Two-stage multi-objective location-routing-inventory model for humanitarian logistics network design under uncertainty

The accidental and unpredictable nature of disasters such as earthquake brings about some plans to deal with critical problems in order to reduce the dangers at the time of their occurrence. Effective distribution of relief goods and supplies plays an important role in the rescue operation after an earthquake. Therefore, a two-phase, multi-objective mixed integer, multi-period and multi-commodity mathematical modeling in the three-level relief chain was offered, in which, locating of the distribution centers and warehouses with various levels of capacity, related decisions to the stored goods in the warehouses and established distribution centers were considered in the first phase, and considering the limited hard time windows, in the second phase, operational programming was performed for vehicle routing and distribution of goods to the affected areas, so minimizing the total cost and travel time also increased the reliability of the route. In addition to the features considered in this model, in special cases, it is possible that each critical area receives service more than once; to consider split delivery assumption in the problem, a different model will be presented for this purpose. Since some parameters are uncertain during the crisis, in order to let the model approach the reality, using a robust optimization approach, the model was developed in an uncertain condition. Two meta-heuristic algorithms of NSGAII and MOPSO were used to solve the given problem, in which the accuracy of the mathematical model and the proposed algorithms efficiency were assessed through numerical examples. The results of algorithms were presented for 35 various problems.