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Solving nonlinear multiple‐facility network location problems
Author(s) -
Hooker J. N.
Publication year - 1989
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/net.3230190110
Subject(s) - facility location problem , mathematical optimization , server , 1 center problem , variety (cybernetics) , computer science , regular polygon , norm (philosophy) , mathematics , nonlinear system , computer network , artificial intelligence , physics , geometry , quantum mechanics , political science , law
We show how to locate optimally p new facilities (servers) on a network so as to minimize cost, where cost can be any convex function of the distances between demand points (nodes) and a closest server. The algorithm is generally practical only for small p (perhaps 2, 3, or 4), but it admits a large number of servers with locations fixed beforehand. The classical p ‐median, p ‐center, and p ‐facility cent‐dian problems are special cases. Other problems of this form include a large number of obnoxious facility problems, problems in which the objective is to minimize an L k norm of distances, and a wide variety of problems, problems in which the objective is to minimize an L k norm of distances, and a wide variety of problems in which equity or social welfare is a a factor.