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A hierarchical hub location model for the integrated design of urban and rural logistics networks under demand uncertainty

Author

Listed:
  • Zhi-Chun Li

    (Huazhong University of Science and Technology)

  • Xue Bing

    (Huazhong University of Science and Technology)

  • Xiaowen Fu

    (Hong Kong Polytechnic University)

Abstract

This paper contributes to the integrated design issue of urban and rural logistics networks under demand uncertainty. A hierarchical hub location model is proposed, which minimizes the expected total system cost by optimizing the locations, number and capacities of “urban-town‒village” hierarchical logistics hubs. The interactions among the logistics hubs and among the hub‒and‒spoke connections, as well as the hub capacity constraints are explicitly considered in the presence of logistics demand uncertainty. A demand scenario‒based branch‒and‒Benders‒cut algorithm is developed to solve the proposed model. A case study of Jiangling urban‒rural region in Hubei province of China is conducted for the illustration of the model and solution algorithm. The results generated by the proposed algorithm are benchmarked against those obtained by GUROBI solver and the practical scheme being currently implemented in the region. The results showed that the proposed methodology can greatly improve the efficiency of the urban‒rural logistics system in terms of expected total system cost. It is important to explicitly model the demand uncertainty, otherwise a significant decision bias may emerge. The proposed algorithm outperforms the GUROBI solver in terms of problem size solved and computational time.

Suggested Citation

  • Zhi-Chun Li & Xue Bing & Xiaowen Fu, 2025. "A hierarchical hub location model for the integrated design of urban and rural logistics networks under demand uncertainty," Annals of Operations Research, Springer, vol. 348(2), pages 1087-1108, May.
    • Handle: RePEc:spr:annopr:v:348:y:2025:i:2:d:10.1007_s10479-023-05189-6
    DOI: 10.1007/s10479-023-05189-6
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    References listed on IDEAS

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    1. Isabel Correia & M. Captivo, 2003. "A Lagrangean Heuristic for a Modular Capacitated Location Problem," Annals of Operations Research, Springer, vol. 122(1), pages 141-161, September.
    2. Zhiyang Wang & Sizhong Sun, 2016. "Transportation infrastructure and rural development in China," China Agricultural Economic Review, Emerald Group Publishing Limited, vol. 8(3), pages 516-525, September.
    3. Shiva Zokaee & Armin Jabbarzadeh & Behnam Fahimnia & Seyed Jafar Sadjadi, 2017. "Robust supply chain network design: an optimization model with real world application," Annals of Operations Research, Springer, vol. 257(1), pages 15-44, October.
    4. Lixin Tang & Wei Jiang & Georgios Saharidis, 2013. "An improved Benders decomposition algorithm for the logistics facility location problem with capacity expansions," Annals of Operations Research, Springer, vol. 210(1), pages 165-190, November.
    5. Ivan Contreras & Jean-François Cordeau & Gilbert Laporte, 2012. "Exact Solution of Large-Scale Hub Location Problems with Multiple Capacity Levels," Transportation Science, INFORMS, vol. 46(4), pages 439-459, November.
    6. Alumur, Sibel A. & Campbell, James F. & Contreras, Ivan & Kara, Bahar Y. & Marianov, Vladimir & O’Kelly, Morton E., 2021. "Perspectives on modeling hub location problems," European Journal of Operational Research, Elsevier, vol. 291(1), pages 1-17.
    7. Campbell, James F., 1994. "Integer programming formulations of discrete hub location problems," European Journal of Operational Research, Elsevier, vol. 72(2), pages 387-405, January.
    8. Jabbarzadeh, Armin & Fahimnia, Behnam & Seuring, Stefan, 2014. "Dynamic supply chain network design for the supply of blood in disasters: A robust model with real world application," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 70(C), pages 225-244.
    9. Hu, Dapeng, 2002. "Trade, rural-urban migration, and regional income disparity in developing countries: a spatial general equilibrium model inspired by the case of China," Regional Science and Urban Economics, Elsevier, vol. 32(3), pages 311-338, May.
    10. Zhiyang Wang & Sizhong Sun, 2016. "Transportation infrastructure and rural development in China," China Agricultural Economic Review, Emerald Group Publishing Limited, vol. 8(3), pages 516-525, September.
    11. Chandra Ade Irawan & Dylan Jones, 2019. "Formulation and solution of a two-stage capacitated facility location problem with multilevel capacities," Annals of Operations Research, Springer, vol. 272(1), pages 41-67, January.
    12. Firoozeh Kaveh & Reza Tavakkoli-Moghaddam & Chefi Triki & Yaser Rahimi & Amin Jamili, 2021. "A new bi-objective model of the urban public transportation hub network design under uncertainty," Annals of Operations Research, Springer, vol. 296(1), pages 131-162, January.
    13. Correia, Isabel & Nickel, Stefan & Saldanha-da-Gama, Francisco, 2010. "Single-assignment hub location problems with multiple capacity levels," Transportation Research Part B: Methodological, Elsevier, vol. 44(8-9), pages 1047-1066, September.
    14. Büyüközkan, Gülçin & Ilıcak, Öykü, 2022. "Smart urban logistics: Literature review and future directions," Socio-Economic Planning Sciences, Elsevier, vol. 81(C).
    15. Yaman, Hande, 2011. "Allocation strategies in hub networks," European Journal of Operational Research, Elsevier, vol. 211(3), pages 442-451, June.
    16. Walter Rei & Jean-François Cordeau & Michel Gendreau & Patrick Soriano, 2009. "Accelerating Benders Decomposition by Local Branching," INFORMS Journal on Computing, INFORMS, vol. 21(2), pages 333-345, May.
    17. Aalaei, Amin & Davoudpour, Hamid, 2017. "A robust optimization model for cellular manufacturing system into supply chain management," International Journal of Production Economics, Elsevier, vol. 183(PC), pages 667-679.
    18. M. Jenabi & S. M. T. Fatemi Ghomi & S. A. Torabi & Moeen Sammak Jalali, 2022. "An accelerated Benders decomposition algorithm for stochastic power system expansion planning using sample average approximation," OPSEARCH, Springer;Operational Research Society of India, vol. 59(4), pages 1304-1336, December.
    19. Yu, Bin & Zhu, Hanbing & Cai, Wanjun & Ma, Ning & Kuang, Qiji & Yao, Baozhen, 2013. "Two-phase optimization approach to transit hub location – the case of Dalian," Journal of Transport Geography, Elsevier, vol. 33(C), pages 62-71.
    20. Wei Zhong & Zhicai Juan & Fang Zong & Huishuang Su, 2018. "Hierarchical hub location model and hybrid algorithm for integration of urban and rural public transport," International Journal of Distributed Sensor Networks, , vol. 14(4), pages 15501477187, April.
    21. Joe Naoum-Sawaya & Samir Elhedhli, 2013. "An interior-point Benders based branch-and-cut algorithm for mixed integer programs," Annals of Operations Research, Springer, vol. 210(1), pages 33-55, November.
    22. Jain, Manisha & Korzhenevych, Artem & Hecht, Robert, 2018. "Determinants of commuting patterns in a rural-urban megaregion of India," Transport Policy, Elsevier, vol. 68(C), pages 98-106.
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