Mathematical Modeling for a Vehicle Routing Problem with Backhaul Solved by a New Multi-Ant Colony Optimization Algorithm

This paper considers the vehicle routing problem with backhaul (VRPB) and some applicable constraints, in which a set of costumers are divided into two subsets of linehaul and backhaul costumers. Each linehaul costumer requires its demands to be delivered from the depot. In addition, a specified quantity of products should be picked up from the backhaul nodes to the depot. The main point in this study is that the customer demands, which are over than the maximum of available vehicles, can be divided to different customers. In addition, there is limited vehicle access availability for some costumers. The central depot includes a fleet of vehicles with different capacities, in which the number of vehicles of each type is not limited and customer demands are dynamic and can change in each period. This problem is a well-known NP-hard one; therefore, a new multi-ant colony optimization algorithm is proposed to solve the given problem. This proposed algorithm contains two phases, namely clustering and routing. Finally, the numerical results of designed test problems have been discussed and analyzed.