On the ordered anti-Weber problem for any norm in R2

In this paper, a family of single-obnoxious-facility location problems is modelled by considering the same objective function as is used in the ordered median location problem. This function involves distances defined with any arbitrary norm and hence it can be used in a general framework. We prove that the solutions to these obnoxious location problems, restricted to a polygonal region with m vertices and considering n existing population centers, can be found in a set defined in terms of the weighted equidistant points. For many usual norms, this dominating set is finite and can be Constructed in O(mn(2) + n(4)). (C) 2009 Elsevier B.V. All rights reserved.