One of the important issues in transportation and logistics systems is vehicle routing problem (VRP) which in general involves a set of problems including the number of vehicles located in depot are expected to meet and service a set of customers, each requiring a certain amount of demands. On the other hand, regarding the increasing environmental concerns, economic problems and pressure of laws, green logistics (GL) and reverse logistics (RL) have received increasing attention during recent years. In this regard, this study investigates a vehicle routing problem in reverse logistics with split demand of customers in which the demand of different points can be divided among vehicles and fuel consumption optimization. In this paper, fuel cost of vehicles was assumed to be dependent on their traveled path and load. For this problem, a mixed integer linear programming model was proposed. Finally, to validate the proposed model, some examples were solved by GAMS software. As the problem was NP-hard and its solution time increased exponentially, a simulated annealing algorithm was proposed to solve the problem in large-sized cases. Computational results and related comparisons showed algorithm efficiency.
