IDEAS home Printed from https://ideas.repec.org/a/pal/jorsoc/v58y2007i6d10.1057_palgrave.jors.2602172.html
   My bibliography  Save this article

Planar maximal covering location problem under block norm distance measure

Author

Listed:
  • H Younies

    (United Arab Emirate University)

  • G O Wesolowsky

    (McMaster University, Hamilton)

Abstract

This paper introduces a new model for the planar maximal covering location problem (PMCLP) under different block norms. The problem involves locating g facilities anywhere on the plane in order to cover the maximum number of n given demand points. The generalization, in this paper, is that the distance measures assigned to facilities are block norms of different types and different proximity measures. First, the PMCLP under different block norms is modelled as a maximum clique partition problem on an equivalent multi-interval graph. Then, the equivalent graph problem is modelled as an unconstrained binary quadratic problem (UQP). Both the maximum clique partition problem and the UQP are NP-hard problems; therefore, we solve the UQP format through a genetic algorithm heuristic. Computational examples are given.

Suggested Citation

  • H Younies & G O Wesolowsky, 2007. "Planar maximal covering location problem under block norm distance measure," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(6), pages 740-750, June.
    • Handle: RePEc:pal:jorsoc:v:58:y:2007:i:6:d:10.1057_palgrave.jors.2602172
    DOI: 10.1057/palgrave.jors.2602172
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1057/palgrave.jors.2602172
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1057/palgrave.jors.2602172?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. J.-F. Thisse & J. E. Ward & R. E. Wendell, 1984. "Some Properties of Location Problems with Block and Round Norms," Operations Research, INFORMS, vol. 32(6), pages 1309-1327, December.
    2. Durier, Roland & Michelot, Christian, 1985. "Geometrical properties of the Fermat-Weber problem," European Journal of Operational Research, Elsevier, vol. 20(3), pages 332-343, June.
    3. S. Salhi & M.D.H. Gamal, 2003. "A Genetic Algorithm Based Approach for the Uncapacitated Continuous Location–Allocation Problem," Annals of Operations Research, Springer, vol. 123(1), pages 203-222, October.
    4. Nickel, Stefan, 1998. "Restricted center problems under polyhedral gauges," European Journal of Operational Research, Elsevier, vol. 104(2), pages 343-357, January.
    5. Younies, Hassan & Wesolowsky, George O., 2004. "A mixed integer formulation for maximal covering by inclined parallelograms," European Journal of Operational Research, Elsevier, vol. 159(1), pages 83-94, November.
    6. James E. Ward & Richard E. Wendell, 1985. "Using Block Norms for Location Modeling," Operations Research, INFORMS, vol. 33(5), pages 1074-1090, October.
    7. Aytug, Haldun & Saydam, Cem, 2002. "Solving large-scale maximum expected covering location problems by genetic algorithms: A comparative study," European Journal of Operational Research, Elsevier, vol. 141(3), pages 480-494, September.
    8. J. E. Ward & R. E. Wendell, 1980. "Technical Note—A New Norm for Measuring Distance Which Yields Linear Location Problems," Operations Research, INFORMS, vol. 28(3-part-ii), pages 836-844, June.
    9. U Aickelin, 2002. "An indirect genetic algorithm for set covering problems," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 53(10), pages 1118-1126, October.
    10. Aneja, Y. P. & Chandrasekaran, R. & Nair, K. P. K., 1988. "A note on the m-center problem with rectilinear distances," European Journal of Operational Research, Elsevier, vol. 35(1), pages 118-123, April.
    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. Dong-Guen Kim & Yeong-Dae Kim, 2013. "A Lagrangian heuristic algorithm for a public healthcare facility location problem," Annals of Operations Research, Springer, vol. 206(1), pages 221-240, July.
    2. Tedeschi, Danilo & Andretta, Marina, 2021. "New exact algorithms for planar maximum covering location by ellipses problems," European Journal of Operational Research, Elsevier, vol. 291(1), pages 114-127.
    3. Andretta, M. & Birgin, E.G., 2013. "Deterministic and stochastic global optimization techniques for planar covering with ellipses problems," European Journal of Operational Research, Elsevier, vol. 224(1), pages 23-40.

