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Cost Minimization Problems Treated by Geometric Means

Author

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  • R. J. Duffin

    (Carnegie Institute of Technology and Westinghouse Research Laboratories)

Abstract

It is supposed that the cost of an engineering design is a generalized polynomial function in the design parameters. The terms of such a polynomial are products of the parameters raised to powers. Fractional and negative powers are permitted but the coefficients of the terms are taken to be positive. The problem of concern is the adjustment of the parameters so as to minimize the cost. By use of the classical inequality to the effect that the arithmetic mean exceeds the geometric mean it is found that the cost function exceeds a certain function termed the dual. Moreover it is shown that the maximum of the dual function gives the minimum cost. This relation furnishes a simple method of estimating the minimum cost.

Suggested Citation

  • R. J. Duffin, 1962. "Cost Minimization Problems Treated by Geometric Means," Operations Research, INFORMS, vol. 10(5), pages 668-675, October.
    • Handle: RePEc:inm:oropre:v:10:y:1962:i:5:p:668-675
    DOI: 10.1287/opre.10.5.668
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    Cited by:

    1. Lu, Yao-Chi, 1970. "Geometric Programming: A Tool in Agricultural Economics Analysis," WAEA/ WFEA Conference Archive (1929-1995) 323632, Western Agricultural Economics Association.
    2. Elmor L. Peterson, 1972. "Generalization and Symmetrization of Duality in Geometric Programming," Discussion Papers 19, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. Vedran Kojić & Zrinka Lukač, 2018. "An alternative approach to solving cost minimization problem with Cobb–Douglas technology," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 26(3), pages 629-643, September.

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