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
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.
production model, optimal control, Bellman equation, contraction mapping, working capital deficit.
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Computational Mathematics and Mathematical Physics, 2014, 54:9, 1411–1440
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
\by N.~K.~Obrosova, A.~A.~Shananin
\paper Study of the Bellman equation in a production model with unstable demand
\jour Zh. Vychisl. Mat. Mat. Fiz.
\jour Comput. Math. Math. Phys.
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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
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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