Research on optimization of multimodal hub-and-spoke transport network under uncertain demand




Highway railway intermodal transportation, bi-objective programming, hub-and-spoke network, routing and network design, fuzzy planning, NSGA-Ⅱ


In the cargo transportation system, the hub-and-spoke transport network can make full use of the scale effect between logistics hubs and reduce logistics costs. Joint transportation of multiple modes of transportation can give full play to the advantages of different modes of transportation, which not only reduces logistics costs but also improves transportation efficiency. Therefore, this paper combines the advantages of multimodal transportation and hub-and-spoke network, and establishes an optimization model of multimodal hub-and-spoke transport network under demand uncertainty. The model takes into account hub capacity constraints and customer satisfaction with respect to transportation time, and to facilitate the model solution, we utilize the fuzzy expected value method and the fuzzy chance constraints based on credibility to clarify the uncertain variables in the model. We use mixed coding to describe the selection of hubs, assignment of nodes, and choice of transportation modes in this study and use the NSGA-II algorithm with local reinforcement to solve the problem. Finally, numerical experiments are designed to verify the validity of the model and algorithm through sensitivity analysis of relevant parameters, determine the reasonable number of hubs and confidence level, and obtain the influence of the change of hub capacity limit and the ratio of single and double hub transit on the research objectives. The results show that: the NSGA-II algorithm with local reinforcement can significantly improve the convergence speed of the algorithm; There is benefit inversion between economic cost and time cost, and the pursuit of economic cost minimization and time cost minimization, respectively, will lead to different choices of the number of hubs; Increasing the ratio of goods transfer between hubs is beneficial for fully utilizing the scale effect between hubs, achieving the goal of reducing economic costs, but at the same time, it will increase time costs.


Alumur, S. A., Kara, B. Y., Karasan, O. E. (2012). Multimodal hub location and hub network de-sign. Omega, 40(6), 927–939.

Arnold, P., Peeters, D., Thomas, I. (2004). Modelling a rail/road intermodal transportation system. Transportation Research Part E: Logistics and Transportation Review, 40(3), 255–270.

Baoding Liu, Yian-Kui Liu. (2002). Expected value of fuzzy variable and fuzzy expected value models. IEEE Transactions on Fuzzy Systems, 10(4), 445–450.

Campbell, J. F. (1994). Integer programming formulations of discrete hub location problems. Eu-ropean Journal of Operational Research, 72(2), 387–405.

Chen, J.-F. (2007). A hybrid heuristic for the uncapacitated single allocation hub location problem. Omega, 35(2), 211–220.

Chou, Y. (1990). The hierarchical‐hub model for airline networks. Transportation Planning and Technology, 14(4), 243–258.

da Graça Costa, M., Captivo, M. E., Clímaco, J. (2008). Capacitated single allocation hub location problem—A bi-criteria approach. Computers & Operations Research, 35(11), 3671–3695.

Demir, I., Kiraz, B., Fatma Corut Ergin. (2022). Experimental evaluation of meta-heuristics for multi-objective capacitated multiple allocation hub location problem. DOAJ (DOAJ: Directory of Open Access Journals).

Ghodratnama, A., Tavakkoli-Moghaddam, R., Azaron, A. (2015). Robust and fuzzy goal pro-gramming optimization approaches for a novel multi-objective hub location-allocation problem: A supply chain overview. Applied Soft Computing, 37, 255–276.

Han, W., Chai, H., Zhang, J., Li, Y. (2023). Research on path optimization for multimodal trans-portation of hazardous materials under uncertain demand. Archives of Transport, 67(3), 91–104.

K P, A., Panicker, V. V. (2020). Multimodal transportation planning with freight consolidation and volume discount on rail freight rate. Transportation Letters, 1–18.

Korani, E., Eydi, A. (2021). Bi-level programming model and KKT penalty function solution ap-proach for reliable hub location problem. Expert Systems with Applications, 184, 115505.

Leleń, P., Wasiak, M. (2019). The model of selecting multimodal technologies for the transport of perishable products. Archives of Transport, 50(2), 17–33.

