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Untimely responses to emergency situations in urban areas contribute to a rising mortality rate and impact society's primary capital. The efficient dispatch and relocation of ambulances pose operational and momentary challenges, necessitating an optimal policy based on the system's real-time status. While previous studies have addressed these concerns, limited attention has been given to the optimal allocation of technicians to respond to emergency situation and minimize overall system costs.

In this paper, a bi-objective mathematical model is proposed to maximize system coverage and enable flexible movement across bases for location, dispatch and relocation of ambulances. Ambulances relocation involves two key decisions: (1) allocating ambulances to bases after completing services and (2) deciding to change the current ambulance location among existing bases to potentially improve response times to future emergencies. The model also considers the varying capabilities of technicians for proper allocation in emergency situations.

The Augmented Epsilon-Constrained (AEC) method is employed to solve the proposed model for small-sized problem. Due to the NP-Hardness of the model, the NSGA-II and MOPSO metaheuristic algorithms are utilized to obtain efficient solutions for large-sized problems. The findings demonstrate the superiority of the MOPSO algorithm.

This study can be useful for emergency medical centers and healthcare companies in providing more effective responses to emergency situations by sending technicians and ambulances.

In this study, a two-objective mathematical model is developed for ambulance location and dispatch and solved by using the AEC method as well as the NSGA-II and MOPSO metaheuristic algorithms. The mathematical model encompasses three primary types of decision-making: (1) Allocating ambulances to bases after completing their service, (2) deciding to relocate the current ambulance among existing bases to potentially enhance response times to future emergencies and (3) considering the diverse abilities of technicians for accurate allocation to emergency situations.