Minimax location problem with A-distance

In this paper a single facility location problem for an ambulance service station in a polygonal area X is considered. Our objective is to locate an ambulance service station so as to minimize the maximum distance of the route which passes from the facility to the hospital by way of the scene of accident. In this paper, we consider A-distance which is a generalization of rectilinear distance and was introduced by Widmayer et al. Assuming m hospitals at the points H-1,H-2,...,H-m and denoting the nearest hospital to a point Q of X with S(Q), the following problem P-M is considered. P-M : Minimize max(Q is an element of X) R(P*,Q) = {d(A)(P*,Q) + d(A)(Q,S(Q))}, where P* = (x*,y*) is the location of an ambulance service station to be determined. Then we show P-M can be reduced to the messenger boy problem with A-distance. Utilizing this result, we propose an efficient solution procedure by extending Elzinga & Hearn Algorithm to A-distance case.