.png)
Hybrid MINLP-FNS Framework for Solving Large-Scale LIRP in E-Retail Logistics
Abstract
This research proposes a hybrid optimization framework to address the large-scale, multi-echelon Location-Inventory-Routing Problem (LIRP) in e-retail logistics. The proposed method combines a Mixed-Integer Nonlinear Programming (MINLP) model with a tailored Feasible Neighborhood Search (FNS) algorithm to solve complex decision-making problems involving facility location, inventory control, and vehicle routing simultaneously. Distinct from conventional models, the framework is integrated with a Business Intelligence (BI) environment to enable real-time decision support and dynamic data processing. Experimental evaluations were conducted using realistic logistics scenarios involving four distribution echelons. The results show that the hybrid MINLP-FNS approach achieves a total logistics cost reduction of 13.6% and a runtime improvement of 48% compared to the baseline MINLP-only model. It also significantly outperforms traditional GRG-based methods in scalability and computational stability across large datasets. These findings demonstrate that the proposed hybrid framework offers a more effective and scalable solution for complex logistics optimization, while its BI integration ensures practical applicability in real-world operations. This study contributes a novel data-driven framework that advances current research in intelligent supply chain and optimization systems.
Keywords
Full Text:
PDFReferences
G. A. Ogunmola and V. Kumar, “A strategic model for attracting and retaining environmentally conscious customers in E-retail,” International Journal of Information Management Data Insights, vol. 4, no. 2, p. 100274, 2024, doi: https://doi.org/10.1016/j.jjimei.2024.100274.
N. Andrei, C. Scarlat, and A. Ioanid, “Transforming E-Commerce Logistics: Sustainable Practices through Autonomous Maritime and Last-Mile Transportation Solutions,” Logistics, vol. 8, no. 3, 2024, doi: 10.3390/logistics8030071.
X. Shang, G. Zhang, B. Jia, and M. Almanaseer, “The healthcare supply location-inventory-routing problem: A robust approach,” Transportation Research Part E: Logistics and Transportation Review, vol. 158, p. 102588, 2022, doi: https://doi.org/10.1016/j.tre.2021.102588.
X. Shang, B. Miao, G. Zhang, and B. Jia, “The location-inventory-routing problem in the pallet pooling system,” International Journal of General Systems, vol. 0, no. 0, pp. 1–31, 2025, doi: 10.1080/03081079.2025.2541767.
L. Liu, L. S. Lee, H.-V. Seow, and C. Y. Chen, “Logistics Center Location-Inventory-Routing Problem Optimization: A Systematic Review Using PRISMA Method,” Sustainability, vol. 14, no. 23, 2022, doi: 10.3390/su142315853.
F. Habibi, E. Asadi, and S. J. Sadjadi, “A location-inventory-routing optimization model for cost effective design of microalgae biofuel distribution system: A case study in Iran,” Energy Strategy Reviews, vol. 22, pp. 82–93, 2018, doi: https://doi.org/10.1016/j.esr.2018.08.006.
Q. Yuchi, Z. He, Z. Yang, and N. Wang, “A Location-Inventory-Routing Problem in Forward and Reverse Logistics Network Design,” Discrete Dynamics in Nature and Society, vol. 2016, no. 1, p. 3475369, 2016, doi: https://doi.org/10.1155/2016/3475369.
O. D. Montoya, L. F. Grisales-Noreña, and O. D. Florez-Cediel, “Exact Mixed-Integer Nonlinear Programming Formulation for Conductor Size Selection in Balanced Distribution Networks: Single and Multi-Objective Analyses,” Electricity, vol. 6, no. 1, 2025, doi: 10.3390/electricity6010014.
J. Hu, H. Morais, T. Sousa, and M. Lind, “Electric vehicle fleet management in smart grids: A review of services, optimization and control aspects,” Renewable and Sustainable Energy Reviews, vol. 56, pp. 1207–1226, 2016, doi: https://doi.org/10.1016/j.rser.2015.12.014.
