On the 3-dimensional Weber problem with Tchebychev distances

This research presents a new method to find optimal/near optimal solutions for the single facility location problem in three-dimensional Tchebychev space. This new method is based upon a technique presented by Francis, McGinnis, and White in their seminal layout and location text, where they solved the analogous two-dimensional problem in Tchebychev space by rotating the problem about the z-axis through an angle of 45 degrees, thus converting the problem to one in rectilinear space. The method specified herein extends this methodology for the analogous problem in three dimensions. From experimentation with problem sets (including one very large data set) with known optimal solutions, it is suggested the error term is within one-percent of optimality. A detailed example is included as part of this research.

On the 3-dimensional Weber problem with Tchebychev distances Conference Paper