A fractional optimal control problem for maximizing advertising efficiency
AbstractWe 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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Bibliographic InfoPaper provided by Department of Applied Mathematics, Università Ca' Foscari Venezia in its series Working Papers with number 158.
Length: 17 pages
Date of creation: Nov 2007
Date of revision:
Find related papers by 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 - - Marketing and Advertising - - - Advertising
This paper has been announced in the following NEP Reports:
- NEP-ALL-2007-11-24 (All new papers)
- NEP-MIC-2007-11-24 (Microeconomics)
- NEP-MKT-2007-11-24 (Marketing)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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, vol. 4(2), pages 301-318, December.
- 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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