G. Thakur, A. Pal, N. Mittal, M. S. A. Yajid, and F. Gared, “A significant exploration on meta-heuristic based approaches for optimization in the waste management route problems,” Scientific Reports, vol. 14, no. 1, p. 14853, 2024, doi: 10.1038/s41598-024-64133-1.
S. O. Duffuaa and A. Mohammed, “Performance evaluation of meta-heuristic algorithms for designing multi-objective multi-product multi-echelon supply chain network,” Soft Computing, vol. 27, no. 17, pp. 12223–12248, 2023, doi: 10.1007/s00500-023-08446-9.
V. Kourepinis, C. Iliopoulou, I. X. Tassopoulos, C. Aroniadi, and G. N. Beligiannis, “An Improved Particle Swarm Optimization Algorithm for the Urban Transit Routing Problem,” Electronics, vol. 12, no. 15, 2023, doi: 10.3390/electronics12153358.
Y. Zhang, S. Wang, and G. Ji, “A Comprehensive Survey on Particle Swarm Optimization Algorithm and Its Applications,” Mathematical Problems in Engineering, vol. 2015, no. 1, p. 931256, 2015, doi: https://doi.org/10.1155/2015/931256.
A. Raza, G. Yuan, C. Wang, X. Liu, and T. Hu, “Enhancing Manufacturing Efficiency Through Symmetry-Aware Adaptive Ant Colony Optimization Algorithm for Integrated Process Planning and Scheduling,” Symmetry, vol. 17, no. 6, 2025, doi: 10.3390/sym17060824.
H. Soleimani and G. Kannan, “A hybrid particle swarm optimization and genetic algorithm for closed-loop supply chain network design in large-scale networks,” Applied Mathematical Modelling, vol. 39, no. 14, pp. 3990–4012, 2015, doi: https://doi.org/10.1016/j.apm.2014.12.016.
L. Pan, M. Shan, and L. Li, “Optimizing Perishable Product Supply Chain Network Using Hybrid Metaheuristic Algorithms,” Sustainability, vol. 15, no. 13, 2023, doi: 10.3390/su151310711.
T. Liu, J. Liu, and H. Xu, “A multi-population multi-objective maritime inventory routing optimization algorithm with three-level dynamic encoding,” Scientific Reports, vol. 15, no. 1, p. 13242, 2025, doi: 10.1038/s41598-025-86091-y.
A. Jarašūnienė and D. Paulauskas, “Enhancing the Sustainability of Retail Supply Chains Through an Integrated Industry 4.0 Model,” Sustainability, vol. 17, no. 18, 2025, doi: 10.3390/su17188191.
T. S. Deepu and V. Ravi, “A review of literature on implementation and operational dimensions of supply chain digitalization: Framework development and future research directions,” International Journal of Information Management Data Insights, vol. 3, no. 1, p. 100156, 2023, doi: https://doi.org/10.1016/j.jjimei.2023.100156.
W. Chen, Y. Men, N. Fuster, C. Osorio, and A. A. Juan, “Artificial Intelligence in Logistics Optimization with Sustainable Criteria: A Review,” Sustainability, vol. 16, no. 21, 2024, doi: 10.3390/su16219145.
R. E. Franzoi, B. C. Menezes, J. D. Kelly, J. A. W. Gut, and I. E. Grossmann, “Large-scale optimization of nonconvex MINLP refinery scheduling,” Computers & Chemical Engineering, vol. 186, p. 108678, 2024, doi: https://doi.org/10.1016/j.compchemeng.2024.108678.
A. Zhadan, A. Martemyanov, A. Allahverdyan, O. Petrosian, and H. Gao, “Linearization method for MINLP energy optimization problems,” Scientific Reports, vol. 15, no. 1, p. 27853, 2025, doi: 10.1038/s41598-025-11380-5.
Z. Xue, Y. Fang, W. Peng, and X. Chen, “A Hybrid Heuristic Algorithm for Maximizing the Resilience of Underground Logistics Network Planning,” Applied Sciences, vol. 13, no. 23, 2023, doi: 10.3390/app132312588.
