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On Locating a Semi‐desirable Facility on the Continuous Plane
Author(s) -
Brimberg J.,
Juel H.
Publication year - 1998
Publication title -
international transactions in operational research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.032
H-Index - 52
eISSN - 1475-3995
pISSN - 0969-6016
DOI - 10.1111/j.1475-3995.1998.tb00102.x
Subject(s) - facility location problem , euclidean distance , mathematical optimization , euclidean geometry , set (abstract data type) , decision maker , regular polygon , computer science , minification , cutting plane method , mathematics , plane (geometry) , operations research , artificial intelligence , integer programming , geometry , programming language
The paper considers a bicriteria model for locating a semi‐desirable facility on the plane. One criterion is that of minimizing the sum of weighted distances between customers and facility, where distances are given by an arbitrary norm. The other criterion is that of maximizing the weighted Euclidean distance from the facility to the closest customer. The objective is to generate the set of efficient points, from which the decision maker must choose the preferred one. Two reformulations are considered: in one, the sum of weighted distances is minimized, subject to constraints requiring that each customer must have a weighted Euclidean distance to the facility of at least a given parameter; varying the parameter yields the efficient set. In the other, both criteria are viewed as minimization problems and a convex combination of them is minimized. Properties of the reformulations are given, and the reformulations are compared. Finally, a solution procedure is outlined.