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Zh. Vychisl. Mat. Mat. Fiz., 2014, Volume 54, Number 9, Pages 1465–1496 (Mi zvmmf10088)  

This article is cited in 4 scientific papers (total in 4 papers)

Study of the Bellman equation in a production model with unstable demand

N. K. Obrosovaa, A. A. Shananinb

a Dorodnicyn Computing Center, 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 the urgency of analyzing well-known problems of functioning low competitive macroeconomic structures. The original formulation of the task represents an infinite-horizon optimal control problem. As a result, the model is formalized in the form of a Bellman equation. It is proved that the corresponding Bellman operator is a contraction and has a unique fixed point in the chosen class of functions. A closed-form solution of the Bellman equation is found using the method of steps. The influence of the credit interest rate on the firm market value assessment is analyzed by applying the developed model.

Key words: production model, optimal control, Bellman equation, contraction mapping, working capital deficit.

DOI: https://doi.org/10.7868/S0044466914090105

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English version:
Computational Mathematics and Mathematical Physics, 2014, 54:9, 1411–1440

Bibliographic databases:

UDC: 519.626
Received: 03.04.2013
Revised: 24.03.2014

Citation: N. K. Obrosova, A. A. Shananin, “Study of the Bellman equation in a production model with unstable demand”, Zh. Vychisl. Mat. Mat. Fiz., 54:9 (2014), 1465–1496; Comput. Math. Math. Phys., 54:9 (2014), 1411–1440

Citation in format AMSBIB
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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. 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”, Comput. Math. Math. Phys., 55:4 (2015), 699–723  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. 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  scopus
    3. 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
    4. 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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