عنوان مقاله [English]
Supply chain management is considered one of the most important pillars of today's businesses, and a large portion of the cost of any manufacturing and service organization is spent in this cycle.One of the most important components of the efficiency of each supply chain is the availability of an optimal transportation system. The mathematical approach governing the modeling and optimization of this transportation system is the Vehicle Routing Problem Approach. In this paper, with the aim of minimizing supply chain costs and maximizing customer satisfaction, modeling, solving and verifying the distribution system in a bi-level closed loop supply chain with uncertain variables has been undertaken.Here, due to the uncertainty of the modeling variables, and that the optimal answer can be any vector combination of the studied graph nodes, the problem is classified in terms of the degree of complexity of the NP-hard issues and its optimal solution through methods Classical mathematical programming is not possible.In this study, a metaheuristic fire-fly algorithm used to solve the problem. In this regard, the main variables and parameters included in the model are the number, speed, capacity, average loaded and distance traveled,and the number, Geographical distribution, the amount of goods requested and returned of retailers. In order to investigate the validity of the obtained response, we also modeling and solving of 3 scenarios and comparing the results with a random method(current method in distribution company), which shows the effectiveness of the proposed method.