Locating Median Lines and Hyperplanes with a Restriction on the Slope

Book excerpt: In this thesis, we consider the location of median lines when there is a restriction on the slope of the line to locate as well as the more general location of median hyperplanes when there is a restriction on the slope vector of the hyperplane to locate. We are given a set of existing facilities in R^2 or R^n and we are searching for a new facility that is a line or a hyperplane, respectively, minimizing the sum of distances between the existing facilities and the new facility while satisfying a restriction on its slope. We investigate this problem in the plane R^2 using different distance ...