IDEAS home Printed from https://ideas.repec.org/a/kap/netspa/v19y2019i1d10.1007_s11067-018-9424-z.html
   My bibliography  Save this article

Benders Decomposition Algorithms for Two Variants of the Single Allocation Hub Location Problem

Author

Listed:
  • Nader Ghaffarinasab

    (University of Tabriz)

  • Bahar Y. Kara

    (Bilkent University)

Abstract

The hub location problem (HLP) is a special type of the facility location problem with numerous applications in the airline industry, postal services, and computer and telecommunications networks. This paper addresses two basic variants of the HLP, namely the uncapacitated single allocation hub location problem (USAHLP) and the uncapacitated single allocation p-hub median problem (USAp HMP). Exact solution procedures based on Benders decomposition algorithm are proposed to tackle large sized instances of these problems. The standard Benders decomposition algorithm is enhanced through implementation of several algorithmic refinements such as using a new cut disaggregation scheme, generating strong optimality cuts, and an efficient algorithm to solve the dual subproblems. Furthermore, a modern implementation of the algorithm is used where a single search tree is established for the problem and Benders cuts are successively added within a branch-and-cut framework. Extensive computational experiments are conducted to examine the efficiency of the proposed algorithms. We have been able to solve all the instances of the problems from all three main data sets of the HLP to optimality in reasonable computational times.

