The vehicle routing problem (VRP) is the problem of designing optimal delivery from a given depot in order to satisfy the customer population demand by a similar fleet of vehicles. It is noted that a considerable part of the drivers’ benefits is related to their traveled distance; therefore, the balance of the route based on 'vehicles travelled distance' is important to obtain drivers’ satisfaction. This paper presents a balance, based on the vehicles traveled route called balanced vehicle routing problem (BVRP) and then, a model integer linear programming is proposed for solving the BVRP. Because this problem belongs to NP-hard problems, an effective rank based ant system (ERAS) algorithm is proposed in this paper. In addition, a number of test problems involving 10 to 199 customers have been considered and solved to show the efficiency of the proposed ERAS. The computational results show that the proposed algorithm results are better than the results of classical rank based ant system (RAS) and exact algorithm for solving the BVRP within a comparatively shorter time period.
