This study presents a Green Vehicle Routing Problem (GVRP) with two core objectives: Reducing total travel distance and cutting vehicle emissions. This dual focus aims to advance both cost-effectiveness and ecological responsibility in logistics. To effectively handle the dual objectives, the model is initially reformulated using the -constraint method, which facilitates the generation of a Pareto front representing optimal trade-offs between the conflicting goals. To solve the problem at various scales, both exact and metaheuristic approaches are employed. The exact method, implemented via a branch-and-cut algorithm, is capable of producing optimal solutions for small- and medium-sized problem instances. However, when applied to large-scale instances, this method becomes computationally expensive and only yields high-quality upper bounds after extended runtimes. To overcome these limitations, two metaheuristic algorithms are developed: A standard Ant Colony Optimization (ACO) and a hybrid version combining ACO with Simulated Annealing (ACO-SA). While the classical ACO provides strong global search capabilities, the integration of SA enhances local exploitation and increases solution diversity. Comprehensive computational experiments confirm the effectiveness of both metaheuristics. Notably, the hybrid ACO-SA consistently outperforms the standalone ACO and the exact approach achieving higher-quality solutions with greater computational efficiency, particularly for large-scale scenarios. The findings confirm that the hybrid framework offers significant scalability and direct practical value for planning sustainable logistics operations.
