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Locating an obnoxious facility on a euclidean network to minimize neighborhood damage
Author(s) -
Sung Chang Sup,
Joo Cheol Min
Publication year - 1994
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.3230240102
Subject(s) - euclidean distance , facility location problem , mathematical optimization , piecewise , euclidean geometry , point (geometry) , mathematics , function (biology) , set (abstract data type) , radius , computer science , scale (ratio) , algorithm , geometry , mathematical analysis , computer security , evolutionary biology , biology , programming language , physics , quantum mechanics
This paper considers the problem of locating an obnoxious facility on a Euclidean network that could inflict damage within a λ distance of its location point. The objective is to find a location point that minimizes the sum of weights within the circle of radius λ centered at the location point, where each weight (assigned to a point on the network) represents a numerical scale that typically signifies the extent of the undesirability (or the damage cost) due to the facility located near the weighted point. The weights are assumed discretely distributed over all the nodes but uniformly distributed on all the links of the network. In the problem analysis, some optimal solution properties are found, e.g., the objective function is lower semicontinuous piecewise concave and there is at least one optimal location point in a finite set of candidate points. Using these properties, an efficient solution algorithm is derived and tested with several numerical problems. © 1994 by John Wiley & Sons, Inc.