Mathematical Methods of Operations Research

, Volume 87, Issue 3, pp 431–450 | Cite as

Reverse selective obnoxious center location problems on tree graphs

Original Article

Abstract

In this paper, we investigate a variant of the reverse obnoxious center location problem on a tree graph \(T=(V,E)\) in which a selective subset of the vertex set V is considered as locations of the existing customers. The aim is to augment or reduce the edge lengths within a given budget with respect to modification bounds until a predetermined undesirable facility location becomes as far as possible from the customer points under the new edge lengths. An \({\mathcal {O}}(|E|^2)\) time combinatorial algorithm is developed for the problem with arbitrary modification costs. For the uniform-cost case, one obtains the improved \({\mathcal {O}}(|E|)\) time complexity. Moreover, optimal solution algorithms with \({\mathcal {O}}(|E|^2)\) and \({\mathcal {O}}(|E|)\) time complexities are proposed for the integer version of the problem with arbitrary and uniform cost coefficients, respectively.

Keywords

Obnoxious center location Combinatorial optimization Reverse optimization Time complexity 

Mathematics Subject Classification

90B80 90B85 90C27 90C35 

Notes

Acknowledgements

The authors sincerely thank the editor and anonymous referees, whose constructive and insightful comments led to an improved presentation of this paper.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of Applied Mathematics, Faculty of Basic SciencesSahand University of TechnologyTabrizIran

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