Abstract
The problem of optimization of the composition of a production association of diverse enterprises is considered. The participating enterprises in the association model can be represented by relations of the input-output balance. Decomposition methods are used to construct models, describing the operation of such a system in the market environment for various methods of its regulation and to find conditions of asymptotic stability for the equilibrium. It is shown that this equilibrium coincides with the optimal solution to the global problem of the association, depending on the properties of the association balance matrix, the equilibrium can be inflationary rather than economical, when the production volume and income diminish to zero for rather high prices.
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References
V. I. Tsurkov, Decomposition in Large-Scale Problems (Nauka, Moscow, 1981) [in Russian].
V. S. Nemchinov, “A Model of an Economical Region,” in Application of Mathematics in Economical Investigations Vol. 2 (Sotsekgiz, Moscow, 1961) [in Russian].
Yu. I. Chernyak, “Unity of Production Planning, Supply, and Financing in a System of Matrix Models,” in Application of Mathematics in Economical Investigations Vol.3 (Mysl’, Moscow, 1965) [in Russian].
N. V. Makhrov, “A Method of Input-Output Balance—The Ground of a System of Low-Level Plans,” in Application of Mathematics in Economical Investigations Vol. 3 (Mysl’, Moscow, 1965) [in Russian].
N. I. Voloshin, “A System of Matrix Models of Infactory Planning,” in Application of Mathematics in Economical Investigations Vol.3 (Mysl’, Moscow, 1965) [in Russian].
V. Leont’ev, Economical Essay (Politizdat, Moscow, 1990) [in Russian].
D. Gale, “Linear inequalities and Related Problems,” in The Closed Linear Model of Production, Linear Inequalities and Related Systems, Ed. by H. W. Kuhn and A. W. Tucker (Princeton Univ. Press, Princeton 1956; Inostrannaya Literatura, Moscow, 1959).
R. T. Rockafeller, Convex Analysis (Princeton University Press, Princeton, 1970; Mir, Moscow, 1973).
D. Gale, The Theory of Linear Economic Models (McGrawHill, New York, 1960; Inostrannaya Literatura, Moscow, 1963).
P. A. Samuel’son, Foundations of Economic Analysis (Harvard Univ. Press, Cambridge, 1948; Progress, Moscow, 1964).
V. G. Mednitskii, Special Methods of Solving Optimization Problems (Nauka, Moscow, 1978) [in Russian].
V. G. Mednitskii and Yu. V. Mednitskii, “Application of the Decomposition Method to the Calculation of Extremal States of Production Systems with a Multibranch Structure of Production Output That Are Consistent with Balanced Growth Conditions,” Izv. Ross. Akad. Nauk, Teor. Sist. Upr., No. 1, (2003) [Comp. Syst. Sci. 42 (1), 136–144 (2003)].
V. G. Mednitskii and Yu. V. Mednitsii, “Dynamics Analysis in Models of Production Systems,” Izv. Ross. Akad. Nauk, Teor. Sist. Upr., No. 6, (2003) [Comp. Syst. Sci. 42 (6), 957–965 (2003)].
D. B. Yudin and E. G. Gol’shtein, Problems and Methods of Linear Programming (Sovetskoe Radio, Moscow, 1961) [in Russian].
H. Nikaido, Convex Structures and Economic Theory (Academic, New York, 1968; Mir, Moscow, 1972).
D. R. Merkin, Introduction to the Motion Stability Theory (Nauka, Moscow, 1978) [in Russian].
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Original Russian Text © V.G. Mednitskii, Yu.V. Mednitskii, V.Yu. Leonov, 2009, published in Izvestiya Akademii Nauk. Teoriya i Sistemy Upravleniya, 2009, No. 5, pp. 156–168.
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Mednitskii, V.G., Mednitskii, Y.V. & Leonov, V.Y. Application of decomposition methods in optimization. J. Comput. Syst. Sci. Int. 48, 827–838 (2009). https://doi.org/10.1134/S1064230709050165
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DOI: https://doi.org/10.1134/S1064230709050165