Planar Location Problems with Line Barriers

  • The Weber Problem for a given finite set of existing facilities {cal E}x = {Ex_1,Ex_2, ... ,Ex_M} subset R^2 with positive weights w_m (m = 1, ... ,M) is to find a new fcility X* such that sum_{m=1}^{M} w_{m}d(X,Ex_m) is minimized for some distance function d. A variation of this problem is obtained of the existing facilities are situated on two sides of a linear barrier. Such barriers like rivers, highways, borders or mountain ranges are frequently encountered in practice. Structural results as well as algorithms for this non-convex optimization problem depending on the distance function and on the number and location of passages through the barrier are presented. A reduction to convex optimization problems is used to derive efficient algorithms.

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Author:Kathrin Klamroth
URN (permanent link):urn:nbn:de:hbz:386-kluedo-4549
Serie (Series number):Report in Wirtschaftsmathematik (WIMA Report) (13)
Document Type:Preprint
Language of publication:English
Year of Completion:1999
Year of Publication:1999
Publishing Institute:Technische Universität Kaiserslautern
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:510 Mathematik

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