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Exact Solution of Large-Scale Hub Location Problems with Multiple Capacity Levels

Author

Listed:
  • Ivan Contreras

    (Concordia University and Interuniversity Research Centre on Enterprise Networks, Logistics and Transportation (CIRRELT), Montréal, Quebec H3T 2A7, Canada)

  • Jean-François Cordeau

    (HEC Montréal and Interuniversity Research Centre on Enterprise Networks, Logistics and Transportation (CIRRELT), Montréal, Quebec H3T 2A7, Canada)

  • Gilbert Laporte

    (HEC Montréal and Interuniversity Research Centre on Enterprise Networks, Logistics and Transportation (CIRRELT), Montréal, Quebec H3T 2A7, Canada)

Abstract

This paper presents an extension of the classical capacitated hub location problem with multiple assignments in which the amount of capacity installed at the hubs is part of the decision process. An exact algorithm based on a Benders decomposition of a strong path-based formulation is proposed to solve large-scale instances of two variants of the problem: the splittable and nonsplittable commodities cases. The standard decomposition algorithm is enhanced through the inclusion of features such as the generation of strong optimality cuts and the integration of reduction tests. Given that in the nonsplittable case the resulting subproblem is an integer program, we develop an efficient enumeration algorithm. Extensive computational experiments are performed to evaluate the efficiency and robustness of the proposed algorithms. Computational results obtained on benchmark instances with up to 300 nodes and five capacity levels confirm their efficiency.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ortrsc:v:46:y:2012:i:4:p:439-459
    DOI: 10.1287/trsc.1110.0398
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    References listed on IDEAS

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    3. 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.
    4. Julia Sender & Thomas Siwczyk & Petra Mutzel & Uwe Clausen, 2017. "Matheuristics for optimizing the network in German wagonload traffic," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 5(3), pages 367-392, September.
    5. Nader Azizi & Navneet Vidyarthi & Satyaveer S. Chauhan, 2018. "Modelling and analysis of hub-and-spoke networks under stochastic demand and congestion," Annals of Operations Research, Springer, vol. 264(1), pages 1-40, May.
    6. Basallo-Triana, Mario José & Bravo-Bastidas, Juan José & Contreras, Ivan & Cordeau, Jean-François & Vidal-Holguín, Carlos Julio, 2023. "Intermodal hub network design with generalized capacity constraints and non-synchronized train–truck operations," Transportation Research Part B: Methodological, Elsevier, vol. 174(C).
    7. Sneha Dhyani Bhatt & Sachin Jayaswal & Ankur Sinha & Navneet Vidyarthi, 2021. "Alternate second order conic program reformulations for hub location under stochastic demand and congestion," Annals of Operations Research, Springer, vol. 304(1), pages 481-527, September.
    8. Mohammadi, Mehrdad & Jula, Payman & Tavakkoli-Moghaddam, Reza, 2019. "Reliable single-allocation hub location problem with disruptions," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 123(C), pages 90-120.
    9. Ghaffarinasab, Nader & Kara, Bahar Y., 2022. "A conditional β-mean approach to risk-averse stochastic multiple allocation hub location problems," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 158(C).
    10. Milad , Keshvari Fard & Laurent, Alfandari, 2018. "Trade-offs between the Stepwise Cost Function and its Linear Approximation for the Modular Hub Location Problem," ESSEC Working Papers WP1805, ESSEC Research Center, ESSEC Business School.
    11. Milad Keshvari Fard & Laurent Alfandari, 2018. "Trade-offs between the Stepwise Cost Function and its Linear Approximation for the Modular Hub Location Problem," Working Papers hal-01821280, HAL.
    12. Nader Ghaffarinasab & Bahar Y. Kara, 2019. "Benders Decomposition Algorithms for Two Variants of the Single Allocation Hub Location Problem," Networks and Spatial Economics, Springer, vol. 19(1), pages 83-108, March.
    13. Dhyani, Sneha & Jayaswal, Sachin & Sinha, Ankur & Vidyarthi, Navneet, 2019. "Alternate Second Order Conic Programming Reformulations for Hub Location with Capacity Selection under Demand," IIMA Working Papers WP 2018-12-04, Indian Institute of Management Ahmedabad, Research and Publication Department.
    14. Correia, Isabel & Nickel, Stefan & Saldanha-da-Gama, Francisco, 2018. "A stochastic multi-period capacitated multiple allocation hub location problem: Formulation and inequalities," Omega, Elsevier, vol. 74(C), pages 122-134.
    15. 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.
    16. 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).
    17. Ghaffarinasab, Nader & Çavuş, Özlem & Kara, Bahar Y., 2023. "A mean-CVaR approach to the risk-averse single allocation hub location problem with flow-dependent economies of scale," Transportation Research Part B: Methodological, Elsevier, vol. 167(C), pages 32-53.
    18. Marufuzzaman, Mohammad & Eksioglu, Sandra D. & Li, Xiaopeng & Wang, Jin, 2014. "Analyzing the impact of intermodal-related risk to the design and management of biofuel supply chain," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 69(C), pages 122-145.
    19. Nader Azizi, 2019. "Managing facility disruption in hub-and-spoke networks: formulations and efficient solution methods," Annals of Operations Research, Springer, vol. 272(1), pages 159-185, January.
    20. Sushil Poudel & Mohammad Marufuzzaman & Md Abdul Quddus & Sudipta Chowdhury & Linkan Bian & Brian Smith, 2018. "Designing a Reliable and Congested Multi-Modal Facility Location Problem for Biofuel Supply Chain Network," Energies, MDPI, vol. 11(7), pages 1-24, June.
    21. J. Fabian Meier & Uwe Clausen, 2018. "Solving Single Allocation Hub Location Problems on Euclidean Data," Transportation Science, INFORMS, vol. 52(5), pages 1141-1155, October.
    22. Hu, Lu & Zhu, Juan Xiu & Wang, Yuan & Lee, Loo Hay, 2018. "Joint design of fleet size, hub locations, and hub capacities for third-party logistics networks with road congestion constraints," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 118(C), pages 568-588.
    23. Ivan Contreras & Elena Fernández, 2014. "Hub Location as the Minimization of a Supermodular Set Function," Operations Research, INFORMS, vol. 62(3), pages 557-570, June.
    24. Azizi, Nader & Salhi, Said, 2022. "Reliable hub-and-spoke systems with multiple capacity levels and flow dependent discount factor," European Journal of Operational Research, Elsevier, vol. 298(3), pages 834-854.

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