This research was conducted to study the issue of relief facility location hierarchically by consideration of possible road closure during the crisis conditions, road safety, and arrival time of relief facilities under disaster circumstances. High costs are allocated for facilities deployment in a suitable location to meet the demands of injured people. Therefore, location-allocation of emergency facility should be considered in a way to use them for long-term periods. To this end, the extant research designed a multi-objective optimization model to minimize the pre-disaster costs including costs of facilities deployment and road use, and to minimize the post-disaster costs such as cost transportation innetwork roads. Moreover, the innovative part of the studied model in this research examined the road safety and reduction in time taken to have critical facilities in affected areas. To investigate the functional accuracy of the mathematical model, a numerical example with small dimensions was solved using CPLEX Solver, and required sensitivity analysis was described. As the facility location-allocation is an NP-hard issue, two meta-heuristic algorithms were used to solve numerical representations in real dimensions to examine numerical analyses effectively. Results showed that the dragonfly algorithm had the highest efficiency compared to other developed algorithms. The obtained results can be considered as an efficient managerial tool in management organizations involved in the crisis.