Multi-objective location-routing model with multiple transportation modes for designing relief networks under uncertainty Running Title: location-routing model under uncertainty

Natural disasters and crisis are inevitable and each year impose destructive e ects on human as injuries and damage to property. In natural disasters and after the outbreak of the crisis, demand for logistical goods and services increase. E ective distribution of emergency aid could have a signi cant role in minimizing the damage and fatal accident. In this study, a three-level relief chain including a number of suppliers in xed locations, candidate distribution centers and a ected areas at certain points are considered. For this purpose a mixed integer nonlinear programming model is proposed for open transportation location routing problem by considering split delivery of demand. In order to solve a realistic problem, foregoing parameters are considered as fuzzy in our proposed mode. The objectives of the proposed model include total cost minimization, minimization of the maximum travel time of vehicles and minimization of unmet demands. In order to solve the problem of the proposed model, fuzzy multi-objective planning is used. For e ciency and e ectiveness of the proposed model and solution approach, several numerical examples are studied. Computational results show the e ectiveness and e ciency of the model and the proposed approach.