Application of a sampling and clustering-based heuristic search algorithm to find an efficient staff configuration in an emergency department

Emergency Departments (EDs) are among the most complex areas in healthcare, requiring immediate medical attention for acute and urgent conditions. Optimizing staff configurations to reduce patient Length of Stay (LoS) and improve operational efficiency poses a significant challenge due to the combinatorial and high-dimensional nature of the problem. To identify the most effective staff configuration, we propose a heuristic optimization strategy that is based on the Montecarlo Clustering Search Algorithm (MCSA), which efficiently explores the multidimensional solution space. MCSA leverages an agent-based simulation (ABM) model that evaluates each proposed staff configuration under realistic operational conditions, providing Key Performance Indicator (KPI) feedback values related to each proposed staff configuration. Through this strategy, we explore staff configurations capable of handling patient volumes with varying acuity levels in an ED to optimize the LoS KPI. Results demonstrate that our methodology is capable to find a solution as a staff configuration that reduces LoS compared to a baseline, offering a computationally efficient and practical tool for decision-makers. We identified solutions by exploring less than 1% of the total search space, demonstrating the efficiency of the proposed approach in addressing complex optimization problems. This approach supports informed planning in healthcare environments while maintaining system feasibility and scalability.