The point of optimal transportation is based on the costs of distance to the "material index (MI)" – the ratio of weights of the intermediate products (raw materials or RM) to finished product or FP. a) RM is more than FP; MI>1 found the first direct (non iterative) numerical solution of the
Fermat and
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. It was formulated by the famous French mathematician
Pierre de Fermat before 1640. As for the Weber triangle problem, which is a generalization of the Fermat triangle problem, it was first formulated by
Thomas Simpson in 1750, and popularized by Alfred Weber in 1909. In 1985, in a book entitled ''Économie spatiale: rationalité économique de l'espace habité'',
Tellier formulated an all-new problem called the "attraction-repulsion problem", which constitutes a generalization of both the Fermat and 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
spatial economics 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 analyzed by mathematicians like Chen, Hansen, Jaumard and Tuy (1992), and Jalal and Krarup (2003). The attraction-repulsion problem is seen by Ottaviano and Thisse (2005) as a prelude to the
New Economic Geography that developed in the 1990s, and earned
Paul Krugman a
Nobel Memorial Prize in Economic Sciences in 2008. ==Works==