inverse facility location

In this paper we consider the inverse and reverse network facility location problems with considering the equity on servers. The inverse facility location with equality measure deals with modifying the weights of vertices with minimum cost, such that the difference between the maximum and minimum weights of clients allocated to the given facilities is minimized. On the other hand, the reverse case of facility location problem with equality measure considers modifying the weights of vertices with a given budget constraint, such that the difference between the maximum and minimum weights of vertices allocated to the given facilities is reduced as much as possible. Two algorithms with time complexity O(nlogn) are presented for the inverse and reverse 2-facility location problems with equality measures. Computational results show their superiority with respect to the linear programming models.

Traditionally, the minimax circle location problems concern finding a circle C in the plane such that the maximum distance from the given points to the circumference of the circle is minimized. The radius of the circle can be fixed or variable. In this paper we consider the inverse case, that is: a circle C with radius r0 is given and we want to modify the coordinate of existing points with the minimum cost such that the given circle becomes optimal. Mathematical models and some properties of the cases that circle C becomes optimal with comparing to all other circles, and circle C becomes the best circle with comparing to the circles with radius r0 are presented.

This paper deals with the case of variable weights of the inverse model of the minimax circle location problem. The goal of the classic minimax circle location problem is finding a circle in the plane such that the maximum weighted distance from a given set of existing points to the circumference of the circle is minimized.  In the corresponding inverse model, a circle is given and we should modify the weights of existing points with minimum cost, such that the given circle becomes optimal. The radius of the given circle can be fixed or variable. In this paper, both of these cases are investigated and mathematical models are presented for solving them.