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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2014, Volume 54, Number 9, Pages 1465–1496
DOI: https://doi.org/10.7868/S0044466914090105 (Mi zvmmf10088) 		 
This article is cited in 10 scientific papers (total in 10 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
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DOI: https://doi.org/10.7868/S0044466914090105
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.
Received: 03.04.2013
Revised: 24.03.2014
English version:
Computational Mathematics and Mathematical Physics, 2014, Volume 54, Issue 9, Pages 1411–1440
DOI: https://doi.org/10.1134/S0965542514090097
Bibliographic databases:
Document Type: Article
UDC: 519.626
Language: Russian
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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    • This publication is cited in the following 10 articles:
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