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Gate points in continuous location between regions with different ℓp norms

Author

Listed:
  • Franco, L.
  • Velasco, F.
  • Gonzalez-Abril, L.

Abstract

In this paper, a set of notable points is given from the ℓp-distance between a point P and a straight line r. The problem of the geodesic path between two points of R2 separated by a straight line r with different norms in each half-plane is then studied from the notable points of these points. This geodesic path provides a point in r, called the “Gate point”, which is studied by varying ℓp- and ℓq-distances, and the slope m of the straight line r. The analytical expression of the Gate point is given in some particular cases.

Suggested Citation

  • Franco, L. & Velasco, F. & Gonzalez-Abril, L., 2012. "Gate points in continuous location between regions with different ℓp norms," European Journal of Operational Research, Elsevier, vol. 218(3), pages 648-655.
    • Handle: RePEc:eee:ejores:v:218:y:2012:i:3:p:648-655
    DOI: 10.1016/j.ejor.2011.11.047
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    References listed on IDEAS

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    1. Zaferanieh, M. & Taghizadeh Kakhki, H. & Brimberg, J. & Wesolowsky, G.O., 2008. "A BSSS algorithm for the single facility location problem in two regions with different norms," European Journal of Operational Research, Elsevier, vol. 190(1), pages 79-89, October.
    2. Jack Brimberg & H. Kakhki & George Wesolowsky, 2003. "Location Among Regions with Varying Norms," Annals of Operations Research, Springer, vol. 122(1), pages 87-102, September.
    3. 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.
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    Cited by:

    1. Franco, L. & Velasco, F. & Gonzalez-Abril, L. & Mesa, Juan A., 2018. "Single-facility location problems in two regions with ℓ1- and ℓq-norms separated by a straight line," European Journal of Operational Research, Elsevier, vol. 269(2), pages 577-589.
    2. Marco Botte, 2021. "Fixed gate point location problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 547-582, July.
    3. Gökhan Altay & M. Hakan Akyüz & Temel Öncan, 2023. "Solving a minisum single facility location problem in three regions with different norms," Annals of Operations Research, Springer, vol. 321(1), pages 1-37, February.

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