A single facility location problem with a weighted maximin-minimax rectilinear distance

Abstract

This paper provides an algorithm for locating a single facility in a region, where the objective function is composed of the weighted maximin and minimax rectilinear distances from a set of given demand points. This weighted objective function is applicable when the facility to be located is somewhat desirable but it should not be too close to the demand points, since it also has some undesirable effects. It has been proven in this paper, that it is enough to test for optimality all the intersection points of any two lines forming the equirectilinear distances between any pair of demand points or boundary lines of the region. The algorithm developed here tests these intersection points. The efficient set of points and their optimality range are found. This parametric form of the solution provides an optimal solution for any desired weight.