Map projection errors in the Weber problem

 When demand points are given as a planar map where projection method is explicitly stated, we usually know the latitudes and longitudes of these points from the map. Then we can solve the Weber problem on the globe, and we do not suffer from errors. This paper analyses how cylindrical projections cause distortion in the Weber problem when demands are distributed on the Northern Hemisphere. First, we demonstrate that planar solutions are always located south of the spherical solution if the Mercator projection, the equirectangular projections with standard parallels near the demands, or the equal-area projection with the same characteristic is chosen. Second, we verify that this geographical tendency is inclined to hold when the demand points, are distributed symmetrically, widely or toward the north.