Introduction to Location Science - Location Science - page 3

Fig. 1.2 Torricelli's
geometric construction for the
Fermat problem
be constructed on the sides of this triangle, their vertices pointing outwards.
A circumscribing circle can then be drawn around each of these three triangles.
The circles will intersect at a single point called the Torricelli point or, as some
authors call it, the Fermat-Torricelli point. If all the angles in the initial triangle are
at most equal to 120 ı , this point is the optimal solution to the problem; otherwise,
the Torricelli point falls outside the initial triangle. In this case, the optimal solution
is the initial point located at the apex of the angle greater than 120 ı (Heinen 1834 ).
It is interesting to note that nowadays this problem still attracts the attention of
the scientific community (see, for instance, Nam 2013 ).
The first documented attempt to position location analysis within an economic
context is due to Johann Heinrich von Thünen (1783-1850), an educated landowner
in northern Germany. Von Thünen wished to understand the rural developments
around an urban center. The results of his analysis were presented in 1826 in a
treatise entitled Die isolierte Staat in Beziehung auf Landwirtschaft und Nation-
alökonomie , which was edited as a topic in 1842 and translated into English in
1966 (von Thünen 1842 ). Figure 1.3 depicts the cover of the 1842 edition. Von
Thünnen (1842) considered an isolated and homogeneous area with an urban center
and aimed to discover laws which then governed agricultural prices translating them
into land usage patterns. He also considered several types of agricultural activities
(e.g., grain farming and livestock) grouped according to their relative economic
yield per unit area, their perishability, and the difficulty in delivering the products to
the (central) market. His findings led him to postulate that three factors should have
a crucial impact on the spacial distribution of the activities: (1) the more perishable
a product is, the closer to the market it will be grown; (2) the higher the economic
productivity of a product per land area, the closer to the market it will be grown;
(3) higher transportation difficulty leads to locating an activity closer to the market.
One should therefore expect that the different agriculture activities will evolve in
concentric rings around the urban center (Fig. 1.4 ).