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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
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    References listed on IDEAS

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    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. 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.
    3. James E. Ward & Richard E. Wendell, 1985. "Using Block Norms for Location Modeling," Operations Research, INFORMS, vol. 33(5), pages 1074-1090, October.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Nickel, Stefan, 1998. "Restricted center problems under polyhedral gauges," European Journal of Operational Research, Elsevier, vol. 104(2), pages 343-357, January.
    9. 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.
    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.
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    Cited by:

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    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.

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