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A note on the Weber location problem

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Abstract

In this note, we collect some interesting and useful results about the Weber problem. We investigate an accelerated Weiszfeld procedure which increases the step size and find a formula for the step size that empirically produces the fastest convergence rate. We also derive an estimate for the optimal cost of the system.

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References

  1. R. Chen, Solution of location problems with radial cost function, Comput. Math. Appl. 10(1984)87–94.

    Article  Google Scholar 

  2. R. Chen, Location problems with costs being sums of powers of Euclidean distances, Comput. Oper. Res. 11(1984)285–294.

    Article  Google Scholar 

  3. W. Domschke and A. Drexel,Location and Layout Planning, Lecture Notes in Economics and Mathematical Systems No. 238 (Springer, 1985).

  4. Z. Drezner, The planar two-center and two-median problems, Transp. Sci. 18(1984)351–361.

    Article  Google Scholar 

  5. Z. Drezner and D. Simchi-Levi, Asymptotic behavior of the Weber location problem in the plane, this issue.

  6. R.L. Francis and J.A. White,Facility Layout and Location (Prentice-Hall, Englewood Cliffs, NJ, 1974).

    Google Scholar 

  7. I.N. Katz, On the convergence of a numerica scheme for solving some locational equilibrium problems, SIAM J. Appl. Math. 17(1969)1224–1231.

    Article  Google Scholar 

  8. I.N. Katz, Local convergence in Fermat's problem, Math. Progr. 6(1974)89–104.

    Article  Google Scholar 

  9. H.W. Kuhn, On a pair of dual non-linear problems, in:Non-Linear Programming, ed. J. Abadie (Wiley, New York, 1967).

    Google Scholar 

  10. R.F. Love and P.D. Dowling, A generalized bounding method for multifacility location models, Oper. Res. 37(1989)653–657.

    Article  Google Scholar 

  11. R.F. Love, J.G. Morris and G.O. Wesolowsky,Facilities Location Models and Methods (North-Holland, New York, 1988).

    Google Scholar 

  12. J.G. Morris, Convergences of the Weiszfeld algorithm for the Weber problem using generalized “distance” functions, Oper. Res. 29(1981)37–48.

    Article  Google Scholar 

  13. L.M. Ostresh, Jr., On the convergence of a class of iterative methods for solving the Weber location problem, Oper. Res. 26(1978)597–609.

    Article  Google Scholar 

  14. E. Weiszfeld, Sur le point pour lequel la somme des distances den points donnés est minimum, Tohoku Math. J. 43(1937)355–386.

    Google Scholar 

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Drezner, Z. A note on the Weber location problem. Ann Oper Res 40, 153–161 (1992). https://doi.org/10.1007/BF02060474

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  • DOI: https://doi.org/10.1007/BF02060474

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