Solving a vehicle routing problem considering customers’ satisfaction and energy consumption by a bee algorithm

In this paper, a new method for a vehicle routing problem (VRP) with reducing the fuel consumption and maximizing customers’ satisfaction. To reduce the hazardous effects of transportation like land usage, resource and energy consumption, air pollution, global warming, damage to ecosystems and human health, researchers developed optimization models like vehicle routing problem (VRP) and its variants. Generally, the amount of pollution emitted by a vehicle over an arc (i,j) depends on many factors like vehicle load, travel speed, travel distance, road slop and etc. Vehicle load has a major effect among other factors on amount of emissions and influences the route selection. On the other hand, this paper considers customers’ satisfaction via considering earliest and latest service time in customer nodes. It is proven that VRPs belong to the category of NP-Hard problems thus due to the complexity of VRP with exact methods in large-scale problems, a meta-heuristic method based on bee algorithm (BA) is proposed. Furthermore, to show the efficiency of the proposed BA, a number of test problems in small and large sizes are solved. Finally, the obtained results are evaluated with the results obtained by GAMS and PSO algorithm. On the other hand, this paper considers customers’ satisfaction via considering earliest and latest service time in customer nodes. It is proven that VRPs belong to the category of NP-Hard problems thus due to the complexity of VRP with exact methods in large-scale problems, a meta-heuristic method based on bee algorithm (BA) is proposed. Furthermore, to show the efficiency of the proposed BA, a number of test problems in small and large sizes are solved. Finally, the obtained results are evaluated with the results obtained by GAMS and PSO algorithm.