Inverse 2-Center Location Problem for Unweighted Tree Networks (A Case Study)

Abstract

This paper studies the inverse 2-center location problem by increasing and decreasing the edge length on unweighted tree networks. The goal is to increase and decrease the edge lengths at minimum total cost subject to the given modification bounds such that the predetermined vertices becomes absolute 2-center. In order to demonstrate the practical application of this issue, we consider Bojnourd urban network and two important fire stations of the city as center locations. Moreover, an example is generated for computational analysis. Results show that when the predetermined vertices are close to the ends of the tree, higher cost will be imposed. Yet, in most cases, this condition is impossible.