Rescheduling of physician allocation with control charts in an emergency department

This study proposes a data-driven framework for stochastic physician rescheduling in emergency departments (EDs) based on detecting structural changes in the patient arrival process, using three time-between-events (TBE) control charts: a gamma, a range-based, and a generalized likelihood ratio (GLR) chart. Patient arrivals are modeled as a nonhomogeneous Poisson process (NHPP) and transformed into a homogeneous Poisson process (HPP) with standard exponentially distributed interarrival times, representing the TBE data. The proposed control charts are employed on empirical arrival and treatment time data from a German ED. Our contribution is threefold: we introduce an integrated simulation–optimization and monitoring framework for physician rescheduling; we assess the effectiveness of the TBE charts in identifying different structural breaks in the patient arrival process; and we quantify the impact on waiting time statistics, which directly supports objective physician capacity planning. Across the investigated scenarios, including overall volume shifts, crowded weekends, and stronger seasonality, structural changes are detected within a medium-term horizon and under different patient volume shifts in almost all cases. Only the most subtle scenario (stronger seasonality with a 10% volume shift) is detected more slowly. Especially, the GLR chart, but also the gamma chart, show particular efficacy in detecting complex process shifts. The proposed framework enables continuous monitoring of patient arrivals and objective, data-driven physician staffing decisions to mitigate adverse impacts on patient waiting times and associated health risks. Additionally, it is transferable to other hospital staff or service systems with time-varying demand, demonstrating its broad adaptability.