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Designing a multi-objective multiple allocation-routing problem in a humanitarian supply chain is important because it improves efficiency and productivity in the supply chain. By designing a multi-objective multiple assignment-routing problem, we can consider different objectives at the same time and seek to optimize them. As a result, designing a multiple multi-objective allocation-routing problem in a humanitarian supply chain can improve the overall performance of the company and lead to the economic and social growth of the region.

In this article, an integer mathematical model for the allocation of essential product to all destinations through multiple hub allocation-routing coverage is presented in a way that reduces the cost of allocation and the number of possible paths for allocation in a humanitarian supply chain. The proposed model is able to estimate well the binary optimal solutions of the problem that is route and vehicle allocation through the solution using the scattering search method. Based on the solution of the proposed model, the shortest possible route for allocating essential items to different considered cities is provided. Also, the lowest possible cost has been determined for allocating the route for relief. Finally, the allocation of each vehicle according to their type to each city has been specified. This allocation of vehicles to each of the cities has been done in such a way that each of the vehicles covers each of the cities at least once.

Based on the obtained results, the lowest routing allocation cost was gained using the suggested model. The results of the research show that the proposed model improves both the efficiency and effectiveness of humanitarian aid logistics, and its findings provide valuable guidance for improving decision-making regarding route allocation, the type of dispatch vehicle and cost in the field of humanitarian logistics, and for designing a suitable strategy for Dealing with disasters will be beneficial in the future.