A generalized three-stage optimization model for emergency medical services under uncertainties: Integrating rescue station locations, ambulance deployment, and vehicle dispatch

The rapid pace of urbanization and increasing social complexity have made the efficiency of Emergency Medical Services (EMS) crucial for public safety and societal stability. Most existing studies analyze rescue station locations, ambulance deployment, and vehicle dispatch separately. However, these studies mainly focus on deterministic factors, such as travel time and rescue demand, without addressing uncertainties in real-world transportation networks and resource constraints. To overcome these limitations, this paper proposes a three-stage optimization model. The first two stages aim to determine the optimal layout of rescue stations and the number of vehicles to deploy, considering effective travel time instead of traditional Euclidean distance. The concepts of “contribution” and “fairness” are introduced to maximize vehicle service efficiency. The third stage applies a multi-objective scheduling strategy that integrates road network data. This study proposes an exact algorithm based on the greedy (EABG) approach. The results show significant improvements in demand coverage and response efficiency, despite limited resources. Sensitivity analysis confirms that fuzzy logic effectively handles demand uncertainty. These results offer actionable insights for EMS resource allocation and policy design, advancing emergency response strategies in complex urban environments. In addition, the proposed algorithm significantly outperforms GA in terms of solution speed and quality.