On the convergence of the Weiszfeld algorithm for continuous single facility location–allocation problems

• Frank Plastria ^[1] ; Mohamed Elosmani ^[2]
  1. [1] Université Libre de Bruxelles

     Université Libre de Bruxelles

     Arrondissement Brussel-Hoofdstad, Bélgica

     
  2. [2] École Normale Supérieure

     École Normale Supérieure

     Francia

     
• Localización: Top, ISSN-e 1863-8279, ISSN 1134-5764, Vol. 16, Nº. 2, 2008, págs. 388-406
• Idioma: inglés
• DOI: 10.1007/s11750-008-0056-1
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• Resumen

  • A general family of single facility continuous location–allocation problems is introduced, which includes the decreasingly weighted ordered median problem, the single facility Weber problem with supply surplus, and Weber problems with alternative fast transportation network. We show in this paper that the extension of the well known Weiszfeld iterative decrease method for solving the corresponding location problems with fixed allocation yields an always convergent scheme for the location allocation problems. In a generic way, from each starting point, the limit point will be a locally minimal solution, whereas for each possible exceptional situation, a possible solution is indicated. Some computational results are presented, comparing this method with an alternating location–allocation approach.