Traortation dedicates remarkable part of national gross production in every country and a large part of researches. One of the traortation problems is vehicle routing problem with backhaul in which vehicles departed from origin and on the way deliver required goods or products to the consumers and with the completion of visiting part or whole of them, on the way back can visit another part of consumers and pick up items from them and return to the origin. Often distribution of goods occurs in the urban areas and not considering traffic affect the quality of solution. In this thesis, for time dependent vehicle routing problem with backhaul a mathematical mixed integer model is presented to reduce travel time. In order to get closer this problem to the real world the First Input First Output (FIFO) assumption is considered. Considering the issue that the proposed problem is NP-hard, in order to optimally solve the proposed model, the Cplex solver is used for small-scale instances. Using large-scale instances, results of two suggested methods including variable neighborhood search, mat-variable neighborhood search Algorithms are compared. Results show that, mat-variable neighborhood search in terms of quality of solutions has better performance than other suggested algorithm. Finally in order to investigate the effectiveness of the proposed model, a case study in Qomeini-shahr was considered; results show about 19% reduction in travel time.
