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A Minimax Facility-Configuration Problem Involving Lattice Points

Richard L. Francis
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Richard L. Francis: The University of Florida, Gainesville, Florida

Operations Research, 1973, vol. 21, issue 1, 101-111

Abstract: 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.

Date: 1973
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