which has unfortunately been compromised by crowding in many emergency departments (EDs). To address this issue, we study patient scheduling in EDs so that mandatory targets imposed on each patient’s door-to-provider time and length of stay can be collectively met with the largest probability. Exploiting patient flow data from the ED, we propose a hybrid robust–stochastic approach to formulating the patient scheduling problem, which allows for practical features such as a time-varying patient arrival process, general consultation time distributions, and multiple heterogeneous physicians. In contrast to the conventional formulation of maximizing the joint probability of target attainment, which is computationally excruciating, the hybrid approach provides a computationally amiable formulation that yields satisfactory solutions to the patient scheduling problem. This formulation enables us to develop a dynamic scheduling algorithm for making recommendations about the next patient to be seen by each available physician. In numerical experiments, the proposed hybrid approach outperforms both the sample average approximation method and an asymptotically optimal scheduling policy.