This article is cited in 3 scientific papers (total in 3 papers)
Production model in the conditions of unstable demand taking into account the influence of trading infrastructure: Ergodicity and its application
N. K. Obrosovaa, A. A. Shananinb
a Dorodnicyn Computing Center, Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia
b Moscow Institute of Physics and Technology (Technical University), Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141700, Russia
A production model with allowance for a working capital deficit and a restricted maximum possible sales volume is proposed and analyzed. The study is motivated by an attempt to analyze the problems of functioning of low competitive macroeconomic structures. The model is formalized in the form of a Bellman equation, for which a closed-form solution is found. The stochastic process of product stock variations is proved to be ergodic and its final probability distribution is found. Expressions for the average production load and the average product stock are found by analyzing the stochastic process. A system of model equations relating the model variables to official statistical parameters is derived. The model is identified using data from the Fiat and KAMAZ companies. The influence of the credit interest rate on the firm market value assessment and the production load level are analyzed using comparative statics methods.
production model, Bellman equation, working capital deficit, ergodicity, firm market value assessment, stochastic process.
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Computational Mathematics and Mathematical Physics, 2015, 55:4, 699–723
MSC: Primary 90B30; Secondary 60H30, 91B38, 91B42
N. K. Obrosova, A. A. Shananin, “Production model in the conditions of unstable demand taking into account the influence of trading infrastructure: Ergodicity and its application”, Zh. Vychisl. Mat. Mat. Fiz., 55:4 (2015), 704–729; Comput. Math. Math. Phys., 55:4 (2015), 699–723
Citation in format AMSBIB
\by N.~K.~Obrosova, A.~A.~Shananin
\paper Production model in the conditions of unstable demand taking into account the influence of trading infrastructure: Ergodicity and its application
\jour Zh. Vychisl. Mat. Mat. Fiz.
\jour Comput. Math. Math. Phys.
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D. A. Alimov, “On the existence and uniqueness of a solution of the Bellman equation in a model of operation of a manufacturing company with regard to the debt load”, Differ. Equ., 54:3 (2018), 392–400
D. A. Alimov, N. K. Obrosova, A. A. Shananin, “Methodology for assessing the value of an enterprise in the depressed sector of economy based on solving of the Bellman equation”, IFAC-PapersOnLine, 51:32 (2018), 788–792
Alimov D.A., Obrosova N.K., Shananin A.A., “Enterprise Debts Analysis Using a Mathematical Model of Production, Considering the Deficit of Current Assets”, Lobachevskii J. Math., 40:4, SI (2019), 385–399
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