A multi-objective mathematical model for emergency and medical routing to provide healthcare services to victims

Effective Emergency Medical Services (EMS) management demands meticulous planning to enhance routing strategies, allocate resources efficiently, and ensure seamless coordination between responders and vehicles. This research introduces a comprehensive multi-objective mathematical model that jointly optimizes the routing and scheduling of both medical personnel and emergency vehicles. Distinct from earlier single-service frameworks, the proposed model captures complex scenarios where the concurrent presence of a paramedic and a vehicle is essential, while integrating practical constraints such as time windows, synchronization requirements, and equitable workload distribution. Recognizing the NP-hard nature of the problem, the study employs two powerful metaheuristic algorithms NSGA-II and PESA-II for solving large-scale instances effectively, and applies the Augmented Epsilon Constraint (AEC) method to handle smaller instances with high precision. Experimental results demonstrate that NSGA-II surpasses PESA-II in terms of performance metrics such as Mean Ideal Distance (MID) and spacing. Furthermore, Pareto front analysis provides insights into trade-offs between minimizing operational costs, improving paramedic productivity, and reducing patient response time. The findings highlight the importance of balancing these competing objectives to enhance the overall performance and responsiveness of EMS systems. This study offers valuable guidance for informed operational and managerial decision-making in emergency healthcare logistics.