A Geometrical Solution Procedure for a Rectilinear Distance Minimax Location Problem1

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Abstract
A minimax location problem is considered which involves finding the location of a facility in the plane so that the maximum rectilinear distance between the facility and an arbitrary, but fixed, nonempty and bounded set in the plane will be minimized. A geometrical procedure is developed for finding all solutions to the problem. The derivation of the solution procedure, which is based on the fact that the minimax problem is equivalent to the problem of enclosing the representation of the set after a 45 degree rotation within a smallest square, is believed to be a particularly intuitive one.