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Jamali H, Kabiri Naeini M, Elahi Z. A Two-echelon Model of Location-routing Problem for Optimizing Relief Operations in Natural Disasters. Disaster Prev. Manag. Know. 2025; 15 (2) :202-229
URL: http://dpmk.ir/article-1-735-en.html

Background and objective The location-routing problem (LRP) during disasters is a fundamental challenge in managing relief efforts to the affected areas. One of the most significant limitations in this context is the effective coverage of relief bases and the ability to provide timely aid to the affected area. In this study, a two-echelon model for LRP is developed, where each relief base can only provide services within a designed coverage radius. The goal is to determine the optimal locations for relief bases and routing relief teams to minimize relief time and cost at both levels. 
Method We combined the covering tour problem (CTP) with the two-echelon LRP to propose a model named “two-echelon relief covering tour location routing problem” (2E-RCTLRP). To solve the LRP in a large scale, a metaheuristic genetic algorithm (GA) was developed and utilized. To validate the proposed model, five small-scale problems were solved, and the solutions obtained from the proposed GA were compared with the exact solutions obtained from GAMS software. Also, a sensitivity analysis of the CTP was conducted to determine the necessary conditions for using the CTP and two-echelon methods for relief problems.
Results The developed GA was efficient and converged to the optimal solution. The sensitivity analysis results showed that two-echelon methods provide significantly better results than single-echelon methods. Additionally, the comparison of the solution for the non-synchronization of tours at two levels and the proposed model demonstrated the necessity of using the proposed model. 
Conclusion The proposed model is an effective method to improve relief operations and strengthen crisis management during natural disasters.