Optimal algorithms for some inverse uncapacitated facility location problems on networks

Abstract

This paper is concerned with two variants of the inverse uncapacitated facility location problem with service cost modifications on tree networks under the rectilinear norm. In the first variant, the aim is to modify the underlying service costs in the cheapest possible way with respect to modification bounds such that a set of predetermined facility locations becomes optimal under the new parameters. Two types of this problem are investigated. The second variant asks to modify the service costs within an associated budget until the predetermined facility locations become as close as possible to the customers. Two types of this problem are also studied. We develop exact optimal algorithms for solving the problems under investigation. By an example, the efficiency of the proposed algorithms is illustrated.