An equivalence result for single facility planar location problems with rectilinear distance and barriers

An equivalence result for single facility planar location problems with rectilinear distance and barriers

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Article ID: iaor20031318
Country: Netherlands
Volume: 111
Issue: 1
Start Page Number: 89
End Page Number: 110
Publication Date: Mar 2002
Journal: Annals of Operations Research
Authors: ,
Abstract:

This paper considers planar location problems with rectilinear distance and barriers, where the objective function is any convex, nondecreasing function of distance. Such problems have a non-convex feasible region and a non-convex objective function. A modification of the barriers is developed based on properties of the rectilinear distance. It is shown that the original problem with barriers is equivalent to the problem with modified barriers. A particular modification is given that reduces the feasible region and permits its partitioning into convex subsets on which the objective function is convex. A solution algorithm based on the partitioning is the subject of a companion paper.

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