Open selective vehicle routing problem with pricing, Solved by improved Imperialist competitive algorithm

In this paper, modeling and solving an open selective vehicle routing problem with pricing are introduced. We will discuss optimal pricing when using a homogeneous fleet of vehicles. Furthermore, in some real world applications, companies prefer to distribute their products using rented vehicles so returning to the depot is not required. Therefore we face an open routing problem. Despite the applicability of such problem, we did not find any published research that examines it.also an Improved Imperialist Competitive Algorithm (IICA) is proposed to solve proposed model. For validating this method, some small scale problems are solved and results are compared to the results of an exact method and Simulated Annealing (SA) algorithm. The comparison of results shows that the proposed method is suitable for solving the model. For investigating its efficiency in dealing with real world problems, some large scale problems are solved and the results are compared to the results of Simulated Annealing (SA) algorithm. Results show that IICA is more efficient than SA.