Ma, Y., Shi, X., Qiu, Y. (2020). Hierarchical Multimodal Hub Location With Time Restriction for China Railway (CR) Express Network. IEEE Access, 8, 61395–61404.

Meng, Q., Wang, X. (2011). Intermodal hub-and-spoke network design: Incorporating multiple stakeholders and multi-type containers. Transportation Research Part B: Methodological, 45(4), 724–742.

Mohammadi, M., Tavakkoli-Moghaddam, R., Siadat, A., Rahimi, Y. (2016). A game-based meta-heuristic for a fuzzy bi-objective reliable hub location problem. Engineering Applications of Artifi-cial Intelligence, 50, 1–19.

O’Kelly, M. E. (1986). The Location of Interacting Hub Facilities. Transportation Science, 20(2), 92–106.

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.

Shang, X., Yang, K., Jia, B., Gao, Z., Ji, H. (2021). Heuristic algorithms for the bi-objective hierar-chical multimodal hub location problem in cargo delivery systems. Applied Mathematical Model-ling, 91, 412–437.

Shang, X., Yang, K., Wang, W., Zhang, H., Celic, S. (2020). Stochastic Hierarchical Multimodal Hub Location Problem for Cargo Delivery Systems: Formulation and Algorithm. IEEE Access, 8, 55076–55090.

Sheu, J.-B., Lin, A. Y.-S. . (2012). Hierarchical facility network planning model for global logistics network configurations. Applied Mathematical Modelling, 36(7), 3053–3066.

Sim, T., Lowe, T. J., Thomas, B. W. (2009). The stochastic -hub center problem with service-level constraints. Computers & Operations Research, 36(12), 3166–3177.

Skorin-Kapov, D., Skorin-Kapov, J., O’Kelly, M. (1996). Tight linear programming relaxations of uncapacitated p-hub median problems. European Journal of Operational Research, 94(3), 582–593.

Sun, X., Zhang, Y., Wandelt, S. (2017). Air Transport versus High-Speed Rail: An Overview and Research Agenda. Journal of Advanced Transportation, 2017, 1–18.

Sun, Y., Li, X., Liang, X., Zhang, C. (2019). A Bi-Objective Fuzzy Credibilistic Chance-Constrained Programming Approach for the Hazardous Materials Road-Rail Multimodal Routing Problem under Uncertainty and Sustainability. Sustainability, 11(9), 2577.

Xu, W., Huang, J., Qiu, Y. (2021). Study on the Optimization of Hub-and-Spoke Logistics Network regarding Traffic Congestion. Journal of Advanced Transportation, 2021, 1–16.

Yang, K., Liu, Y.-K., Yang, G.-Q. (2013). Solving fuzzy p-hub center problem by genetic algo-rithm incorporating local search. Applied Soft Computing, 13(5), 2624–2632.

Yang, K., Yang, L., Gao, Z. (2016). Planning and optimization of intermodal hub-and-spoke net-work under mixed uncertainty. Transportation Research Part E: Logistics and Transportation Re-view, 95, 248–266.

Yang, T.-H. (2009). Stochastic air freight hub location and flight routes planning. Applied Mathe-matical Modelling, 33(12), 4424–4430.

Zarandi, M. H. F., Hemmati, A., Davari, S. (2011). The multi-depot capacitated location-routing problem with fuzzy travel times. Expert Systems with Applications, 38(8), 10075–10084.

Zhalechian, M., Tavakkoli-Moghaddam, R., Rahimi, Y. (2017). A self-adaptive evolutionary algo-rithm for a fuzzy multi-objective hub location problem: An integration of responsiveness and so-cial responsibility. Engineering Applications of Artificial Intelligence, 62, 1–16.

Zhang, W., Wang, X., Yang, K. (2019). Uncertain multi-objective optimization for the water–rail–road intermodal transport system with consideration of hub operation process using a memetic al-gorithm. Soft Computing, 24(5), 3695–3709.

Zheng, Y., Liu, B. (2006). Fuzzy vehicle routing model with credibility measure and its hybrid intelligent algorithm. Applied Mathematics and Computation, 176(2), 673–683.




Data Availability Statement

The data used in the article are listed in the text and are derived from data published by the National Bureau of Statistics of China.



Original articles

How to Cite

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.


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