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Minimization of communication expenditure for seasonal products

Published online by Cambridge University Press:  15 December 2002

Igor Bykadorov ,
Andrea Ellero  and
Elena Moretti
Igor Bykadorov
Affiliation:
Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Science, Acad. Koptyug Prospect 4, Novosibirsk 630090, Russia, and Università Ca'Foscari di Venezia, Italy; bykad@math.nsc.ru, bykadoro@unive.it
Andrea Ellero
Affiliation:
Dipartimento di Matematica Applicata, Università Ca'Foscari di Venezia, Dorsoduro 3825/E, 30123 Venezia, Italy; ellero@unive.it,tomasin@unive.it
Elena Moretti
Affiliation:
Dipartimento di Matematica Applicata, Università Ca'Foscari di Venezia, Dorsoduro 3825/E, 30123 Venezia, Italy; ellero@unive.it,tomasin@unive.it
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Abstract

We consider a firm that sells seasonal goods. The firm seeks to reach a fixed level of goodwill at the end of the selling period, with the minimum total expenditure in promotional activities. We consider the linear optimal control problem faced by the firm which can only control the communication expenditure rate; communication is performed by means of advertising and sales promotion. Goodwill and sales levels are considered as state variables and word-of-mouth effect and saturation aversion are taken into account. The optimal control problem is addressed by means of the classical Pontryagin Maximum Principle and the solution can be easily found solving, in some cases numerically, a system of two non linear equations. Moreover, a parametric analysis is performed to understand how the total expenditure in communication should be divided between advertising and sales promotion.

Keywords

Optimal controladvertisingsales promotionsseasonal products.
Type
Research Article
Information
RAIRO - Operations Research , Volume 36 , Issue 2 , April 2002 , pp. 109 - 127
Copyright
© EDP Sciences, 2002

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