, 16:388

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

Original Paper

DOI: 10.1007/s11750-008-0056-1

Cite this article as:
Plastria, F. & Elosmani, M. TOP (2008) 16: 388. doi:10.1007/s11750-008-0056-1


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.


Planar facility locationLocation allocationLocal decrease methodConvergence

Mathematics Subject Classification (2000)


Copyright information

© Sociedad de Estadística e Investigación Operativa 2008

Authors and Affiliations

  1. 1.MOSIVrije Universiteit BrusselBrusselsBelgium
  2. 2.Ecole Normale Supérieure d’Enseignement Technique (ENSET)OranAlgeria