IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v275y2019i3p882-896.html
   My bibliography  Save this article

Benders decomposition for very large scale partial set covering and maximal covering location problems

Author

Listed:
  • Cordeau, Jean-François
  • Furini, Fabio
  • Ljubić, Ivana

Abstract

Covering problems constitute a fundamental family of facility location problems. This paper introduces a new exact algorithm for two important members of this family: (i) the maximal covering location problem (MCLP), which requires finding a subset of facilities that maximizes the amount of customer demand covered while respecting a budget constraint on the cost of the facilities; and (ii) the partial set covering location problem (PSCLP), which minimizes the cost of the open facilities while forcing a certain amount of customer demand to be covered. We study an effective decomposition approach to the two problems based on the branch-and-Benders-cut reformulation. Our new approach is designed for the realistic case in which the number of customers is much larger than the number of potential facility locations. We report the results of a series of computational experiments demonstrating that, thanks to this decomposition techniques, optimal solutions can be found very quickly for some benchmark instances with one hundred potential facility locations and involving up to 15 and 40 million customer demand points for the MCLP and the PSCLP, respectively.

Suggested Citation

  • Cordeau, Jean-François & Furini, Fabio & Ljubić, Ivana, 2019. "Benders decomposition for very large scale partial set covering and maximal covering location problems," European Journal of Operational Research, Elsevier, vol. 275(3), pages 882-896.
    • Handle: RePEc:eee:ejores:v:275:y:2019:i:3:p:882-896
    DOI: 10.1016/j.ejor.2018.12.021
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221718310737
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2018.12.021?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. Edson Luiz França Senne & Marcos Antonio Pereira & Luiz Antonio Nogueira Lorena, 2010. "A Decomposition Heuristic for the Maximal Covering Location Problem," Advances in Operations Research, Hindawi, vol. 2010, pages 1-12, May.
    2. Galvao, Roberto D. & Gonzalo Acosta Espejo, Luis & Boffey, Brian, 2000. "A comparison of Lagrangean and surrogate relaxations for the maximal covering location problem," European Journal of Operational Research, Elsevier, vol. 124(2), pages 377-389, July.
    3. Brian T. Downs & Jeffrey D. Camm, 1996. "An exact algorithm for the maximal covering problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(3), pages 435-461, April.
    4. Constantine Toregas & Ralph Swain & Charles ReVelle & Lawrence Bergman, 1971. "The Location of Emergency Service Facilities," Operations Research, INFORMS, vol. 19(6), pages 1363-1373, October.
    5. Warren Walker, 1974. "Using the Set-Covering Problem to Assign Fire Companies to Fire Houses," Operations Research, INFORMS, vol. 22(2), pages 275-277, April.
    6. Nimrod Megiddo, 1981. "The Maximum Coverage Location Problem," Discussion Papers 490, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    7. Alan T. Murray, 2016. "Maximal Coverage Location Problem," International Regional Science Review, , vol. 39(1), pages 5-27, January.
    8. 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.
    9. Berman, Oded & Krass, Dmitry & Drezner, Zvi, 2003. "The gradual covering decay location problem on a network," European Journal of Operational Research, Elsevier, vol. 151(3), pages 474-480, December.
    10. Galvao, Roberto Dieguez & ReVelle, Charles, 1996. "A Lagrangean heuristic for the maximal covering location problem," European Journal of Operational Research, Elsevier, vol. 88(1), pages 114-123, January.
    11. Richard Church & Charles R. Velle, 1974. "The Maximal Covering Location Problem," Papers in Regional Science, Wiley Blackwell, vol. 32(1), pages 101-118, January.
    12. ReVelle, Charles, 1993. "Facility siting and integer-friendly programming," European Journal of Operational Research, Elsevier, vol. 65(2), pages 147-158, March.
    13. S. L. Hakimi, 1965. "Optimum Distribution of Switching Centers in a Communication Network and Some Related Graph Theoretic Problems," Operations Research, INFORMS, vol. 13(3), pages 462-475, June.
    14. Fischetti, Matteo & Ljubić, Ivana & Sinnl, Markus, 2016. "Benders decomposition without separability: A computational study for capacitated facility location problems," European Journal of Operational Research, Elsevier, vol. 253(3), pages 557-569.
    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. Yimeng Shi & Hongyuan Zhang & Zheng Chen & Yueyue Sun & Xuecheng Liu & Jin Gu, 2023. "A Study on the Deployment of Mesoscale Chemical Hazard Area Monitoring Points by Combining Weighting and Fireworks Algorithms," Sustainability, MDPI, vol. 15(7), pages 1-19, March.
