Takeshi Koshizuka

Approximate formulas of average distances associated with regions and their applications to location problems

This study is concerned with the problem of measuring average distances between two points in two different coplanar regions. The objectives are: (1) to derive the approximated average distances associated with circular regions and to check their accuracy; and (2) to apply these approximated distances to location problems. Results show that the simple approximate formulas are accurate and useful. The approximated average distances can be applied to the analyses of varied kinds of movement phenomena in cities.

Map projection errors in the Weber problem

Abstract. 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.