Spatial Function of Influence on Center Optimal Location Based on L-p-Norms

We propose a sensitivity analysis using generalized L-p-norm (Minkowski distance) applied on center optimal location (1 facility). The results show that there exists in one dimension an underlying (log) linear relation between influence and distance of the demand points on the center. New L-p-norms are emphasized with interesting properties in statistics (e.g. with p = 3) although they are not used in location optimization. The law we enhance is of interest in both statistics and and spatial analysis domains and highlights in a new way the impact of the metrics choice on the center location, through the induced spatial influence function, those metrics aiming at spatial equity (L-8), equality (L-2) or efficiency (L-1).

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