Mathematical Model for Special Capacitated Vehicle Routing Problem Considering Environmental Factors
Keywords:
Vehicle Routing Problem, Green Logistics, Carbon Dioxide Emissions, Mixed-Integer Linear Programming, Sustainable TransportationAbstract
This research proposes a mathematical model for the capacitated vehicle routing problem with special operational constraints, incorporating environmental considerations in a real-world beverage distribution case study. The model determines the optimal selection of vehicles, routes, truck types, and loading configurations to minimize total carbon dioxide (CO₂) emissions while satisfying practical capacity and operational requirements. The proposed model is formulated as a mixed integer linear programming problem and solved using the GUROBI Solver. Computational results indicate that the optimized routing plans achieve a minimum total emission of 145.70 kgCO₂eq/L, outperforming the company’s existing delivery strategy. Furthermore, experiments using daily demand data over a 10-day period demonstrate an average CO₂ emission reduction of 7.96%, implying improved fuel efficiency and more sustainable transportation operations. These findings highlight the practical relevance of applying exact optimization models to address current challenges in emission-aware logistics planning. Future research may extend the proposed framework to larger-scale networks, multi-objective formulations, and additional environmental indicators to further enhance decision-making in sustainable transportation systems.References
[1] J. Faulin, A. Juan, F. Lera and S. Grasman, Solving the capacitated vehicle routing problem with environmental criteria based on real estimations in road transportation: A case study, Procedia - Social and Behavioral Sciences, 20, 2011, 323-334.
[2] A. C. Mario Marinelli and Mauro Dell’Orco, A novel dynamic programming approach for two-echelon capacitated vehicle routing problem in city logistics with environmental consideration, Proceedings of the EURO Mini Conference on Advances in Freight Transportation and Logistics, Padova, Italy, 30, 2018, 147-156.
[3] R. Bernardino and A. Paias, The family capacitated vehicle routing problem, European Journal of Operational Research, 314(3), 2024, 836-853.
[4] H. Pollaris, K. Braekers, A. Caris, G. K. Janssens and S. Limbourg, Capacitated vehicle routing problem with sequence-based pallet loading and axle weight constraints, EURO Journal on Transportation and Logistics, 5(2), 2016, 231-255.
[5] N. Huang, H. Qin, G. Xu and F. Wan, An enhanced exact algorithm for the multi-trip vehicle routing problem with time windows and capacitated unloading station, Computers and Operations Research, 168, 2024, 1-16.
[6] J. Chi and S. He, Pickup capacitated vehicle routing problem with three-dimensional loading constraints: Model and algorithms, Transportation Research Part E: Logistics and Transportation Review, 176, 2023, 1-35.
[7] E. Jabir, V. V. Panicker and R. Sridharan, Multi-objective optimization model for a green vehicle routing problem, Procedia - Social and Behavioral Sciences, 189, 2015, 33-39.
[8] B. Sawik and E. Perez-Bernabeu, A multicriteria analysis for the green vehicle routing problem: A case discussion for the distribution problem of a Spanish retailer, Transportation Research Procedia, 22, 2017, 305-313.
[9] S. Xu, Y. Zhai, J. Feng and G. Liu, A framework of carbon-neutral waste transportation: Modeling and sensitivity analysis, Circular Economy, 2, 2023, 1-13.
[10] H. M. Stellingwerf, A. Kanellopoulos, J. G. A. J. van der Vorst and J. M. Bloemhof, Reducing carbon dioxide emissions in temperature-controlled road transportation using the LDVRP model, Transportation Research Part D: Transport and Environment, 58, 2018, 80-93.
[11] W. Gao, Z. Luo and H. Shen, A branch-and-price-and-cut algorithm for time-dependent pollution routing problem,
Transportation Research Part C: Emerging Technologies, 156, 2023, 1-18.
[12] H. Li, T. Lv and Y. Li, The tractor and semitrailer routing problem with many-to-many demand considering carbon dioxide emissions, Transportation Research Part D: Transport and Environment, 34, 2015, 68-82.
[13] L. F. López-Castro, E. L. Solano-Charris and A. Pagès-Bernaus, Environmental approach for the design of raw milk collection routes with a heterogeneous fleet, Computers and Electronics in Agriculture, 211, 2023, 1-17.
[14] H. Labidia, N. B. Azzounaa, K. Hassineb and M. S. Gouider, An improved genetic algorithm for solving the multi-objective vehicle routing problem with environmental considerations, Procedia Computer Science, 225, 2023, 3866-3875
[15] G. F. Mohammad Javad Jafari, A. Magni, A. Mereu, R. Minciardi, M. Paolucci and M. Robba, Optimizing a capacitated vehicle routing problem with scheduled arrival, split deliveries within time windows and emission consideration, IFAC PaperOnLine, 58(2), 2024, 180-185.
[16] P. N. Dias, S. M. Vieira and J. M. C. Sousa, Fast late acceptance local search for mixed capacitated arc routing problems, IFAC PaperOnLine, 59(10), 2025, 2439-2444.
[17] S. Schoepf, J. Senoner, L. Xu, T. Netland and A. Brintrup, Towards scalable three-dimensional loading capacitated vehicle routing, IFAC PaperOnLine, 59(10), 2025, 2939-2944.
[18] S. Phongmoo, K. Leksakul, N. Charoenchai and C. Boonmee. Artificial bee colony algorithm with pareto-based approach for multi-objective three-dimensional single container loading problems, Applied Sciences, 13(11), 2023, 1-20.
[19] C. Boonmee, M. Arimura and C. Kasemset, Post-disaster waste management with carbon tax policy consideration,
Energy Reports, 7, 2021, 89-97.
[20] C. Boonmee, J. Mangkalakeeree and Y. Jeong, Towards sustainable digital transformation: Artificial intelligence adoption barriers and enablers among small and medium-sized enterprises in Northern Thailand, Sustainable Futures, 10, 2025, 1-17
[21] C. Boonmee and N. Tanpruttianunt, A fuzzy multi-criteria decision framework for community isolation center site selection to enhance public health resilience, Journal of Safety Science and Resilience, 7(1), 2026, 1-24.
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