Journal of Optimization and Supply Chain Management

Journal of Optimization and Supply Chain Management

A MILP-Based Framework for Sustainable and Service-Aware Dairy Vehicle Routing under Cold Chain Constraints

Document Type : ODSIE 2025

Authors
Deniz Şeref
Beyza Aksoku
Kıvılcım Naz Böke
Syed Shah Sultan Mohiuddin Qadri
Department of Industrial Engineering, Faculty of Engineering, Çankaya University, Ankara, Türkiye
10.22034/ISS.2026.10254.1075
Abstract
Objective: To present a mixed-integer linear programming (MILP) model for the Sustainable and Service-Aware Dairy Vehicle Routing Problem (SS-DVRP) that minimizes a composite cost including transportation cost, service-delay penalties, undelivered or spoilage penalties, and emissions, while considering customer time windows, vehicle load and refrigeration capacities, and a network-wide CO₂ emissions cap.
Methods: Three refrigerated vehicles serve ten customers from a single depot. In addition, a 3×3×3 full-factorial experiment (27 scenarios) is conducted on three parameters: vehicle refrigeration capacity (Rₖ), service-delay penalty (gᵢ), and maximum route length (Dmaxₖ). Heat maps, main-effect plots, and eta-squared (η²) analysis are used to evaluate how these parameters influence performance metrics.
Results: The results show that the service-delay penalty (gᵢ) has a clearly large effect on both the total objective value and minimum waste. Vehicle refrigeration capacity (Rₖ) has a small but non-negligible effect, including on transport cost. In contrast, the maximum route length (Dmaxₖ) remains relatively negligible within the tested range.
Conclusion: The SS-DVRP framework provides a practical decision-support approach that improves on-time delivery and product integrity while keeping environmental impact under control.
Keywords
vehicle routing
cold-chain logistics
time windows
MILP
emissions cap
Deng, F., Qin, H., Li, J., & Cheng, C. (2022). The pickup and delivery problem with time windows and incompatibility constraints in cold chain transportation. Transportation Science, 57(2), 444–462. https://doi.org/10.1287/trsc.2022.1167
Utama, D. M., Dewi, S. K., Wahid, A., & Santoso, I. (2020). The vehicle routing problem for perishable goods: A systematic review. Cogent Engineering, 7(1), Article 1816148. https://doi.org/10.1080/23311916.2020.1816148,
Chandran, J.G.D., & Shanmugam, J. (2025). Enhancing Dairy Supply Chains: A Framework for Cold Chain Performance Evaluation. Journal of Optimization and Supply Chain Management, 2(2), 82-94. https://doi.org/10.22034/ISS.2025.9026.1036   
Zhao, Z., Li, X., & Zhou, X. (2020). Optimization of transportation routing problem for fresh food in time-varying road network: Considering both food safety reliability and temperature control. PLoS ONE, 15(7), e0235950. https://doi.org/10.1371/journal.pone.0235950
Wang, S., Tao, F., Shi, Y., & Wen, H. (2017). Optimization of vehicle routing problem with time windows for cold chain logistics based on carbon tax. Sustainability, 9(5), 694. https://doi.org/10.3390/su9050694
Ariyasingha, I. D. I. D., & Fernando, T. G. I. (2015). Performance analysis of multi-objective ant colony optimization algorithms for the traveling salesman problem. Swarm and Evolutionary Computation, 23, 11–26 https://doi.org/10.1016/j.swevo.2015.02.003
Laporte, G., Gendreau, M., Potvin, J.-Y., & Semet, F. (2000). Classical and modern heuristics for the vehicle routing problem. International Transactions in Operational Research, 7(4–5), 285–300. https://doi.org/10.1111/j.1475-3995.2000.tb00200.x
Abu-Monshar, A., & Al-Bazi, A. (2022). A multi-objective centralized agent-based optimization approach for vehicle routing problem with unique vehicles. Applied Soft Computing, 125, 109187. https://doi.org/10.1016/j.asoc.2022.109187
Cheng, F., Jia, S., & Gao, W. (2024). Low-carbon logistics distribution vehicle routing optimization based on INNC-GA. Applied Sciences, 14(7), 3061.https://doi.org/10.3390/app14073061 
Fang, C., Cai, Y., & Wu, Y. (2025). The two-echelon unmanned ground vehicle routing problem: Extreme-weather goods distribution as a case study. Biomimetics, 10(5), 255. https://doi.org/10.3390/biomimetics10050255
Gkiotsalitis, K., & Nikolopoulou, A. (2023).The pickup and delivery problem with cross-dock for perishable goods. arXiv  https://arxiv.org/abs/2311.15428
Karimi, A., Zhang, L., Fackrell, M., & Thompson, R. (2024). A multi-objective two-echelon vehicle routing problem with multiple delivery options. Transportation Research Procedia, 79, 377–384. https://doi.org/10.1016/j.trpro.2024.03.050
Liu, Y., Tao, F., & Zhu, R. (2025). Vehicle routing problem for low-carbon cold chain logistics based on the idea of cost–benefit. Complex & Intelligent Systems, 11(2), Article 1756. https://doi.org/10.1007/s40747-024-01756-x 
Qi, B., & Li, G. (2024). The evolution of the cold chain logistics vehicle routing problem: A bibliometric and visualization review. Digital Transportation and Safety, 3(3), 92–114. https://doi.org/10.48130/dts-0024-0010
Tyapukhin, A. P. (2025). Classification, Digitalization and Structure of Integrated Logistics Chains. Management Science and Information Technology, 2(3), 189–215. https://doi.org/10.22034/ISS.2025.9029.1031
Shi, H., Zhang, X., Liu, Y., & Wang, Z. (2025). Research on cold chain logistics joint distribution vehicle routing optimization based on uncertainty entropy and time-varying network. Entropy, 27(5), 455. https://doi.org/10.3390/e27050455
Norouzian, R., & Plonsky, L. (2018). Eta- and partial eta-squared in L2 research: A cautionary review and guide to more appropriate usage. Second Language Research, 34(2), 257–271. https://doi.org/10.1177/0267658316684904
Journal of Optimization and Supply Chain Management
Volume 3, Issue 1
Winter 2026
Pages 43-56