Smart Logistics Optimization with Fractional Order Models and Artificial Intelligence Techniques

Subject Areas : International Journal of Smart Electrical Engineering

Hosein Esmaili ¹ , Mohammad Ali Afshar Kazemi ² , Reza Radfar ³ , Nazanin Pilevari ⁴

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Received: 2025-01-23 Accepted : 2025-06-05 Published : 2025-07-12

Keywords: Multi-modal logistics optimization, Fractional differential equations, Fire Hawk Optimization Algorithm, Stochastic demand modeling, Dynamic network flow analysis.,

Abstract :

Optimizing dynamic multi-modal logistics networks is vital for efficient resource allocation and cost minimization under stochastic demand. This study develops a robust framework integrating fractional differential equations for modeling temporal flow dynamics and employs the Fire Hawk Optimization Algorithm (FHOA) to address the resulting complex optimization problem. The proposed framework represents logistics networks as directed graphs, incorporating stochastic demand modeled using Gaussian perturbations and fractional derivatives to capture memory effects. Validation using the Barcelona logistics dataset reveals a total cost reduction of 8,835 units, average flow stabilization at 3.05 units, and resilience under demand variance of 52.32. The model effectively identifies critical edges with high flows, balancing throughput and minimizing costs across scenarios. Furthermore, the algorithm enhances decision-making by optimizing transportation policies and resource allocations, ensuring operational efficiency under uncertainty. The study's findings emphasize the significance of integrating advanced mathematical modeling with metaheuristic optimization techniques to tackle the inherent complexities of logistics systems. These insights provide a scalable and adaptive solution for real-world multi-modal logistics networks.

References:

[1] . Zhang, J., Li, H., Han, W., & Li, Y. (2024). Research on optimization of multimodal hub-and-spoke transport network under uncertain demand. Archives of Transport, 70(2), 137-157. https://doi.org/10.61089/aot2024.1g17bx18

[2] . Mishra, S., & Lamba, K. (2024). Integrated decisions for global supply chain network configuration: a dynamic multi-modal perspective. International Journal of Management Science and Engineering Management, 1-11. https://doi.org/10.1080/17509653.2024.2324185

[3] . Meng, L., Wang, X., He, J., Han, C., & Hu, S. (2023). A two-stage chance constrained stochastic programming model for emergency supply distribution considering dynamic uncertainty. Transportation Research Part E: Logistics and Transportation Review, 179, 103296. https://doi.org/10.1016/j.tre.2023.103296

[4] . Peng, Y., Gao, S. H., Yu, D., Xiao, Y. P., & Luo, Y. J. (2023). Multi-objective optimization for multimodal transportation routing problem with stochastic transportation time based on data-driven approaches. RAIRO-Operations Research, 57(4), 1745-1765. https://doi.org/10.1051/ro/2023090

[5] . Han, W., Chai, H., Zhang, J., & Li, Y. (2023). Research on path optimization for multimodal transportation of hazardous materials under uncertain demand. Archives of transport, 67(3), 91-104. https://doi.org/10.5604/01.3001.0053.7259

[6] . Postan, M. Y., Dashkovskiy, S., & Daschkovska, K. (2020). Dynamic Optimization Model for Planning of Multi-echelon Logistic System Activity. In Dynamics in Logistics: Proceedings of the 7th International Conference LDIC 2020, Bremen, Germany (pp. 331-340). Springer International Publishing. https://doi.org/10.1007/978-3-030-44783-0_32

[7] . Zarbakhshnia, N., Kannan, D., Kiani Mavi, R., & Soleimani, H. (2020). A novel sustainable multi-objective optimization model for forward and reverse logistics system under demand uncertainty. Annals of Operations Research, 295, 843-880. https://doi.org/10.1007/s10479-020-03744-z

[8] . Jiang, J., Zhang, D., Li, S., & Liu, Y. (2019). Multimodal green logistics network design of urban agglomeration with stochastic demand. Journal of Advanced Transportation, 2019(1), 4165942. https://doi.org/10.1155/2019/4165942

[9] . Orozco-Fontalvo, M., Cantillo, V., & Miranda, P. A. (2019, September). A stochastic, multi-commodity multi-period inventory-location problem: Modeling and solving an industrial application. In International Conference on Computational Logistics (pp. 317-331). Cham: Springer International Publishing. https://doi.org/10.1007/978-3-030-31140-7_20

[10] . Karimi, B., Bashiri, M., & Nikzad, E. (2018). Multi-commodity multimodal splittable logistics hub location problem with stochastic demands. International Journal of Engineering, 31(11), 1935-1942. https://doi.org/10.5829/ije.2018.31.11b.18

[11] . Li, S. X., Sun, S. F., Wang, Y. Q., Wu, Y. F., & Liu, L. P. (2017). A two-stage stochastic programming model for rail-truck intermodal network design with uncertain customer demand. Journal of Interdisciplinary Mathematics, 20(3), 611-621. https://doi.org/10.1080/09720502.2016.1258831

[12] . Desticioğlu Taşdemir, B., & Özyörük, B. (2024). Mathematical Model for Multi Depot Simultaneously Pick Up and Delivery Vehicle Routing Problem with Stochastic Pick Up Demand. Gazi University Journal of Science1-1. https://doi.org/10.35378/gujs.1288093

[13] . Al-Ashhab, M. S. (2016). Supply Chain Network Design Optimization Model for Multi-period Multi-product Under Uncertainty. American Journal of Management Science and Engineering, 1(1), 36-47. https://doi.org/10.11648/j.ijmea.20170501.14
[14] . Yu, F., Liu, W., Bai, L., & Li, G. (2016). Optimization of logistics distribution network model based on random demand. In Wireless Communications, Networking and Applications: Proceedings of WCNA 2014 (pp. 1223-1231). Springer India. https://doi.org/10.1007/978-81-322-2580-5_111

[15] . Shahraki, N., & Türkay, M. (2016). Urban Logistics: Multi-modal Transportation Network Design Accounting for Stochastic Passenger Demand and Freight Logistics. Sustainable Logistics and Supply Chains: Innovations and Integral Approaches, 131-148. https://doi.org/10.1007/978-3-319-17419-8_7

[16] . Transportation Networks for Research Core Team. Transportation Networks for Research. https://github.com/bstabler/TransportationNetworks. Accessed December 5, 2024.

[17] . Azizi, M., Talatahari, S., & Gandomi, A. H. (2023). Fire Hawk Optimizer: A novel metaheuristic algorithm. Artificial Intelligence Review, 56(1), 287-363. https://doi.org/10.1007/s10462-022-10173-w