Z. Li, Y. Liu, and Z. Yang, “An effective kernel search and dynamic programming hybrid heuristic for a multimodal transportation planning problem with order consolidation,” Transportation Research Part E: Logistics and Transportation Review, vol. 152, p. 102408, 2021, doi: https://doi.org/10.1016/j.tre.2021.102408.
G. Cao et al., “Coordination Decision-Making for Intelligent Transformation of Logistics Services under Capital Constraint,” Sustainability, vol. 15, no. 6, 2023, doi: 10.3390/su15065421.
R. F. Roldán, R. Basagoiti, and L. C. Coelho, “A survey on the inventory-routing problem with stochastic lead times and demands,” Journal of Applied Logic, vol. 24, pp. 15–24, 2017, doi: https://doi.org/10.1016/j.jal.2016.11.010.
S. Voigt, M. Frank, and H. Kuhn, “Last mile delivery routing problem with some-day option,” European Journal of Operational Research, vol. 324, no. 2, pp. 477–491, 2025, doi: https://doi.org/10.1016/j.ejor.2025.02.001.
A. S. Shuaibu, A. S. Mahmoud, and T. R. Sheltami, “A Review of Last-Mile Delivery Optimization: Strategies, Technologies, Drone Integration, and Future Trends,” Drones, vol. 9, no. 3, 2025, doi: 10.3390/drones9030158.
I. D. Wangsa, H. M. Wee, Y. L. Hsiao, and N. Rizky, “Identifying an effective last-mile customer delivery option with an integrated eco-friendly inventory model,” INFOR: Information Systems and Operational Research, vol. 60, no. 2, pp. 165–200, 2022, doi: 10.1080/03155986.2021.2012403.
L. Liu, A. He, T. Tian, L. S. Lee, and H.-V. Seow, “Bi-Objective Mixed Integer Nonlinear Programming Model for Low Carbon Location-Inventory-Routing Problem with Time Windows and Customer Satisfaction,” Mathematics, vol. 12, no. 15, 2024, doi: 10.3390/math12152367.
A. Wang, X. Li, J. E. Arbogast, Z. Wilson, and C. E. Gounaris, “A novel mixed-integer linear programming formulation for continuous-time inventory routing,” Computers & Operations Research, vol. 174, p. 106883, 2025, doi: https://doi.org/10.1016/j.cor.2024.106883.
M. Abbasian, Z. Sazvar, and M. Mohammadisiahroudi, “A hybrid optimization method to design a sustainable resilient supply chain in a perishable food industry,” Environmental Science and Pollution Research, vol. 30, no. 3, pp. 6080–6103, 2023, doi: 10.1007/s11356-022-22115-8.
D. B. M. M. Fontes, S. M. Homayouni, and J. F. Gonçalves, “A hybrid particle swarm optimization and simulated annealing algorithm for the job shop scheduling problem with transport resources,” European Journal of Operational Research, vol. 306, no. 3, pp. 1140–1157, 2023, doi: https://doi.org/10.1016/j.ejor.2022.09.006.
M. D. L. G. Neves, “Leveraging Business Intelligence for Sustainable Operations: An Operations Research Perspective in Logistics 4.0,” Sustainability, vol. 17, no. 18, 2025, doi: 10.3390/su17188120.
F. Goodarzian, V. Kumar, and A. Abraham, “Hybrid meta-heuristic algorithms for a supply chain network considering different carbon emission regulations using big data characteristics,” Soft Comput., vol. 25, no. 11, pp. 7527–7557, Jun. 2021, doi: 10.1007/s00500-021-05711-7.
DOI: https://doi.org/10.47738/jads.v7i3.1114
Refbacks
- There are currently no refbacks.
Journal of Applied Data Sciences
| ISSN | : | 2723-6471 (Online) |
| Publisher | : | Bright Publisher |
| Website | : | http://bright-journal.org/JADS |
| : | taqwa@amikompurwokerto.ac.id (principal contact) | |
| support@bright-journal.org (technical issues) |
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0