    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. M. Hakan Akyüz & Temel Öncan & İ. Kuban Altınel, 2019. "Branch and bound algorithms for solving the multi-commodity capacitated multi-facility Weber problem," Annals of Operations Research, Springer, vol. 279(1), pages 1-42, August.
    2. Frank Plastria, 2009. "Asymmetric distances, semidirected networks and majority in Fermat–Weber problems," Annals of Operations Research, Springer, vol. 167(1), pages 121-155, March.
    3. Jack Brimberg & Robert F. Love, 1991. "Estimating travel distances by the weighted lp norm," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(2), pages 241-259, April.
    4. Stefan Nickel & Justo Puerto & Antonio M. Rodriguez-Chia, 2003. "An Approach to Location Models Involving Sets as Existing Facilities," Mathematics of Operations Research, INFORMS, vol. 28(4), pages 693-715, November.
    5. Kafer, Barbara & Nickel, Stefan, 2001. "Error bounds for the approximative solution of restricted planar location problems," European Journal of Operational Research, Elsevier, vol. 135(1), pages 67-85, November.
    6. Avella, P. & Benati, S. & Canovas Martinez, L. & Dalby, K. & Di Girolamo, D. & Dimitrijevic, B. & Ghiani, G. & Giannikos, I. & Guttmann, N. & Hultberg, T. H. & Fliege, J. & Marin, A. & Munoz Marquez, , 1998. "Some personal views on the current state and the future of locational analysis," European Journal of Operational Research, Elsevier, vol. 104(2), pages 269-287, January.
    7. Pawel Kalczynski & Atsuo Suzuki & Zvi Drezner, 2023. "Obnoxious facility location in multiple dimensional space," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 331-354, July.
    8. Enrique R. Venta & Francis J. Nourie, 1989. "Facility location on a grid with a diagonal line," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(5), pages 709-717, October.
    9. M. Akyüz & İ. Altınel & Temel Öncan, 2014. "Location and allocation based branch and bound algorithms for the capacitated multi-facility Weber problem," Annals of Operations Research, Springer, vol. 222(1), pages 45-71, November.
    10. Nickel, Stefan, 1998. "Restricted center problems under polyhedral gauges," European Journal of Operational Research, Elsevier, vol. 104(2), pages 343-357, January.
    11. Vahid Hajipour & Parviz Fattahi & Hasan Bagheri & Samaneh Babaei Morad, 2022. "Dynamic maximal covering location problem for fire stations under uncertainty: soft-computing approaches," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 13(1), pages 90-112, February.
    12. J. Fliege, 1997. "Nondifferentiability Detection and Dimensionality Reduction in Minisum Multifacility Location Problems," Journal of Optimization Theory and Applications, Springer, vol. 94(2), pages 365-380, August.
    13. B. Pelegrin & F. R. Fernandez, 1988. "Determination of efficient points in multiple‐objective location problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(6), pages 697-705, December.
    14. Xueping Li & Zhaoxia Zhao & Xiaoyan Zhu & Tami Wyatt, 2011. "Covering models and optimization techniques for emergency response facility location and planning: a review," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 74(3), pages 281-310, December.
    15. Díaz-Báñez, J.M. & Korman, M. & Pérez-Lantero, P. & Ventura, I., 2013. "The 1-median and 1-highway problem," European Journal of Operational Research, Elsevier, vol. 225(3), pages 552-557.
    16. Carrizosa, Emilio & Rodriguez-Chia, Antonio M., 1997. "Weber problems with alternative transportation systems," European Journal of Operational Research, Elsevier, vol. 97(1), pages 87-93, February.
    17. Jack Brimberg & Robert Love & Nenad Mladenović, 2009. "Extension of the Weiszfeld procedure to a single facility minisum location model with mixed ℓ p norms," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 70(2), pages 269-283, October.
    18. Romero-Morales, Dolores & Carrizosa, Emilio & Conde, Eduardo, 1997. "Semi-obnoxious location models: A global optimization approach," European Journal of Operational Research, Elsevier, vol. 102(2), pages 295-301, October.
    19. Eva K. Lee & Chien-Hung Chen & Ferdinand Pietz & Bernard Benecke, 2009. "Modeling and Optimizing the Public-Health Infrastructure for Emergency Response," Interfaces, INFORMS, vol. 39(5), pages 476-490, October.
    20. M. Neema & K. Maniruzzaman & A. Ohgai, 2011. "New Genetic Algorithms Based Approaches to Continuous p-Median Problem," Networks and Spatial Economics, Springer, vol. 11(1), pages 83-99, March.

    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:pal:jorsoc:v:58:y:2007:i:6:d:10.1057_palgrave.jors.2602172. 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.palgrave-journals.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.