On the convergence of the Weiszfeld algorithm for continuous single facility location–allocation problems |
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Authors: | Frank Plastria Mohamed Elosmani |
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Institution: | (1) MOSI, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussels, Belgium;(2) Ecole Normale Supérieure d’Enseignement Technique (ENSET), Oran, Algeria |
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Abstract: | 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.
The research of the second author was partially supported by the grant of the Algerian Ministry of High Education 001BIS/PNE/ENSEIGNANTS/BELGIQUE. |
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Keywords: | Planar facility location Location allocation Local decrease method Convergence |
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