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

Authors: Trevor S. Hale; Crystal Welker; Ryan Pepper; Faizul Huq

Addresses: Department of Information and Operations Management, Texas A&M University, College Station, Texas, USA ' enVista LLC, Distribution Centre Optimisation Group, 11555 N Meridian Street, Suite 300, Carmel, Indiana, USA ' Department of Mathematics and Statistics, University of Houston – Downtown, Houston, Texas, USA ' Department of Management, École Supérieure de Commerce de Pau, 3 Rue Saint-John Perse, 64000 Pau, France

Abstract: 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.

Keywords: facility location; k-centra location; distribution network.

DOI: 10.1504/IJOR.2024.142252

International Journal of Operational Research, 2024 Vol.51 No.2, pp.225 - 232

Received: 22 Jun 2021
Accepted: 02 Nov 2021
Published online: 16 Oct 2024 *

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