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A BSSS algorithm for the single facility location problem in two regions with different norms

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  • Zaferanieh, M.
  • Taghizadeh Kakhki, H.
  • Brimberg, J.
  • Wesolowsky, G.O.

Abstract

Suppose the plane is divided by a straight line into two regions with different norms. We want to find the location of a single new facility such that the sum of the distances from the existing facilities to this point is minimized. This is in fact a non-convex optimization problem. The main difficulty is caused by finding the distances between points on different sides of the boundary line. In this paper we present a closed form solution for finding these distances. We also show that the optimal solution lies in the rectangular hull of the existing points. Based on these findings then, an efficient big square small square (BSSS) procedure is proposed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:190:y:2008:i:1:p:79-89
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    References listed on IDEAS

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    1. Pierre Hansen & Dominique Peeters & Denis Richard & Jacques-Francois Thisse, 1985. "The Minisum and Minimax Location Problems Revisited," Operations Research, INFORMS, vol. 33(6), pages 1251-1265, December.
    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. Plastria, Frank, 1992. "GBSSS: The generalized big square small square method for planar single-facility location," European Journal of Operational Research, Elsevier, vol. 62(2), pages 163-174, October.
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    Cited by:

    1. 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.
    2. 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.
    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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