Technical note: a closed form solution to the k -centra location problem

This research delineates a new heuristic that solves the k-centra location problem on a simple distribution network. This treatise differs from most location research in that we employ a novel, graph theoretic based k-centra approach that seeks to find the location that minimises the sum of the distances to the k furthest existing facilities. The k-centra problem generalises the classic minimax and minisum location problems: If k = 2, the problem reduces to the centre (minimax) location problem, whereas if k = n, the problem reduces to the median (minisum) location problem. This research has direct application to the location of a distribution centre on a simple origin-to-destination distribution network to improve service levels.