    2. Fadda, Edoardo & Manerba, Daniele & Tadei, Roberto, 2024. "How to locate services optimizing redundancy: A comparative analysis of K-Covering Facility Location models," Socio-Economic Planning Sciences, Elsevier, vol. 94(C).
    3. Güney, Evren & Leitner, Markus & Ruthmair, Mario & Sinnl, Markus, 2021. "Large-scale influence maximization via maximal covering location," European Journal of Operational Research, Elsevier, vol. 289(1), pages 144-164.
    4. Ljubić, Ivana & Pozo, Miguel A. & Puerto, Justo & Torrejón, Alberto, 2024. "Benders decomposition for the discrete ordered median problem," European Journal of Operational Research, Elsevier, vol. 317(3), pages 858-874.
    5. Amadeu A. Coco & Andréa Cynthia Santos & Thiago F. Noronha, 2022. "Robust min-max regret covering problems," Computational Optimization and Applications, Springer, vol. 83(1), pages 111-141, September.
    6. Duran-Mateluna, Cristian & Ales, Zacharie & Elloumi, Sourour, 2023. "An efficient benders decomposition for the p-median problem," European Journal of Operational Research, Elsevier, vol. 308(1), pages 84-96.
    7. Pelegrín, Mercedes & Xu, Liding, 2023. "Continuous covering on networks: Improved mixed integer programming formulations," Omega, Elsevier, vol. 117(C).
    8. Blanco, Víctor & Gázquez, Ricardo & Saldanha-da-Gama, Francisco, 2023. "Multi-type maximal covering location problems: Hybridizing discrete and continuous problems," European Journal of Operational Research, Elsevier, vol. 307(3), pages 1040-1054.
    9. Baldomero-Naranjo, Marta & Kalcsics, Jörg & Marín, Alfredo & Rodríguez-Chía, Antonio M., 2022. "Upgrading edges in the maximal covering location problem," European Journal of Operational Research, Elsevier, vol. 303(1), pages 14-36.
    10. Chen, Liang & Chen, Sheng-Jie & Chen, Wei-Kun & Dai, Yu-Hong & Quan, Tao & Chen, Juan, 2023. "Efficient presolving methods for solving maximal covering and partial set covering location problems," European Journal of Operational Research, Elsevier, vol. 311(1), pages 73-87.
    11. Diana Puspita Sari & Nur Aini Masruroh & Anna Maria Sri Asih, 2021. "Extended Maximal Covering Location and Vehicle Routing Problems in Designing Smartphone Waste Collection Channels: A Case Study of Yogyakarta Province, Indonesia," Sustainability, MDPI, vol. 13(16), pages 1-23, August.
    12. Ashkan Fakhri & Antonios Fragkogios & Georgios K. D. Saharidis, 2021. "An Accelerated Benders Decomposition Algorithm for Solving a Double-Type Double-Standard Maximal Covering Location Problem," SN Operations Research Forum, Springer, vol. 2(1), pages 1-24, March.
    13. Lin, Yun Hui & Tian, Qingyun, 2021. "Branch-and-cut approach based on generalized benders decomposition for facility location with limited choice rule," European Journal of Operational Research, Elsevier, vol. 293(1), pages 109-119.
    14. Iloglu, Suzan & Albert, Laura A., 2020. "A maximal multiple coverage and network restoration problem for disaster recovery," Operations Research Perspectives, Elsevier, vol. 7(C).
    15. Kahr, Michael, 2022. "Determining locations and layouts for parcel lockers to support supply chain viability at the last mile," Omega, Elsevier, vol. 113(C).
    16. Dezhi Zhang & Shuxin Yang & Shuangyan Li & Jiajun Fan & Bin Ji, 2020. "Integrated Optimization of the Location–Inventory Problem of Maintenance Component Distribution for High-Speed Railway Operations," Sustainability, MDPI, vol. 12(13), pages 1-25, July.
    17. Lin, Yun Hui & Wang, Yuan & Lee, Loo Hay & Chew, Ek Peng, 2022. "Omnichannel facility location and fulfillment optimization," Transportation Research Part B: Methodological, Elsevier, vol. 163(C), pages 187-209.
    18. Delle Donne, Diego & Alfandari, Laurent & Archetti, Claudia & Ljubić, Ivana, 2023. "Freight-on-Transit for urban last-mile deliveries: A strategic planning approach," Transportation Research Part B: Methodological, Elsevier, vol. 169(C), pages 53-81.
    19. Ralf Krohn & Sven Müller & Knut Haase, 2021. "Preventive healthcare facility location planning with quality-conscious clients," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(1), pages 59-87, March.
    20. Kuzbakov, Yerlan & Ljubić, Ivana, 2024. "New formulations for two location problems with interconnected facilities," European Journal of Operational Research, Elsevier, vol. 314(1), pages 51-65.
    21. Vatsa, Amit Kumar & Jayaswal, Sachin, 2021. "Capacitated multi-period maximal covering location problem with server uncertainty," European Journal of Operational Research, Elsevier, vol. 289(3), pages 1107-1126.
    22. Kahr, Michael & Leitner, Markus & Ruthmair, Mario & Sinnl, Markus, 2021. "Benders decomposition for competitive influence maximization in (social) networks," Omega, Elsevier, vol. 100(C).
    23. Cao, Jianing & Han, Yuhang & Pan, Nan & Zhang, Jingcheng & Yang, Junwei, 2024. "A data-driven approach to urban charging facility expansion based on bi-level optimization: A case study in a Chinese city," Energy, Elsevier, vol. 300(C).

