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Improved fixed point optimality conditions for mixed norms minisum location

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Abstract

We improve and extend sufficient conditions for an optimal solution to happen at a fixed point in a single facility minisum location model with mixed transportation modes recently proposed and studied by Brimberg, Love and Mladenović. In particular, conditions are derived that are valid for general mixed metrics, while for mixed p -norms, possibly with rotated axes, much stronger conditions are obtained. An example demonstrates the superiority of the new conditions.

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References

  • Brimberg J, Love R, Mladenović N (2009) Extension of the Weiszfeld procedure to a single facility minisum location model with mixed p norms. Math Methods Oper Res 70:269–283

    Article  Google Scholar 

  • Fliege J (1997) Effiziente Dimensionsreduktion in Multilokationsproblemen (Efficient dimension reduction in multifacility location problems). PhD thesis, Fachbereich Mathematik, Universität Dortmund, Germany. Shaker Verlag, Aachen

  • Francis R, McGinnis L, White J (1992) Facility layout and location: An analytical approach, 2nd edn. Prentice Hall, New York

    Google Scholar 

  • Hiriart-Urruty J-B, Lemaréchal C (2001) Fundamentals of convex analysis. Springer, Berlin

    Book  Google Scholar 

  • Juel H, Love RF (1981) Fixed point optimality criteria for the location problem with arbitrary norms. J Oper Res Soc 32:891–897

    Google Scholar 

  • Plastria F (1983) A note on ‘Fixed point optimality criteria for the location problem with arbitrary norms’. J Oper Res Soc 34:164–165

    Google Scholar 

  • Plastria F (1992) On destination optimality in asymmetric distance Fermat–Weber problems. Ann Oper Res 40:355–369

    Article  Google Scholar 

  • Plastria F (2006) Four-point Fermat location problems revisited. New proofs and extensions of old results. IMA J Manag Math 17:387–396

    Article  Google Scholar 

  • Plastria F (2009) Asymmetric distances, semidirected networks and majority in Fermat–Weber problems. Ann Oper Res 167(1):121–155

    Article  Google Scholar 

  • Plastria F (2011) The Weiszfeld algorithm: Proof, amendments and extensions. In: Eiselt HA, Marianov V (eds) Foundations of location analysis. International series in operations research and management science. Springer, Berlin, pp 357–389

    Chapter  Google Scholar 

  • Weiszfeld E (1937) Sur le point pour lequel la somme des distances de n points donnés est minimum. Tôhoku Math J 43:355–386

    Google Scholar 

  • Weiszfeld E (2009) On the point for which the sum of the distances to n given points is minimum. Ann Oper Res 167:7–41. Translated and annotated by F Plastria

    Article  Google Scholar 

  • Witzgall C (1964) Optimal location of a central facility, mathematical models and concepts. Report 8388, National Bureau of Standards, Washington DC, USA

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Acknowledgements

This research was partially done in the context of the project GOA62 of the OZR at the Vrije Universiteit Brussel.

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Correspondence to F. Plastria.

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Plastria, F. Improved fixed point optimality conditions for mixed norms minisum location. TOP 22, 170–184 (2014). https://doi.org/10.1007/s11750-011-0246-0

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