The periodic vehicle routing problem is a generalization of the normal" . City logistics aims to reduce the nuisances associated with freight traortation in urban areas while supporting their economic and social development. Indeed freight traortation in the city areas is one of the main causes of traffics, air and noise pollutions. Thus a two-echelon distribution system could tackle this problem. In a two-echelon system goods from the main depot are distributed through intermediate facilities called satellites. A two-echelon distribution system could reduce the traortation costs by up to 30 percent. In this reasearch, a mathematical model is proposed for PVRP. The proposed model is NP-hard and in order to solve it, two meta-heuristics named Variable Neighborhood Search and Adaptive Large Neighborhood Search are used. Some numerical sample are solved by the exact approach to verify the solution approach. The results of the two proposed algorithms for large instances proved the better performance of Adaptive Large Neighborhood Search in comparison with Variable Neighborhood Search for the given data.
