Robust possibilistic programming for vehicle routing, scheduling and resource distribution in post-earthquake relief operations regarding disruption and under uncertainty

Since natural disasters often lead to the loss of human lives and property, the proper design of a post-disaster relief distribution network is essential. Besides, because the affected people cannot survive more than a few days without water, food, medicine and shelter, the routing and distribution of relief goods at maximum speed is crucial and is one of the main goals of this research. Minimizing the number of equipment needed to reduce costs and equal distribution of relief goods, so that there is not too much shortage in one shelter than another is the other goal of the study. To achieve these objectives, a tri-objective mathematical model for a distribution logistics system is designed to route and schedule relief vehicles for distributing relief goods from distribution centers (DCs) to shelters under uncertainty, and disruptive distribution. In order to deal with the uncertainty, two different methods have been used, including a credibility-based possibilistic programming method, and the robust possibilistic method. To solve the proposed multi-objective model, an interactive fuzzy approach has been used. Then, to investigate the applicability of the proposed mathematical model, it has been implemented on a real case study in the city of Tabriz, Iran. According to the obtained results and the decision maker's priority to reduce the unmet demand in this paper, the robust possibilistic method is finally selected as the best method to handle this problem. Also, the results of solving the case study show that there is an inverse relationship between the supply of relief goods and the distribution time of relief goods, and the percentage of reduction in the distribution time of relief goods in exchange for an excessive increase in the supply of relief goods is very small, which could be ignored.