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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; [email protected], [email protected]
Andrea Ellero
Affiliation:
Dipartimento di Matematica Applicata, Università Ca'Foscari di Venezia, Dorsoduro 3825/E, 30123 Venezia, Italy; [email protected],[email protected]
Elena Moretti
Affiliation:
Dipartimento di Matematica Applicata, Università Ca'Foscari di Venezia, Dorsoduro 3825/E, 30123 Venezia, Italy; [email protected],[email protected]
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Abstract

We consider a firmthat sells seasonal goods. The firm seeks to reach a fixed levelof goodwill at the end of the selling period, with the minimumtotal expenditure in promotional activities. We consider thelinear optimal control problem faced by the firm which can onlycontrol the communication expenditure rate; communication isperformed by means of advertising and sales promotion. Goodwilland sales levels are considered as state variables andword-of-mouth effect and saturation aversion are taken intoaccount. The optimal control problem is addressed by means of theclassical Pontryagin Maximum Principle and the solution can beeasily found solving, in some cases numerically, a system of twonon linear equations. Moreover, a parametric analysis is performedto understand how the total expenditure in communication shouldbe 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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