Revisiting the optimal center location. A spatial thinking based on robustness, sensitivity, and influence analysis
Résumé
In this paper we deal with different metrics using L p norms in the 1‐facility location problem and their properties. We propose to revisit the problem of optimal center location by discussing the properties of three well-known centers in 2‐dimensional space: the 1‐median for L 1 , the 1‐center (Chebyshev center) for L ∞ and the gravity center for L 2 , respectively, the median, the mean, and the center of extreme values in one dimension. The contribution of the research concerns methods to map influence and sensitivity that provide valuable and complementary information on space for decision making in territorial planning. We also discuss the center properties according to the primary objectives of equity, equality, and efficacy in the access to a facility. In a spatial-thinking approach, we present some methodological propositions to obtain robust and durable centers in geographical space, that rely on the adaptation of the general frame of the L p norm to the planning objectives.