Reverse selective obnoxious center location problems on tree graphs

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.