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A fractional optimal control problem for maximizing advertising efficiency


  • 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.

Suggested Citation

  • Igor Bykadorov & Andrea Ellero & Stefania Funari & Elena Moretti, 2007. "A fractional optimal control problem for maximizing advertising efficiency," Working Papers 158, Department of Applied Mathematics, Università Ca' Foscari Venezia.
  • Handle: RePEc:vnm:wpaper:158

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    References listed on IDEAS

    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.
    3. Werner Dinkelbach, 1967. "On Nonlinear Fractional Programming," Management Science, INFORMS, vol. 13(7), pages 492-498, March.
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    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • M37 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Marketing and Advertising - - - Advertising

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