Ordered Weber problems with attraction and repulsion

This paper analyzes a new location model where attractive and repulsive demand points exist and the importance of the existing facilities is only given by the weighted distance between them and the new facility to be located. It is shown that the well-known Weber problem, as well as the Weber problem with some negative weights can be seen as a particular instance of this model. We show that in the general case this problem is neither convex nor d.c. (difference of convex functions). We prove geometrical properties that characterize its optimal solution in the polyhedral norm case. Additionally, we also develop two methods to solve this problem.