Data-driven robust optimization for hub location-routing problem under uncertain environment.

Document Type : Research Paper


School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran


This study addresses the Hub Location-Routing Problem (HLRP) in transportation networks, considering the inherent uncertainty in travel times between nodes. We employed a method centered on data-driven robust optimization, utilizing Support Vector Clustering (SVC) to form an uncertainty set grounded in empirical data. The proposed methodology is compared against traditional uncertainty sets, showcasing its superior performance in providing robust solutions. A comprehensive case study on a retail store's transportation network in Tehran is presented, demonstrating significant differences in hub locations, allocations, and vehicle routes between deterministic and robust models. The SVC-based model proves to be particularly effective, yielding substantially improved objective function values compared to polyhedral and box uncertainty sets. The study concludes by highlighting the practical significance of this research and suggesting future directions for advancing transportation network optimization under uncertainty.


Main Subjects

Alumur, S. A., Campbell, J. F., Contreras, I., Kara, B. Y., Marianov, V., & O’Kelly, M. E. (2021). Perspectives on modeling hub location problems. European Journal of Operational Research, 291(1), 1–17.
Alumur, S., & Kara, B. Y. (2008). Network hub location problems: The state of the art. European Journal of Operational Research, 190(1), 1–21.
Asefi, H., Shahparvari, S., & Chhetri, P. (2019). Integrated Municipal Solid Waste Management under uncertainty: A tri-echelon city logistics and transportation context. Sustainable Cities and Society, 50, 101606.
Ben-Hur, A., Horn, D., Siegelmann, H. T., & Vapnik, V. (2001). Support vector clustering. Journal of Machine Learning Research, 2(Dec), 125–137.
Bertsimas, D., Gupta, V., & Kallus, N. (2018). Data-driven robust optimization. Mathematical Programming, 167, 235–292.
Campbell, J. F. (1994). Integer programming formulations of discrete hub location problems. European Journal of Operational Research, 72(2), 387–405.
Campbell, J. F., & O’Kelly, M. E. (2012). Twenty-five years of hub location research. Transportation Science, 46(2), 153–169.
Catanzaro, D., Gourdin, E., Labbé, M., & Özsoy, F. A. (2011). A branch-and-cut algorithm for the partitioning-hub location-routing problem. Computers & Operations Research, 38(2), 539–549.
Dai, X., Wang, X., He, R., Du, W., Zhong, W., Zhao, L., & Qian, F. (2020). Data-driven robust optimization for crude oil blending under uncertainty. Computers & Chemical Engineering, 136, 106595.
Danach, K., Gelareh, S., & Neamatian Monemi, R. (2019). The capacitated single-allocation p-hub location routing problem: a Lagrangian relaxation and a hyper-heuristic approach. EURO Journal on Transportation and Logistics, 8(5), 597–631.
de Camargo, R. S., de Miranda, G., & Løkketangen, A. (2013). A new formulation and an exact approach for the many-to-many hub location-routing problem. Applied Mathematical Modelling, 37(12), 7465–7480.
Ernst, A. T., & Krishnamoorthy, M. (1999). Solution algorithms for the capacitated single allocation hub location problem. Annals of Operations Research, 86(0), 141–159.
Ghaffarinasab, N., Van Woensel, T., & Minner, S. (2018). A continuous approximation approach to the planar hub location-routing problem: Modeling and solution algorithms. Computers & Operations Research, 100, 140–154.
Gilani, H., Sahebi, H., & Pishvaee, M. S. (2022). A data-driven robust optimization model for integrated network design solar photovoltaic to micro grid. Sustainable Energy, Grids and Networks, 31, 100714.
Goerigk, M., & Kurtz, J. (2023). Data-driven robust optimization using deep neural networks. Computers & Operations Research, 151, 106087.
Gumte, K. M., Pantula, P. D., Miriyala, S. S., & Mitra, K. (2021). Data driven robust optimization for handling uncertainty in supply chain planning models. Chemical Engineering Science, 246, 116889.
Hsu, C.-W., Chang, C.-C., & Lin, C.-J. (2003). A practical guide to support vector classification. Taipei, Taiwan.
Inapakurthi, R. K., Pantula, P. D., Miriyala, S. S., & Mitra, K. (2020). Data driven robust optimization of grinding process under uncertainty. Materials and Manufacturing Processes, 35(16), 1870–1876.
Jiang, J., Zhang, D., Meng, Q., & Liu, Y. (2020). Regional multimodal logistics network design considering demand uncertainty and CO2 emission reduction target: A system-optimization approach. Journal of Cleaner Production, 248, 119304.
Karimi, H. (2018). The capacitated hub covering location-routing problem for simultaneous pickup and delivery systems. Computers & Industrial Engineering, 116, 47–58.
Klincewicz, J. G. (1991). Heuristics for the p-hub location problem. European Journal of Operational Research, 53(1), 25–37.
Lopes, M. C., de Andrade, C. E., de Queiroz, T. A., Resende, M. G. C., & Miyazawa, F. K. (2016). Heuristics for a hub location‐routing problem. Networks, 68(1), 54–90.
Lotfi, R., Kargar, B., Gharehbaghi, A., Afshar, M., Rajabi, M. S., & Mardani, N. (2022). A data-driven robust optimization for multi-objective renewable energy location by considering risk. Environment, Development and Sustainability, 1–22.
Mohseni, S., & Pishvaee, M. S. (2020). Data-driven robust optimization for wastewater sludge-to-biodiesel supply chain design. Computers & Industrial Engineering, 139, 105944.
Mohseni, S., Pishvaee, M. S., & Dashti, R. (2023). Privacy-preserving energy trading management in networked microgrids via data-driven robust optimization assisted by machine learning. Sustainable Energy, Grids and Networks, 34, 101011.
O’kelly, M. E. (1987). A quadratic integer program for the location of interacting hub facilities. European Journal of Operational Research, 32(3), 393–404.
Ratli, M., Urošević, D., El Cadi, A. A., Brimberg, J., Mladenović, N., & Todosijević, R. (2022). An efficient heuristic for a hub location routing problem. Optimization Letters, 1–20.
Rodríguez-Martín, I., Salazar-González, J.-J., & Yaman, H. (2014). A branch-and-cut algorithm for the hub location and routing problem. Computers & Operations Research, 50, 161–174.
Russell, D., Ruamsook, K., & Roso, V. (2020). Managing supply chain uncertainty by building flexibility in container port capacity: a logistics triad perspective and the COVID-19 case. Maritime Economics & Logistics, 1–22.
Shang, C., Huang, X., & You, F. (2017). Data-driven robust optimization based on kernel learning. Computers & Chemical Engineering, 106, 464–479.
Shang, C., & You, F. (2019). A data-driven robust optimization approach to scenario-based stochastic model predictive control. Journal of Process Control, 75, 24–39.
Shen, F., Zhao, L., Du, W., Zhong, W., & Qian, F. (2020). Large-scale industrial energy systems optimization under uncertainty: A data-driven robust optimization approach. Applied Energy, 259, 114199.
Wu, Y., Qureshi, A. G., & Yamada, T. (2022). Adaptive large neighborhood decomposition search algorithm for multi-allocation hub location routing problem. European Journal of Operational Research, 302(3), 1113–1127.
Zhang, C., Wang, Z., & Wang, X. (2022). Machine learning-based data-driven robust optimization approach under uncertainty. Journal of Process Control, 115, 1–11.
Zheng, Y., You, S., Li, X., Bindner, H. W., & Münster, M. (2022). Data-driven robust optimization for optimal scheduling of power to methanol. Energy Conversion and Management, 256, 115338.