Dynamic Physician Rostering in Emergency Departments: Managing Reentrant Patient Flows to Meet Excess Wait Time Targets.

BACKGROUND: This study optimizes physician rostering for emergency departments facing fluctuating patient volumes and complex flow dynamics. Specifically, we address the challenge of patient reentry, including those who leave without being seen and subsequently return (pre-service returns), as well as patients leaving subsequent to being seen requiring repeat evaluation or treatment for unresolved conditions (post-service revisits). These endogenous patient flows significantly disturb the clinical workload and complicate capacity planning. METHODS: We develop a patient flow model that integrates these return loops and formulate a risk-aware physician rostering framework designed to strictly enforce excess wait time targets, for example, tail probability of delay service levels. We employ a simulation-based iterative staffing algorithm to efficiently compute the optimal physician rules required hour-by-hour. RESULTS: Discrete-event simulation experiments demonstrate that this approach effectively aligns workload with demand to maintain care standards without incurring unnecessary labor costs. CONCLUSIONS: This study develops a simulation-based, risk-aware physician rostering framework for emergency departments with reentrant patient flows to meet excess wait time targets such as tail probability of delay while reducing unnecessary workload pressure.