Analysing a few trigonometric solutions for the Fermat-Weber facility location triangle problem with and without repulsion and generalising the solutions. (2017)

• Record Type: Journal Article
• Authors: Baskar, A.
• Is Part Of: International journal of mathematics in operational research. Volume 10:Number 2(2017)
• Page Start: 150
• Page End: 166
• Publication Date: 2017
• Subjects: Fermat-Weber problem -- location theory -- transport costs -- barycentric coordinates -- optimal point -- trigonometry -- facility location triangle -- repulsion -- generalisation; Operations research -- Mathematical models -- Periodicals; Operations research -- Mathematics -- Periodicals; Decision making -- Mathematical models -- Periodicals; 658.4033
• Languages: English
• ISSNs: 1757-5850

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.