Planar p-center problem with Tchebychev distance

Abstract

The p-center problem is a model for locating p facilities to serve clients so that the distance between a farthest client and its closest facility is minimized. Emergency service facilities such as fire stations, hospitals and police stations are most of the time located in this manner. In this thesis, the planar p-center problem with Tchebychev distance is studied. The problem is known to be NPHard. We identify certain polynomial time solvable cases and give an efficient branching method which makes use of polynomial time methods in subproblem solutions whenever possible. In addition, a dual problem is posed in light of the existing duality theory on tree networks.