Developing a Multi-Objective Mathematical Model of a Vehicle Routing Problem for Fuel Transportation with Time Windows and Environmental Factors

This paper considers a vehicle routing problem (VRP) for fuel transportation with time windows and environmental factors. In the presented model, in addition to minimizing the cost and risk reduction, balancing the path of the vehicle is taking into account with environmental impacts in order to find the safest path for the vehicle considering the economical aspects. The selected routes for the vehicles should be determined to do not exceed the certain amount of environmental air pollution. In the previous studies related to the vehicle routing for fuel transportation, there was no any study considering these three objectives with regard to environmental consequences. Due to such an NP-hard problem to solve large-scale problem, two meta-heuristic algorithms, namely NSGA-II and MOVDO, are proposed and the Taguchi method is used to tune the related parameters. The five indices are used to compare the performance of the foregoing algorithms. Finally, to assess the applicability of the presented model, 15 problems with different sizes are considered. Finally, the results obtained by each of these two algorithms are explained. The results obtained by solving the problems with different sizes show the appropriate efficiency and effectiveness in solving the large-sized problems in a short computational time.