Fuzzy approach to the spatial games in the total market area

The paper presents a fuzzy approach to building up a model of spatial hierarchy based on spatial games. It is derived from the analytical model by Bogataj and Bogataj (Int. J. Prod. Econ. 71 (1–3) (2001) 277). The main strategic problems of a supply chain are connected with the question of location and capacity of individual activity cells to achieve the best supply chain coordination. The results of supply chain coordination between two activity cells on the plain originate from Girlich's research paper (Inventory Modelling, Lecture Notes of the International Postgraduate Summer School, Vol. 2, ISIR, Budapest-Protoroz, 1995, pp. 13–24) and have been later transformed in frequency space, using the methodology of input–output analysis, Laplace transforms and MRP developed at Linköping Institute of Technology by Grubbström and his research group. The analytical results developed by Bogataj and Bogataj (2001) are compared with the results achieved by fuzzy set approach. In our paper the problem is formulated as a non-constant sum game. In this case the total market area is constant and the conditions for lower central places are described for different positions of these central places in an urban hierarchy in the case of two-level production. The results of fuzzy approach in logistic games are compared with analytical results.