The Planar k-Centra Location Problem

The objective of this research is to develop a procedure that will solve, contingent on a necessary and sufficient optimality condition, the planar k-centra single facility location problem with Euclidean distances. The planar k-centra location problem seeks to find a location that minimizes the sum of the Euclidean distances to the k furthest existing facilities. The intrigue herein lies in the inability to define the k furthest away a priori of determining the associated median location. Hence, an iterative procedure is developed that can lead to optimal solutions but is subject to degeneracy. Results suggest that this degeneracy is instantiation specific to the k-centra location problem.