Geometrical solution to some planar constrained minimax problems involving the weighted rectilinear metric

The problem of locating a single service centre catering to the demands of customers distributed over a finite set of demand points in a two-dimensional space employing both the symmetric and non-symmetric Manhattan metric minimax criterion is considered. An exact solution technique, based on geometry, is presented, with the assumption that the required facility point should be situated in a convex polyhedral region. The algorithm, methodology of which has been illustrated by means of suitable numerical examples, has polynomial time complexity.