A Minimax Facility-Configuration Problem Involving Lattice Points

This paper considers the problem of assigning n facilities, or departments, to locations so that the maximum of the rectilinear distances between departments is minimized. The locations are considered to be points in a lattice. It develops a simple explicit expression for the minimum value of the objective function for all values of n; this expression has as a corollary a necessary and sufficient condition for an assignment, or a configuration, to be minimax; the paper also develops a simple geometrical procedure for constructing minimax configurations. Some related problems are also examined briefly.