- Volume 19 Issue 2
This article compares the weighted geometric median with the centroid, from the question why they use the centroid when they would find the single facility location(the weighted geometric median) which minimize the sum of weighted Euclidean distances in some text books and papers. Firstly, we show that the demand point whose volume of demand exceeds the half of total demand is the weighted geometric median differently from the centroid, and we examine the weighed geometric median when every demand point is located on a line. Meanwhile, we could simply see that the geometric median and the centroid are coincident in the special case when every demand point is located at a vertex of a regular polygon, and every volume of demand is equal. Furthermore, the geometric medians of convex tetragons could be simply attained unlike triangles.
Single Facility Location;Center of Gravity;Euclidean Distance;Weighted Geometric Median