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IMA Journal of Management Mathematics Advance Access originally published online on October 4, 2007
IMA Journal of Management Mathematics 2008 19(1):51-62; doi:10.1093/imaman/dpm028
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© The authors 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

An inventory model for stock with advertising sensitive demand

Shib Sankar Sana{dagger}

Department of Mathematics, Bhangar Mahavidyalaya, University of Calcutta, P.O. Bhangar, Pin-743502, 24PGS (South), West Bengal, India

K. S. Chaudhuri{ddagger}

Department of Mathematics, Jadavpur University, Kolkata-700 032, West Bengal, India

{dagger} Corresponding author. Email: shib_sankar{at}yahoo.com

{ddagger} Email: k_s_chaudhuri{at}yahoo.com

The effect of advertising media and sales effort on future demand of merchandize is considered. In an oligopolistic marketing system, it is quite natural to boost sales by using advertising and sales effort to earn more money from a business sector. Determination of demand and costs due to advertising and sales effort is quite difficult. The approach in this paper is to concentrate on investment for the purpose of advertising and increasing sales effort in order to maximize profit. The paper extends an inventory model over finite and infinite time horizons where demand is influenced by the level of stock, advertising media and sales effort. The associated profit maximization problem is solved by the ‘Euler–Lagrange method’. The model is illustrated with a numerical example.

Keywords: stock-dependent demand; inventory; inflation


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