Title: Analysing a few trigonometric solutions for the Fermat-Weber facility location triangle problem with and without repulsion and generalising the solutions

Authors: A. Baskar

Addresses: Apollo Engineering College, Mevaloorkuppam, Valarpuram Post, Chennai-602 105, India

Abstract: In location theory, the Weber (1909) problem is one of the most popular problems. It requires locating a unique point that minimises the sum of transportation costs from that point. In a triangular case, the problem is to locate a point with respect to three points in such a way that the sum of distances between the point and the other three points is the minimum. Tellier (1972) found a geometric solution to the problem. In the attraction-repulsion problem, some of the costs may be negative. This was formulated and geometrically solved for a triangular case by Tellier (1985). Gruulich (1999) discussed about the barycentric coordinates solution applied to the optimal road junction problem. Ha and Loc (2011) proposed an easy geometrical solution to the repulsive force and two attraction forces triangular problem. This paper generalises the solutions for both the attractions and repulsion problems and analytical formulae are derived.

Keywords: Fermat-Weber problem; location theory; transport costs; barycentric coordinates; optimal point; trigonometry; facility location triangle; repulsion; generalisation.

DOI: 10.1504/IJMOR.2017.081922

International Journal of Mathematics in Operational Research, 2017 Vol.10 No.2, pp.150 - 166

Received: 02 Mar 2015
Accepted: 08 May 2015
Published online: 31 Jan 2017 *

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