On the Set of Optimal Points to the Weber Problem: Further Results

Roland Durier and Christian Michelot
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Roland Durier: Laboratoire d'Analyse Numérique, Université de Bourgogne, Dijon, France
Christian Michelot: CERMSEM, Université de Paris I, Panthéon-Sorbonne, Paris, France

Transportation Science, 1994, vol. 28, issue 2, 141-149

Abstract: In a recent paper, Z. Drezner and A. J. Goldman address the problem of determining the smallest set among those containing at least one optimal solution to every Weber problem based on a set of demand points in the plane. In the case of arbitrary mixed gauges (i.e., possibly nonsymmetric norms), the authors have shown that the set of strictly efficient points which are also intersection points always meets the set of Weber solutions. As shown by Drezner and Goldman, this set is optimal with the ℓ 1 or ℓ x distance but is not optimal with the ℓ p distance, 1 p p distance case, we disprove a conjecture of Drezner and Goldman about the possibility of extending their result to more than two dimensions. The paper contains a different view of the problem: whereas Drezner and Goldman use algebraic-analytical approach, the authors use a geometrical approach which permits us to obtain more general results and also clarifies the geometric nature of the problem.

Date: 1994
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ortrsc:v:28:y:1994:i:2:p:141-149

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