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Zh. Vychisl. Mat. Mat. Fiz., 2015, Volume 55, Number 4, Pages 704–729 (Mi zvmmf10196)  

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

Abstract: 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.

Key words: production model, Bellman equation, working capital deficit, ergodicity, firm market value assessment, stochastic process.

DOI: https://doi.org/10.7868/S0044466915040110

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English version:
Computational Mathematics and Mathematical Physics, 2015, 55:4, 699–723

Bibliographic databases:

UDC: 519.677
MSC: Primary 90B30; Secondary 60H30, 91B38, 91B42
Received: 10.04.2014
Revised: 12.11.2014

Citation: 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

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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  crossref  mathscinet  zmath  isi
    2. 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  crossref  isi  scopus
    3. 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  crossref  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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