Degree of locational freedom in a single facility Euclidean minimax location model

The facility location model discussed here is a single-facility, unweighted, minimax problem defined in the plane. This paper introduces a procedure for constructing contour lines and computing the degree of locational freedom according to this model, based on the farthest-point Voronoi diagram. Bounds and an approximate expression on the degree of locational freedom are also presented. The magnitude of the degree of locational freedom is important for decision-makers. This is because the larger the magnitude, the easier it will be for them to carry out their facility planning. The results of extensive computational tests identify empirically the availability of these bounds. The results also show that the degree of locational freedoms in the case where the center is determined by two demand points is greater than the degrees where the center is determined by three demand points.