The current competitive environment is drawing increasing attention to green logistics. Road transport is a significant source of carbon emissions, which contribute to environmental pollution. Multi-objective algorithms are typically used to represent transportation problems like the Green Capacity Vehicle Routing Problem (GCVRP). These problems are NP-difficult and provide a Pareto front with incomparable solutions. In this context and in order to divert these issues, the purpose of this article is to propose a new approach to modeling the GCVRP problem in the form of single-objective programming. The idea is to look for the shortest path in a new virtual graph that is designed by integrating CO2 emissions into actual distances. This new modeling approach facilitates digital resolution and decision-making. The numerical results show the effectiveness of the model. In addition, the calculation time and the quality of the solution are much better.