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Benders decomposition for multiple-allocation hub-and-spoke network design with economies of scale and node congestion

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  • Najy, Waleed
  • Diabat, Ali

Abstract

This paper is the first to consider a novel and more realistic variant of the uncapacitated hub location problem where both flow-dependent economies of scale and congestion considerations are incorporated into the multiple-allocation version of the problem. Given an undirected graph with edge per-unit costs and flow requirements for a given set of source-destination pairs of nodes, the goal is to decide where to locate hub nodes and then to route flow through these hubs in a way that minimizes total cost. Transportation costs are influenced by two conflicting effects: consolidation discounts on hub-to-hub flow due to economies of scale, and congestion penalties due to excessive demand through hubs. The problem is formulated as a mixed-integer linear program by piecewise-linearizing non-linear cost elements. Since the resulting model is found to be difficult to solve directly using commercial solvers, a specialized Benders decomposition approach is devised to solve the problem. The proposed method is tested on two standard testbeds (the Civil Aeronautics Board and Australian Post datasets). While the commercial solver is unable to obtain any feasible solution for networks larger than 25 nodes, the proposed algorithm is shown to be able to obtain optimal solutions for networks as large as 70 nodes, and is able to obtain small-gap feasible solutions for networks with up to 100 nodes. Whenever both algorithms are able to solve instances to optimality, the Benders algorithm is able to do so in a fraction of the time needed by the commercial solver. The incorporation of congestion costs into the multiple-allocation topology as opposed to the single-allocation one is also found to lead to significant cost savings.

Suggested Citation

  • Najy, Waleed & Diabat, Ali, 2020. "Benders decomposition for multiple-allocation hub-and-spoke network design with economies of scale and node congestion," Transportation Research Part B: Methodological, Elsevier, vol. 133(C), pages 62-84.
    • Handle: RePEc:eee:transb:v:133:y:2020:i:c:p:62-84
    DOI: 10.1016/j.trb.2019.12.003
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    1. Zetina, Carlos Armando & Contreras, Ivan & Cordeau, Jean-François & Nikbakhsh, Ehsan, 2017. "Robust uncapacitated hub location," Transportation Research Part B: Methodological, Elsevier, vol. 106(C), pages 393-410.
    2. O'Kelly, M. E. & Bryan, D. L., 1998. "Hub location with flow economies of scale," Transportation Research Part B: Methodological, Elsevier, vol. 32(8), pages 605-616, November.
    3. de Sá, Elisangela Martins & de Camargo, Ricardo Saraiva & de Miranda, Gilberto, 2013. "An improved Benders decomposition algorithm for the tree of hubs location problem," European Journal of Operational Research, Elsevier, vol. 226(2), pages 185-202.
    4. Pels, Eric & Verhoef, Erik T., 2004. "The economics of airport congestion pricing," Journal of Urban Economics, Elsevier, vol. 55(2), pages 257-277, March.
    5. T. L. Magnanti & R. T. Wong, 1981. "Accelerating Benders Decomposition: Algorithmic Enhancement and Model Selection Criteria," Operations Research, INFORMS, vol. 29(3), pages 464-484, June.
    6. Meraklı, Merve & Yaman, Hande, 2016. "Robust intermodal hub location under polyhedral demand uncertainty," Transportation Research Part B: Methodological, Elsevier, vol. 86(C), pages 66-85.
    7. Samir Elhedhli & Huyu Wu, 2010. "A Lagrangean Heuristic for Hub-and-Spoke System Design with Capacity Selection and Congestion," INFORMS Journal on Computing, INFORMS, vol. 22(2), pages 282-296, May.
    8. Blanco, Víctor & Puerto, Justo & Ben-Ali, Safae El-Haj, 2016. "Continuous multifacility ordered median location problems," European Journal of Operational Research, Elsevier, vol. 250(1), pages 56-64.
    9. A.T. Ernst & M. Krishnamoorthy, 1999. "Solution algorithms for the capacitated single allocation hub location problem," Annals of Operations Research, Springer, vol. 86(0), pages 141-159, January.
    10. Ricardo Saraiva de Camargo & Gilberto de Miranda & Henrique Pacca L. Luna, 2009. "Benders Decomposition for Hub Location Problems with Economies of Scale," Transportation Science, INFORMS, vol. 43(1), pages 86-97, February.
    11. Aykin, Turgut, 1994. "Lagrangian relaxation based approaches to capacitated hub-and-spoke network design problem," European Journal of Operational Research, Elsevier, vol. 79(3), pages 501-523, December.
    12. Ivan Contreras, 2015. "Hub Location Problems," Springer Books, in: Gilbert Laporte & Stefan Nickel & Francisco Saldanha da Gama (ed.), Location Science, edition 127, chapter 0, pages 311-344, Springer.
    13. James F. Campbell & Morton E. O'Kelly, 2012. "Twenty-Five Years of Hub Location Research," Transportation Science, INFORMS, vol. 46(2), pages 153-169, May.
    14. Ebery, Jamie & Krishnamoorthy, Mohan & Ernst, Andreas & Boland, Natashia, 2000. "The capacitated multiple allocation hub location problem: Formulations and algorithms," European Journal of Operational Research, Elsevier, vol. 120(3), pages 614-631, February.
    15. Alumur, Sibel & Kara, Bahar Y., 2008. "Network hub location problems: The state of the art," European Journal of Operational Research, Elsevier, vol. 190(1), pages 1-21, October.
    16. John Klincewicz, 2002. "Enumeration and Search Procedures for a Hub Location Problem with Economies of Scale," Annals of Operations Research, Springer, vol. 110(1), pages 107-122, February.
    17. Elisangela Martins de Sá & Ivan Contreras & Jean-François Cordeau & Ricardo Saraiva de Camargo & Gilberto de Miranda, 2015. "The Hub Line Location Problem," Transportation Science, INFORMS, vol. 49(3), pages 500-518, August.
    18. Peter G. Grove & Morton E. O'Kelly, 1986. "Hub Networks And Simulated Schedule Delay," Papers in Regional Science, Wiley Blackwell, vol. 59(1), pages 103-119, January.
    19. Kenneth Button, 2010. "Transport Economics, 3rd Edition," Books, Edward Elgar Publishing, number 1863.
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    3. Zhang, Haifeng & Yang, Kai & Gao, Yuan & Yang, Lixing, 2022. "Accelerating Benders decomposition for stochastic incomplete multimodal hub location problem in many-to-many transportation and distribution systems," International Journal of Production Economics, Elsevier, vol. 248(C).
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    5. Jian Zhou & Kexin Xu & Yuxiu Zhao & Haoran Zheng & Zhengnan Dong, 2021. "Hub-and-Spoke Logistics Network Considering Pricing and Co-Opetition," Sustainability, MDPI, vol. 13(17), pages 1-21, September.
    6. Ghaffarinasab, Nader & Kara, Bahar Y. & Campbell, James F., 2022. "The stratified p-hub center and p-hub maximal covering problems," Transportation Research Part B: Methodological, Elsevier, vol. 157(C), pages 120-148.
    7. Shuxia Li & Yuedan Zu & Huimin Fang & Liping Liu & Tijun Fan, 2021. "Design Optimization of a HAZMAT Multimodal Hub-and-Spoke Network with Detour," IJERPH, MDPI, vol. 18(23), pages 1-18, November.

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