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Extensions to the continuous ordered median problem

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  • Jochen Krebs
  • Stefan Nickel

Abstract

Classical location models fix an objective function and then attempt to find optimal points to this objective. In the last years a flexible approach, the ordered median problem, has been introduced. It handles a wide class of objectives, such as the median, the center and the centdian function. In this paper we present new properties of the ordered median problem such as solvability for the situation of attractive and repulsive locations. We also develop a new solution method that even yields local optimal points for non-convex objective functions. Furthermore, we discuss separability of ordered median problems without repulsion and derive a sufficient criterion. Finally, we introduce a useful model extension, the facility class model, which allows to deal with a wider range of real world problems in the ordered median setting. Copyright Springer-Verlag 2010

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:71:y:2010:i:2:p:283-306
    DOI: 10.1007/s00186-009-0296-3
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    1. 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.
    2. 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.
    3. Hamacher, H. W. & Nickel, S., 1996. "Multicriteria planar location problems," European Journal of Operational Research, Elsevier, vol. 94(1), pages 66-86, October.
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