Localization in multifacility location theory
type: Item
instance of: scholarly article
title: Localization in multifacility location theory
zbMATH Open document ID: 0632.90021
DOI: 10.1016/0377-2217(87)90020-8
author: Christian Michelot
published in: European Journal of Operational Research
publication date: 1987-01-01T00:00:00Z
review text: We present two localization theorems for a multifacility location problem involving linear costs and a single norm in a two-dimensional space. It is shown that optimal locations for all the new facilities can be found in the metric hull of existing facilities, whatever the norm is. In the polyhedral norm case we study if only finite sets of intersection points which belong to the metric hull need to be considered; the result is obtained in particular for the \(\ell^ 1\)-norm and a counter example is given for a general polyhedral norm.
Mathematics Subject Classification ID: 90B05
zbMATH DE Number: 4029234
zbMATH Keywords: hull properties
zbMATH Keywords: multifacility location
zbMATH Keywords: linear costs
zbMATH Keywords: single norm in a two-dimensional space
zbMATH Keywords: polyhedral norm case
zbMATH Keywords: \(\ell ^ 1\)-norm
MaRDI profile type: Publication
full work available at URL: 0377-2217(87)90020-8
OpenAlex ID: W1990854886
cites work: Geometrical properties of the Fermat-Weber problem
cites work: Sets of efficient points in a normed space
cites work: Properties of a multifacility location problem involving euclidian distances
cites work: Technical Note—Location Theory, Dominance, and Convexity: Some Further Results
cites work: Hull properties in location problems
cites work: Q3226265
cites work: A computation procedure for the exact solution of location-allocation problems with rectangular distances
cites work: The minimization of lower subdifferentiable functions under nonlinear constraints: An all feasible cutting plane algorithm
cites work: Some Properties of Location Problems with Block and Round Norms
cites work: Technical Note—A New Norm for Measuring Distance Which Yields Linear Location Problems
cites work: Using Block Norms for Location Modeling
description: scientific article; zbMATH DE number 4029234