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A fractional optimal control problem for maximizing advertising efficiency

Listed author(s):
  • Igor Bykadorov

    (Sobolev Institute of Mathematics, Novosibirsk)

  • Andrea Ellero


    (Department of Applied Mathematics, University of Venice)

  • Stefania Funari


    (Department of Applied Mathematics, University of Venice)

  • Elena Moretti


    (Department of Applied Mathematics, University of Venice)

We propose an optimal control problem to model the dynamics of the communication activity of a firm with the aim of maximizing its efficiency. We assume that the advertising effort undertaken by the firm contributes to increase the firm's goodwill and that the goodwill affects the firm's sales. The aim is to find the advertising policies in order to maximize the firm's efficiency index which is computed as the ratio between "outputs" and "inputs" properly weighted; the outputs are represented by the final level of goodwill and by the sales achieved by the firm during the period considered, whereas the inputs are represented by the costs undertaken by the firm, fixed costs and advertising costs. The problem considered is formulated as a fractional optimal control problem. In order to find the optimal advertising policies we use the Dinkelbach's algorithm for fractional programming.

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File Function: First version, 2007
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Paper provided by Department of Applied Mathematics, Università Ca' Foscari Venezia in its series Working Papers with number 158.

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Length: 17 pages
Date of creation: Nov 2007
Handle: RePEc:vnm:wpaper:158
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  1. D. Favaretto & B. Viscolani, 1996. "Optimal purchase and advertising for a product with immediate sale start," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 4(2), pages 301-318, December.
  2. Gustav Feichtinger & Richard F. Hartl & Suresh P. Sethi, 1994. "Dynamic Optimal Control Models in Advertising: Recent Developments," Management Science, INFORMS, vol. 40(2), pages 195-226, February.
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