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Journal of Computational and Engineering Mathematics, 2015, Volume 2, Issue 3, Pages 13–24
DOI: https://doi.org/10.14529/jcem150302
(Mi jcem17)
 

This article is cited in 2 scientific papers (total in 2 papers)

Computational Mathematics

On a discrete model of optimal advertising

V. M. Adukov, N. V. Adukova, K. N. Kudryavtsev

South Ural State University, Chelyabinsk, Russian Federation
Full-text PDF (472 kB) Citations (2)
References:
Abstract: The continuous models are considered in the most works on optimal advertising. Articles on the discrete-time models are more rare because in this case it is difficult to obtain an explicit solution. In this paper a new discrete model of optimal advertising for a monopolist-seller of a new goods is proposed. In the model, the dynamics is given by a nonlinear difference equation. The non-linearity depends on a parameter $\sigma$, $0<\sigma<1$, i.e. a continuous family of the models is considered. The discrete versions of the Vidale – Wolfe model and the Sethi model are particular cases of this model. The seller's problem is to maximize its profit up to the finite horizon $T$ by the optimal advertising expenditure. This problem is a discrete multistep optimal control problem, where an advertising expenditure is a control variable. For our model the optimal control problem can be solved explicitly. The Bellman method of dynaming programming is used to study the problem. Explicit recurrence relations for the optimal control and the market share up to the step $t$, $t=1,\dots,T$, are obtained under the assumption that the difference equation of the model has a solution. Sufficient conditions on the parameters of the model, which ensure the existence of a solution, are found. The proposed algorithm is implemented as the procedure OptimalAdvertising in the package Maple. Numerical experiments with the procedure were carried out.
Keywords: advertising expenditures, optimal control, discrete model, dynamical programming.
Received: 18.08.2015
Bibliographic databases:
Document Type: Article
UDC: 519.863
MSC: 90B60
Language: English
Citation: V. M. Adukov, N. V. Adukova, K. N. Kudryavtsev, “On a discrete model of optimal advertising”, J. Comp. Eng. Math., 2:3 (2015), 13–24
Citation in format AMSBIB
\Bibitem{AduAduKud15}
\by V.~M.~Adukov, N.~V.~Adukova, K.~N.~Kudryavtsev
\paper On a discrete model of optimal advertising
\jour J. Comp. Eng. Math.
\yr 2015
\vol 2
\issue 3
\pages 13--24
\mathnet{http://mi.mathnet.ru/jcem17}
\crossref{https://doi.org/10.14529/jcem150302}
\elib{https://elibrary.ru/item.asp?id=24505443}
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  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Journal of Computational and Engineering Mathematics
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    Full-text PDF :120
    References:86
     
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