人口中心点の研究の歴史的考察

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It had been a great problem to find the central point of population or the point which people can all reach with the minimum aggregate of travel. According to the study by Kuhn and Kuenne, the problem was discussed by Fermat early in 17th century. This problem was resolved mathematically by Kuhn and Kuenne in 1962. This problem can be classified into three types of problems, Steiner's problem, Weber problem, and generalized Weber problem. Characteristics of these problems are expressed by the following equations: φ=Σ^^3__<i=1>d_i (1) φ=Σ^^3__<i=1>W_id_i (2) φ=Σ^^n__<i=1>W_id_i (3) where d_i is a distance between the ith point and a point to which people go to meet and w_i the number of people living at the ith point. In Steiner's problem, a point which minimizes the φ in equation (1 ) is obtained. In Weber and generalized Weber problems, points which minimize the φ's in equations(2) and (3) are obtained, respectively. Many studies are done for obtaining the point which minimizes the φ in equations (1), (2), and (3). In this paper, the studies are examined historically. And, a chronological table of the studies was made. I have read many papers and books to write this paper. I have, especially, much impressed from the following books and papers: Weber, Alfred: Ueber den Standort der Industrien, Tubingen, 1922. Eells, Walter Crosby: "A Mistaken Conception of the Center of Population," Journal of the American Statistical Association, Vol.25, March, 1930, pp.33-40. Isard, Walter: Location and Space Economy, New York, 1956. Flaskamper: Bevlikerungsstatistik, Hamburg, 1962. Kuhn, Harold W. and Robert, E. Kuenne: "An Efficient Algorithm for the Numerical Solution of the Generalized Weber Problem in Spatial Economics," Journal of Regional Science, Vol.4, No.2, Winter, 1962, pp.21-32. Nishioka, Hisao : Keizai Chiri Bunseki (Analysis in Economic Geography), Tokyo, 1976. Okuno, Takashi and Takamori, Hiroshi: Ten to Sen no Sekai (The World of Points and Lines), Tokyo, 1976.
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人口中心点の研究の歴史的考察

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