A four-point direction search heuristic algorithm applied to facility location on plane, sphere, and ellipsoid surfaces

Abstract

A facility location problem (FLP) refers to the best location for establishing a facility to optimally connect and meet the requirements of the demand points. In a supply chain on the earth’s surface, the cost function essentially includes a distance metric to compute the objective function. If the data points are located in a small area, Euclidean Distance (ED) can be considered. When the data points are fairly separated on the earth’s surface, ED cannot give a correct estimate and we have to opt for either a spherical model or an ellipsoidal model. This paper proposes a simple four-point direction search algorithm and a model which can be used for locating a facility on a plane, sphere, and ellipsoid model of earth. The main advantage of the proposed algorithm is that it can be used with any distance metric without changing the algorithm.

Keywords:

• Facility location
• Fermat–Weber problem
• four-point direction search algorithm
• geodetic coordinates
• Haversine formulae
• Vincenty’s formulae

Acknowledgements

The authors are sincerely thankful to the anonymous referees, who provide constructive comments to improve the technical content and presentation of the paper. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.