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Constructing a DC decomposition for ordered median problems

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Abstract

In this paper we show how to express ordered median problems as a difference between two convex functions (DC). Such an expression can be exploited in solving ordered median problems by using the special methodology available for DC optimization. The approach is demonstrated for solving ordered one median problems in the plane. Computational experiments demonstrated the effectiveness of the approach.

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References

  1. Drezner Z.: A general global optimization approach for solving location problems in the plane. J. Global Optim. 37, 305–319 (2007)

    Article  Google Scholar 

  2. Drezner, Z., Hamacher, H.W. (eds): Facility Location: Applications and Theory. Springer-Verlag, Berlin (2002)

    Google Scholar 

  3. Drezner, Z., Nickel, S.: Solving the Ordered One-Median Problem in the plane. Eur. J. Oper. Res. (2008) (to appear). doi:10.1016/j.ejor.2008.02.033

  4. Drezner Z., Suzuki A.: The big triangle small triangle method for the solution of non-convex facility location problems. Oper. Res. 52, 128–135 (2004)

    Article  Google Scholar 

  5. Drezner, T., Drezner, Z., Guyse, J.: The lorenz curve in location analysis. Technical Report (2007)

  6. Horst R., Thoai Ng.V.: DC programming: overview. J. Optim. Theory Appl. 103, 1–43 (1999)

    Article  Google Scholar 

  7. Horst R., Phong T.Q., Thoai Ng.V., de Vries J.: On solving a d.c. programming problem by a sequence of linear programs. J. Global Optim. 1, 183–203 (1991)

    Article  Google Scholar 

  8. Kalcsics J., Nickel S., Puerto J., Tamir A.: Algorithmic results for ordered median problems defined on networks and the plane. Oper. Res. Lett. 30, 149–158 (2002)

    Article  Google Scholar 

  9. Nickel S., Puerto J.: Facility Location—A Unified Approach. Springer-Verlag, Berlin (2005)

    Google Scholar 

  10. Ohya T., Iri M., Murota K.: Improvements of the incremental method of the voronoi diagram with computational comparison of various algorithms. J. Oper. Res. Soc. Jpn. 27, 306–337 (1984)

    Google Scholar 

  11. Plastria F.: Continuous location problems: research, results and questions. In: Drezner, Z. (eds) Facility Location: A Survey of Applications and Methods, pp. 85–127. Springer-Verlag, New York (1995)

    Google Scholar 

  12. Rodríguez-Chía A.M., Nickel S., Puerto J., Fernández F.R.: A flexible approach to location problems. Math. Methods Oper. Res. 51(1), 69–89 (2000)

    Article  Google Scholar 

  13. Sugihara K., Iri M.: A robust topology-oriented incremental algorithm for voronoi diagram. Int. J. Comput. Geometry Appl. 4, 179–228 (1994)

    Article  Google Scholar 

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Authors and Affiliations

  1. Steven G. Mihaylo College of Business and Economics, California State University-Fullerton, Fullerton, CA, 92834, USA

    Zvi Drezner

  2. Saarland University, 66123, Saarbrucken, Germany

    Stefan Nickel

  3. Fraunhofer ITWM, Kaiserslautern, Germany

    Stefan Nickel

Authors
  1. Zvi Drezner
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  2. Stefan Nickel
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Correspondence to Stefan Nickel.

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Drezner, Z., Nickel, S. Constructing a DC decomposition for ordered median problems. J Glob Optim 45, 187–201 (2009). https://doi.org/10.1007/s10898-008-9326-6

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  • DOI: https://doi.org/10.1007/s10898-008-9326-6

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