Weber’s Location Triangle

Webers Location Triangle

Alfred Weber’s work (1909) is considered the foundation of modern location theories and a basic P-median location problem. One of its core assumptions is that firms will choose a location minimizing their total costs through a set of simplifications. Location occurs in an isolated region (no external influences) composed of one market, that space is isotropic (no variations in transport costs except a simple function of distance) and that markets are located in a specific number of centers. Those conditions are quite similar to those behind Von Thunen’s agricultural land use model elaborated almost one hundred years earlier. The model also assumes perfect competition, implying a high number of firms and customers, small firm sizes (to prevent disruptions created by monopolies and oligopolies), and complete knowledge of market conditions, both for the buyers and suppliers. Several natural resources, such as water, are ubiquitous (available everywhere), while many production inputs such as labor, fuel, and minerals, are available at specific locations. According to Weber, three main factors influence industrial location; transport costs, labor costs, and agglomeration economies. Location thus implies an optimal consideration of these factors.

Solving Weber’s location model usually implies three stages; finding the least transport cost location and adjusting this location to consider labor costs and agglomeration economies. Transportation is the most important element of the model since other factors are considered only to have an adjustment effect. To solve this problem, Weber uses the location triangle within which the optimal is located. The above figure illustrates the issue of minimizing transport costs by finding point P. Considering a product of w(M) tons to be sold at market M, w(S1) and w(S2) tons of materials coming respectively from S1 and S2 are necessary. The problem resides in finding an optimal factory location P located at the respective distances of d(M), d(S1), and d(S2). Several methodologies can be used to solve this problem, such as drawing an analogy to a system of weights and pulleys (Varignon’s solution) or using trigonometry. Another way preferred among geographers, particularly with GIS, is to use cost surfaces that are overlaid.

Weber’s location theory explains the location of heavy industries, particularly from the industrial revolution until the mid-twentieth century (the sector that Weber was looking at). Activities using a high level of raw materials tend to locate near supply sources, such as aluminum factories, will locate near energy sources (electricity), or port sites. Activities using ubiquitous raw materials, such as water, tend to be located close to markets. To assess this issue, Weber developed a material index, which is simply the weight of the inputs divided by the weight of the final product (output). If the material index is higher than 1, the location tends toward material sources. If it is less than 1, the location tends toward the market. Contemporary developments in manufacturing, the reduction of transport costs, global supply chains, and new economic sectors (such as high technology) have substantially changed locational behavior, involving much less consideration of Weber’s principles. Still, these principles apply well to industries with a high material index.