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Solving the ordered one-median problem in the plane

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  • Drezner, Zvi
  • Nickel, Stefan

Abstract

In this paper, we propose a general approach solution method for the single facility ordered median problem in the plane. All types of weights (non-negative, non-positive, and mixed) are considered. The big triangle small triangle approach is used for the solution. Rigorous and heuristic algorithms are proposed and extensively tested on eight different problems with excellent results.

Suggested Citation

  • Drezner, Zvi & Nickel, Stefan, 2009. "Solving the ordered one-median problem in the plane," European Journal of Operational Research, Elsevier, vol. 195(1), pages 46-61, May.
    • Handle: RePEc:eee:ejores:v:195:y:2009:i:1:p:46-61
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    References listed on IDEAS

    as
    1. Tammy Drezner & Zvi Drezner, 2007. "Equity Models in Planar Location," Computational Management Science, Springer, vol. 4(1), pages 1-16, January.
    2. Jack Elzinga & Donald W. Hearn, 1972. "Geometrical Solutions for Some Minimax Location Problems," Transportation Science, INFORMS, vol. 6(4), pages 379-394, November.
    3. Zvi Drezner & Atsuo Suzuki, 2004. "The Big Triangle Small Triangle Method for the Solution of Nonconvex Facility Location Problems," Operations Research, INFORMS, vol. 52(1), pages 128-135, February.
    4. Antonio M. Rodríguez-Chía & Stefan Nickel & Justo Puerto & Francisco R. Fernández, 2000. "A flexible approach to location problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 51(1), pages 69-89, February.
    5. O Berman & Z Drezner & G O Wesolowsky, 2003. "The expropriation location problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(7), pages 769-776, July.
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    Citations

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    Cited by:

    1. Victor Blanco & Justo Puerto & Safae El Haj Ben Ali, 2014. "Revisiting several problems and algorithms in continuous location with $$\ell _\tau $$ ℓ τ norms," Computational Optimization and Applications, Springer, vol. 58(3), pages 563-595, July.
    2. Drezner, Tammy & Drezner, Zvi & Hulliger, Beat, 2014. "The Quintile Share Ratio in location analysis," European Journal of Operational Research, Elsevier, vol. 238(1), pages 166-174.
    3. Schöbel, Anita & Scholz, Daniel, 2014. "A solution algorithm for non-convex mixed integer optimization problems with only few continuous variables," European Journal of Operational Research, Elsevier, vol. 232(2), pages 266-275.
    4. Ting L. Lei & Richard L. Church, 2014. "Vector Assignment Ordered Median Problem," International Regional Science Review, , vol. 37(2), pages 194-224, April.
    5. Rodríguez-Chía, Antonio M. & Espejo, Inmaculada & Drezner, Zvi, 2010. "On solving the planar k-centrum problem with Euclidean distances," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1169-1186, December.
    6. Frank Plastria & Mohamed Elosmani, 2013. "Continuous location of an assembly station," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(2), pages 323-340, July.

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