Mihai Calciu and Gregory
Vermeersch ()
The paper builds upon an
optimal location method in the continuous two-dimensional space, proposed by
Drezner (1994). This method adapts a weighted Euclidian distances minimisation
procedure by Weiszfeld (1937) to market-share maximisation using attractiveness
and location. Some improvements of the method and some additional insights that
haven’t been discussed in the original paper are presented. Based upon the conceptual
similarity between the geographic and perceptual space we extend the method
to the multidimensional perceptual space. Recognising the sometimes embarrassing
tendency of Weiszfeld’s original algorithm to converge towards local optima,
several procedures are suggested in order to search for the global optimum location.
The same convergence tendency is finally exploited in order to find some efficient
procedures that are able to identify all or most local optima.
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