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A flexible approach to location problems

Author

Listed:
  • Antonio M. Rodríguez-Chía
  • Stefan Nickel
  • Justo Puerto
  • Francisco R. Fernández

Abstract

When dealing with location problems we are usually given a set of existing facilities and we are looking for the location of one or several new facilities. In the classical approaches weights are assigned to existing facilities expressing the importance of the new facilities for the existing ones.¶In this paper, we consider a pointwise defined objective function where the weights are assigned to the existing facilities depending on the location of the new facility. This approach is shown to be a generalization of the median, center and centdian objective functions. In addition, this approach allows the formulation of completely new location models. Efficient algorithms as well as structural results for this algebraic approach to location problems are presented. A complexity analysis and extensions to the multifacility and restricted case are also considered. Copyright Springer-Verlag Berlin Heidelberg 2000

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:51:y:2000:i:1:p:69-89
    DOI: 10.1007/s001860050003
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    Citations

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    Cited by:

    1. 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.
    2. Schnepper, Teresa & Klamroth, Kathrin & Stiglmayr, Michael & Puerto, Justo, 2019. "Exact algorithms for handling outliers in center location problems on networks using k-max functions," European Journal of Operational Research, Elsevier, vol. 273(2), pages 441-451.
    3. Mark Rozanov & Arie Tamir, 2018. "The nestedness property of location problems on the line," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(2), pages 257-282, July.
    4. J. Puerto & A. M. Rodríguez-Chía & A. Tamir, 2009. "Minimax Regret Single-Facility Ordered Median Location Problems on Networks," INFORMS Journal on Computing, INFORMS, vol. 21(1), pages 77-87, February.
    5. Conde, Eduardo, 2007. "Minmax regret location-allocation problem on a network under uncertainty," European Journal of Operational Research, Elsevier, vol. 179(3), pages 1025-1039, June.
    6. Alfredo Marín & Stefan Nickel & Sebastian Velten, 2010. "An extended covering model for flexible discrete and equity location problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(1), pages 125-163, February.
    7. Blanco, Víctor & Puerto, Justo & Ben-Ali, Safae El-Haj, 2016. "Continuous multifacility ordered median location problems," European Journal of Operational Research, Elsevier, vol. 250(1), pages 56-64.
    8. Andrea Maier & Horst W. Hamacher, 2019. "Complexity results on planar multifacility location problems with forbidden regions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 89(3), pages 433-484, June.
    9. Kalcsics, Jörg & Nickel, Stefan & Puerto, Justo & Rodríguez-Chía, Antonio M., 2010. "Distribution systems design with role dependent objectives," European Journal of Operational Research, Elsevier, vol. 202(2), pages 491-501, April.
    10. Jochen Krebs & Stefan Nickel, 2010. "Extensions to the continuous ordered median problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(2), pages 283-306, April.
    11. R. Francis & T. Lowe & M. Rayco & A. Tamir, 2009. "Aggregation error for location models: survey and analysis," Annals of Operations Research, Springer, vol. 167(1), pages 171-208, March.
    12. 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.
    13. Patricia Domínguez-Marín & Stefan Nickel & Pierre Hansen & Nenad Mladenović, 2005. "Heuristic Procedures for Solving the Discrete Ordered Median Problem," Annals of Operations Research, Springer, vol. 136(1), pages 145-173, April.

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