Introduction: Crises and natural disasters are among the most serious threats to human societies. The Emergency Medical Services (EMS) system plays a vital role in crisis management, and its performance quality can determine the line between life and death. System efficiency heavily depends on strategic station location decisions and operational resource allocation and dispatch decisions. This study presents an integrated multi-objective mathematical model for locating and dispatching emergency service facilities, with special emphasis on coverage radius. The main innovation is the simultaneous integration of three decision-making levels: strategic, tactical, and operational.

Methods: In this study, a Mixed Integer Programming (MIP) model was developed that simultaneously determines the locations of relief stations and field hospitals, the placement of a mixed fleet including ambulances and motorlances, the allocation of patients based on injury severity (normal and acute) to medical centers, and the prioritization of vehicle dispatch. Patients were categorized into two groups based on injury severity: normal (served on-site) and acute (requiring transfer to a hospital). A coverage radius constraint was considered for each vehicle, and to enhance reliability, simultaneous coverage of each demand point by at least two vehicles (backup coverage) was mandated. To prioritize vehicles in each patient's dispatch list, the Rank Sum Weighting (RSW) method was used, which dynamically calculates the weight of each position based on the list length. The objective functions include minimizing total service time (including travel time to the scene, on-site service time, and transfer time to the hospital) and minimizing network development costs (including the construction of new stations and hospitals, and additional coverage costs). Due to the heterogeneity of the objective functions, the normalized goal programming method was used to combine them. The model was implemented in GAMS software and solved using the CPLEX solver on a numerical example consisting of 4 demand points, 4 candidate stations, 3 potential hospitals, and 8 emergency vehicles, and a sensitivity analysis was performed.

Results and discussion: Among 4 potential points, three stations were selected, and 8 vehicles were allocated to them. Dispatch prioritization was determined for each patient type in each region. Among 3 potential hospitals, two were selected, with Hospital 1 covering Region 1 and Hospital 2 covering Regions 2, 3, and 4. Average service time was 28.12 minutes for normal patients and 27.49 minutes for acute patients. Total service time was 3350 minutes (2250 for 80 normal patients, averaging 28.12 minutes; 1100 for 40 acute patients, averaging 27.49 minutes). Total cost was 3600 monetary units. Sensitivity analysis revealed important results: a trade-off between the two objectives is evident; increasing the time objective weight reduces OF1, while increasing the cost objective weight reduces OF2. As the crisis disruption rate increases, available vehicles per patient decrease, but the number of stations and hospitals does not change, indicating that in severe crises, optimal location selection is more important than increasing facility count. Increasing the coverage radius raises the total number of authorized vehicles, and when the radius decreases, additional coverage becomes permitted at some stations. Moreover, increasing coverage radius and list size does not necessarily reduce the time objective, as including more distant vehicles in the priority list raises the average time.

Conclusion: The proposed integrated model, by simultaneously considering strategic, tactical, and operational layers, can significantly improve EMS efficiency and resilience in crises. The main distinction from previous studies is the systemic approach to location-dispatching with emphasis on optimal coverage radius, mixed fleet with dynamic prioritization, and mandatory backup coverage to enhance network reliability. Findings indicate crisis managers should focus on optimal location selection and effective radius determination considering demand dispersion, rather than merely increasing coverage radius or station numbers.