Suggested Citation

  • 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.
    • Handle: RePEc:kap:netspa:v:19:y:2019:i:1:d:10.1007_s11067-018-9424-z
    DOI: 10.1007/s11067-018-9424-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11067-018-9424-z
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11067-018-9424-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Morton O’Kelly & Henrique Luna & Ricardo Camargo & Gilberto Miranda, 2015. "Hub Location Problems with Price Sensitive Demands," Networks and Spatial Economics, Springer, vol. 15(4), pages 917-945, December.
    3. Lixin Tang & Defeng Sun & Jiyin Liu, 2016. "Integrated storage space allocation and ship scheduling problem in bulk cargo terminals," IISE Transactions, Taylor & Francis Journals, vol. 48(5), pages 428-439, May.
    4. 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.
    5. Tony J. Van Roy, 1986. "A Cross Decomposition Algorithm for Capacitated Facility Location," Operations Research, INFORMS, vol. 34(1), pages 145-163, February.
    6. 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.
    7. Gelareh, Shahin & Nickel, Stefan, 2011. "Hub location problems in transportation networks," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 47(6), pages 1092-1111.
    8. Halit Üster & Gopalakrishnan Easwaran & Elif Akçali & Sila Çetinkaya, 2007. "Benders decomposition with alternative multiple cuts for a multi‐product closed‐loop supply chain network design model," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(8), pages 890-907, December.
    9. 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.
    10. Cunha, Claudio B. & Silva, Marcos Roberto, 2007. "A genetic algorithm for the problem of configuring a hub-and-spoke network for a LTL trucking company in Brazil," European Journal of Operational Research, Elsevier, vol. 179(3), pages 747-758, June.
    11. 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.
    12. Sue Abdinnour-Helm & M.A. Venkataramanan, 1998. "Solution approaches to hub location problems," Annals of Operations Research, Springer, vol. 78(0), pages 31-50, January.
    13. 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.
    14. 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.
    15. Ilic, Aleksandar & Urosevic, Dragan & Brimberg, Jack & Mladenovic, Nenad, 2010. "A general variable neighborhood search for solving the uncapacitated single allocation p-hub median problem," European Journal of Operational Research, Elsevier, vol. 206(2), pages 289-300, October.
    16. Skorin-Kapov, Darko & Skorin-Kapov, Jadranka & O'Kelly, Morton, 1996. "Tight linear programming relaxations of uncapacitated p-hub median problems," European Journal of Operational Research, Elsevier, vol. 94(3), pages 582-593, November.
    17. Mehmet R. Taner & Bahar Y. Kara, 2016. "Endogenous Effects of Hubbing on Flow Intensities," Networks and Spatial Economics, Springer, vol. 16(4), pages 1151-1181, December.
    18. 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.
    19. Skorin-Kapov, Darko & Skorin-Kapov, Jadranka, 1994. "On tabu search for the location of interacting hub facilities," European Journal of Operational Research, Elsevier, vol. 73(3), pages 502-509, March.
    20. 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.
    21. 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.
    22. Kratica, Jozef & Stanimirovic, Zorica & Tosic, Dusan & Filipovic, Vladimir, 2007. "Two genetic algorithms for solving the uncapacitated single allocation p-hub median problem," European Journal of Operational Research, Elsevier, vol. 182(1), pages 15-28, October.
    23. Shahin Gelareh & Stefan Nickel, 2008. "A Benders Decomposition for Hub Location Problems Arising in Public Transport," Operations Research Proceedings, in: Jörg Kalcsics & Stefan Nickel (ed.), Operations Research Proceedings 2007, pages 129-134, Springer.
    24. Chen, Jeng-Fung, 2007. "A hybrid heuristic for the uncapacitated single allocation hub location problem," Omega, Elsevier, vol. 35(2), pages 211-220, April.
    25. A. M. Geoffrion & G. W. Graves, 1974. "Multicommodity Distribution System Design by Benders Decomposition," Management Science, INFORMS, vol. 20(5), pages 822-844, January.
    26. Xiaozheng He & Hong Zheng & Srinivas Peeta & Yongfu Li, 2018. "Network Design Model to Integrate Shelter Assignment with Contraflow Operations in Emergency Evacuation Planning," Networks and Spatial Economics, Springer, vol. 18(4), pages 1027-1050, December.
    27. 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.
    28. Abdinnour-Helm, Sue, 1998. "A hybrid heuristic for the uncapacitated hub location problem," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 489-499, April.
    29. A. T. Ernst & M. Krishnamoorthy, 1998. "An Exact Solution Approach Based on Shortest-Paths for p -Hub Median Problems," INFORMS Journal on Computing, INFORMS, vol. 10(2), pages 149-162, May.
    30. Rahmaniani, Ragheb & Crainic, Teodor Gabriel & Gendreau, Michel & Rei, Walter, 2017. "The Benders decomposition algorithm: A literature review," European Journal of Operational Research, Elsevier, vol. 259(3), pages 801-817.
    31. 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.
    32. Meltem Peker & Bahar Y. Kara & James F. Campbell & Sibel A. Alumur, 2016. "Spatial Analysis of Single Allocation Hub Location Problems," Networks and Spatial Economics, Springer, vol. 16(4), pages 1075-1101, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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).
    3. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Juanjo Peiró & Ángel Corberán & Rafael Martí & Francisco Saldanha-da-Gama, 2019. "Heuristic Solutions for a Class of Stochastic Uncapacitated p-Hub Median Problems," Transportation Science, INFORMS, vol. 53(4), pages 1126-1149, July.
    2. 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.
    3. 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.
    4. Neamatian Monemi, Rahimeh & Gelareh, Shahin & Nagih, Anass & Maculan, Nelson & Danach, Kassem, 2021. "Multi-period hub location problem with serial demands: A case study of humanitarian aids distribution in Lebanon," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 149(C).
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Taherkhani, Gita & Alumur, Sibel A., 2019. "Profit maximizing hub location problems," Omega, Elsevier, vol. 86(C), pages 1-15.
    10. Yaman, Hande, 2011. "Allocation strategies in hub networks," European Journal of Operational Research, Elsevier, vol. 211(3), pages 442-451, June.
    11. Erdoğan, Güneş & Battarra, Maria & Rodríguez-Chía, Antonio M., 2022. "The hub location and pricing problem," European Journal of Operational Research, Elsevier, vol. 301(3), pages 1035-1047.
    12. 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).
    13. 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.
    14. 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.
    15. Trung Hieu Tran & Jesse R. O’Hanley & M. Paola Scaparra, 2017. "Reliable Hub Network Design: Formulation and Solution Techniques," Transportation Science, INFORMS, vol. 51(1), pages 358-375, February.
    16. 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.
    17. 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.
    18. Roni, Md.S. & Eksioglu, Sandra D. & Searcy, Erin & Jha, Krishna, 2014. "A supply chain network design model for biomass co-firing in coal-fired power plants," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 61(C), pages 115-134.
    19. 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.
    20. Soylu, Banu & Katip, Hatice, 2019. "A multiobjective hub-airport location problem for an airline network design," European Journal of Operational Research, Elsevier, vol. 277(2), pages 412-425.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kap:netspa:v:19:y:2019:i:1:d:10.1007_s11067-018-9424-z. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.