An extension of the Tobler’s law? Influence of the metric to compute the distance between an optimal facility and its demand points
Résumé
This research work presents an extension of the Tobler’s first law (TFL), that includes the metric used to measure the distance between a center and its demand points, in an optimal facility location problem framework (Hakimi, 1964). It provides a short overview of the works derived from the TFL and opens on the definition of a second law, less geographical and more mathematical. Indeed, its seems the distance, that is to say in our case a Lp-norm (a generalized Minkowski distance) considered to estimate a proximity between two points, has a strong weight on the meaning and on the shape of the TFL.
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