A robust neutrosophic fuzzy-based approach to integrate reliable facility location and routing decisions for disaster relief under fairness and aftershocks concerns

Relief distribution and victim evacuation are the crucial emergency relief operations after sudden-onset disasters to alleviate the repercussions of catastrophes in the concerned areas, although aftershocks and unfair distribution of relief items can affect these planning and beget plenty of undesirable reflections. In this paper, a new multi-objective reliable optimization model to organize a humanitarian relief chain is rendered to make a broad range of decisions, including reliable facility location-allocation, fair distribution of relief items, assignment of victims, and routing of trucks. For this purpose, the first objective function is to minimize the total logistics costs, the second one is to minimize the total time of relief operations, and the third one minimizes the variation between upper and lower bounds of transportation cost of distribution centers to regulate the workload of them. What is more, due to the fact that the uncertain essence of catastrophes, such as demand, the capacity of facilities, miscellaneous costs and transportation times, a novel uncertainty approach, including robust optimization and the neutrosophic set, is proposed to surmount these obstacles. Ultimately, a real case study is examined to illustrate the validity of the proposed model and solution method. The obtained results reveal that via increasing the capacity of the emergency centers by 30%, the total cost of the humanitarian relief network is reduced by 18%, and the operating time is reduced by 9%. What is more, if the probability of disruption in one of the distribution centers reaches zero, the logistics costs will be reduced to approximately 20%, and also the distance between the maximum and minimum distance traveled will be reduced by 30%, and the workload between distribution centers will be more balanced.