    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. Blanquero, Rafael & Carrizosa, Emilio & G.-Tóth, Boglárka, 2016. "Maximal Covering Location Problems on networks with regional demand," Omega, Elsevier, vol. 64(C), pages 77-85.
    2. Mark S. Daskin, 2008. "What you should know about location modeling," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(4), pages 283-294, June.
    3. Wang, Wei & Wu, Shining & Wang, Shuaian & Zhen, Lu & Qu, Xiaobo, 2021. "Emergency facility location problems in logistics: Status and perspectives," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 154(C).
    4. Marianov, Vladimir & Eiselt, H.A., 2024. "Fifty Years of Location Theory - A Selective Review," European Journal of Operational Research, Elsevier, vol. 318(3), pages 701-718.
    5. Chen, Liang & Chen, Sheng-Jie & Chen, Wei-Kun & Dai, Yu-Hong & Quan, Tao & Chen, Juan, 2023. "Efficient presolving methods for solving maximal covering and partial set covering location problems," European Journal of Operational Research, Elsevier, vol. 311(1), pages 73-87.
    6. Alan T. Murray, 2016. "Maximal Coverage Location Problem," International Regional Science Review, , vol. 39(1), pages 5-27, January.
    7. Erhan Erkut & Armann Ingolfsson & Güneş Erdoğan, 2008. "Ambulance location for maximum survival," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(1), pages 42-58, February.
    8. Peker, Meltem & Kara, Bahar Y., 2015. "The P-Hub maximal covering problem and extensions for gradual decay functions," Omega, Elsevier, vol. 54(C), pages 158-172.
    9. Knight, V.A. & Harper, P.R. & Smith, L., 2012. "Ambulance allocation for maximal survival with heterogeneous outcome measures," Omega, Elsevier, vol. 40(6), pages 918-926.
    10. Wajid, Shayesta & Nezamuddin, N., 2023. "Capturing delays in response of emergency services in Delhi," Socio-Economic Planning Sciences, Elsevier, vol. 87(PA).
    11. Xiujuan Zhao & Wei Xu & Yunjia Ma & Fuyu Hu, 2015. "Scenario-Based Multi-Objective Optimum Allocation Model for Earthquake Emergency Shelters Using a Modified Particle Swarm Optimization Algorithm: A Case Study in Chaoyang District, Beijing, China," PLOS ONE, Public Library of Science, vol. 10(12), pages 1-16, December.
    12. Dayanna Rodrigues da Cunha Nunes & Orivalde Soares da Silva Júnior & Renata Albergaria de Mello Bandeira & Yesus Emmanuel Medeiros Vieira, 2023. "A Robust Stochastic Programming Model for the Well Location Problem: The Case of The Brazilian Northeast Region," Sustainability, MDPI, vol. 15(14), pages 1-21, July.
    13. Wajid, Shayesta & Nezamuddin, N., 2022. "A robust survival model for emergency medical services in Delhi, India," Socio-Economic Planning Sciences, Elsevier, vol. 83(C).
    14. James J. Cochran & Martin S. Levy & Jeffrey D. Camm, 2010. "Bayesian coverage optimization models," Journal of Combinatorial Optimization, Springer, vol. 19(2), pages 158-173, February.
    15. ReVelle, C. S. & Eiselt, H. A., 2005. "Location analysis: A synthesis and survey," European Journal of Operational Research, Elsevier, vol. 165(1), pages 1-19, August.
    16. Mahmutoğulları, Özlem & Yaman, Hande, 2023. "Robust alternative fuel refueling station location problem with routing under decision-dependent flow uncertainty," European Journal of Operational Research, Elsevier, vol. 306(1), pages 173-188.
    17. Shaoqing Geng & Hanping Hou & Zhou Zhou, 2021. "A Hybrid Approach of VIKOR and Bi-Objective Decision Model for Emergency Shelter Location–Allocation to Respond to Earthquakes," Mathematics, MDPI, vol. 9(16), pages 1-29, August.
    18. Xu, Jing & Murray, Alan T. & Church, Richard L. & Wei, Ran, 2023. "Service allocation equity in location coverage analytics," European Journal of Operational Research, Elsevier, vol. 305(1), pages 21-37.
    19. ReVelle, C.S. & Eiselt, H.A. & Daskin, M.S., 2008. "A bibliography for some fundamental problem categories in discrete location science," European Journal of Operational Research, Elsevier, vol. 184(3), pages 817-848, February.
    20. Yunjia Ma & Wei Xu & Lianjie Qin & Xiujuan Zhao, 2019. "Site Selection Models in Natural Disaster Shelters: A Review," Sustainability, MDPI, vol. 11(2), pages 1-24, January.

    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:eee:ejores:v:275:y:2019:i:3:p:882-896. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.