Abstract
Facility location problems (FLP) are widely studied in operations research and supply chain domains. The most common metric used in such problems is the distance between two points, generally Euclidean distance (ED). When points/ locations on the earth surface are considered, ED may not be the appropriate distance metric to analyse with. Hence, while modelling a facility location on the earth, great circle distance (GCD) is preferable for computing optimal location(s). The different demand points may be assigned with different weights based on the importance and requirements. Weiszfeld’s algorithm is employed to locate such an optimal point(s) iteratively. The point is generally termed as “Geometric Median”. This paper presents simple models combining GCD, weights and demand points. The algorithm is demonstrated with a single and multi-facility location problems.
Highlights
In any supply chain, the location of a supply point has a great influence on the system parameters like transportation cost, the time required and system efficiency [1]
A study conducted by AssochamResurgent India (2016) concluded that India can save around Rs 3.33 lakh crores if logistics costs reduce from 14 per cent to 9 per cent of GDP
Given a set of „m‟ data points, the procedure for estimating the optimal location is given in several steps: Steps: 1. Estimation of geodetic coordinates of all points in radians with signs.(South latitudes and west longitudes are expressed in negative values)
Summary
The location of a supply point has a great influence on the system parameters like transportation cost, the time required and system efficiency [1]. A single facility Fermat-Weber problem requires finding a point in a real coordinate space of dimension „n‟ (Rn) which minimizes the sum of weighted distances to „m‟ given data points. Cazabal-Valencia et al [21] claim that minimum total coverage distance is achieved with the facility location problem considering the ellipsoid as the model for the Earth‟s surface. This distance is smaller than the total coverage distance achieved under the spherical model. This paper presents two simple models to estimate the optimal facility location point(s) on the earth surface from a data set with known geodetic coordinates (latitudes and longitudes). These formulae work fine for all points in the earth surface except those points on the earth directly opposite to each other
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