Editing Thomas Simpson (section)

==Simpson-Weber triangle problem==

This type of generalisation was later popularised by [[Alfred Weber]] in 1909.  The [[Weber problem|Simpson-Weber triangle problem]] consists in locating a point D with respect to three points A, B, and C in such a way that the sum of the transportation costs between D and each of the three other points is minimised. In 1971, [[Luc-Normand Tellier]]<ref>Tellier, Luc-Normand, 1972, "The Weber Problem: Solution and Interpretation”, Geographical Analysis, vol. 4, no. 3, pp. 215–233.</ref> found the first direct (non iterative) numerical solution of the [[Fermat point|Fermat]] and Simpson-[[Alfred Weber|Weber]] triangle problems. Long before [[Von Thünen]]'s contributions, which go back to 1818, the [[Fermat point]] problem can be seen as the very beginning of space economy.

In 1985, [[Luc-Normand Tellier]]<ref>Tellier, Luc-Normand, 1985, Économie spatiale: rationalité économique de l'espace habité, Chicoutimi, Gaëtan Morin éditeur, 280 pages.</ref> formulated an all-new problem called the “attraction-repulsion problem”, which constitutes a generalisation of both the Fermat and Simpson-Weber problems. In its simplest version, the attraction-repulsion problem consists in locating a point D with respect to three points A1, A2 and R in such a way that the attractive forces exerted by points A1 and A2, and the repulsive force exerted by point R cancel each other out. In the same book, Tellier solved that problem for the first time in the triangle case, and he reinterpreted the [[space economy]] theory, especially, the theory of land rent, in the light of the concepts of attractive and repulsive forces stemming from the attraction-repulsion problem. That problem was later further analysed by mathematicians like Chen, Hansen, Jaumard and Tuy (1992),<ref>Chen, Pey-Chun, Hansen, Pierre, [[Brigitte Jaumard|Jaumard, Brigitte]], and Hoang Tuy, 1992, "Weber's Problem with Attraction and Repulsion," Journal of Regional Science 32, 467–486.</ref> and Jalal and Krarup (2003).<ref>Jalal, G., & Krarup, J. (2003). "Geometrical solution to the Fermat problem with arbitrary weights". Annals of Operations Research, 123, 67{104.</ref> The attraction-repulsion problem is seen by Ottaviano and [[Jacques-François Thisse|Thisse]] (2005)<ref>Ottaviano, Gianmarco and Jacques-François Thisse, 2005, "New Economic Geography: what about the N?”, Environment and Planning A 37, 1707–1725.</ref> as a prelude to the [[Economic geography|New Economic Geography]] that developed in the 1990s, and earned [[Paul Krugman]] a [[Nobel Memorial Prize]] in Economic Sciences in 2008.