An Efficient Algorithm for the Numerical Solution of the Generalized Weber Problem in Spatial Economics

  • Harold W. Kuhn


Spatial economics in the past has been hampered in its progress by certain peculiarities which are inherent in the functional relationships among its variables. The frequency of corner solutions in its extremum problems, a common tendency for the constraints upon these problems to be stated as inequalities, and the importance of discontinuous functions in the field, are examples of these peculiarities. It is not fortuitous that the origins and development of programming techniques are so closely tied to the problems of spatial economics, and these techniques have resulted in an advance of breakthrough proportions in obtaining solutions to formerly insoluble spatial problems.


Convex Hull Shopping Center Weber Problem Spatial Economic Spatial Interdependence 
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  1. [1]
    Courant, R. and H. Robbins, What is Mathematics? New York (1941).Google Scholar
  2. [2]
    Curry, H. B., ‘The Method of Steepest Descent for Non-Linear Minimization Problems’, Quarterly of Applied Mathematics, 2 (1944), pp. 258–60.Google Scholar
  3. [3]
    Dean, W. H., Jr., The Theory of the Geographic Location of Economic Activities, selections from the PhD thesis, University of Michigan, Ann Arbor (1938), p. 19.Google Scholar
  4. [4]
    Eisemann, K., ‘The Optimum Location of a Center’, SIAM Review, 4 (1962), pp. 394–5.CrossRefGoogle Scholar
  5. [5]
    Hoover, E. M., Location Theory and the Shoe and Leather Industries, Harvard University Press, Cambridge, Mass. (1937), pp. 42–52.CrossRefGoogle Scholar
  6. [6]
    Isard, W., Location and Space Economy, New York (1956).Google Scholar
  7. [7]
    Launhardt, W., Mathematische Begründung der Volkswirtschaftslehre. Leipzig (1885).Google Scholar
  8. [8]
    Miehle, W., ‘Link-Length Minimization in Networks’, Operations Research, 6 (1958), pp. 232–43.CrossRefGoogle Scholar
  9. [9]
    National Economy, U. S. S. R. , 1960 Statistical Yearbook, Moscow.Google Scholar
  10. [10]
    Palander, T., Beiträge zur Standortstheorie, Uppsala (1935).Google Scholar
  11. [11]
    Palermo, F. P., ‘A Network Minimization Problem’, IBM Journal of Research and Development, 5 (1961), pp. 335–7.CrossRefGoogle Scholar
  12. [12]
    Polya, G., Induction and Analogy in Mathematics, Princeton University Press (1954).Google Scholar
  13. [13]
    Weber, A., Über den Standort der Industrien, Tübingen (1909). Translated as Alfred Weber’s Theory of the Location of Industries, University of Chicago Press (1929), by C. J. Friedrich.Google Scholar

Copyright information

© Robert E. Kuenne 1992

Authors and Affiliations

  • Harold W. Kuhn
    • 1
  1. 1.Princeton UniversityUSA

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