Mathematical Modelling for a Semi-obnoxious Inverse Line Location Problem

This paper is the first study considering the inverse median line location problem in the plane with positive and negative weights by using Euclidean and rectilinear norms. A positive weight means that the line has desirable effects on the existing facilities, whereas a negative weight represents undesirable effects of the line to the facilities. When a feasible solution for a line location problem is given, an inverse line location problem is related to improve the problem parameters at the minimum total cost. The problem is considered for two cases. If the inverse line location problem with modifying the vertex weight is concerned, a linear model is presented to study the problem. And if coordinates of demand points are given to be modified by using rectilinear and Euclidean norms, a linear and a nonlinear models are provided to investigate the problem, respectively. Then, a numerical example is presented to illustrate the problem.