Natural disasters and crisis are inevitable and each year impose destructive effects 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. Effective distribution of emergency aid could have a significant role in minimizing the damage and fatal accident. In this study, a three-level relief chain including a number of suppliers in fixed locations, candidate distribution centers and affected 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 efficiency and effectiveness of the proposed model and solution approach, several numerical examples are studied. Computational results show the effectiveness and efficiency of the model and the proposed approach.

Keywords: location-routing model, Optimization, mixed integer nonlinear programming, network

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