Minimization of communication expenditure for seasonal products

Igor Bykadorov; Andrea Ellero; Elena Moretti

RAIRO - Operations Research (2010)

  • Volume: 36, Issue: 2, page 109-127
  • ISSN: 0399-0559

Abstract

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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.

How to cite

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Bykadorov, Igor, Ellero, Andrea, and Moretti, Elena. "Minimization of communication expenditure for seasonal products." RAIRO - Operations Research 36.2 (2010): 109-127. <http://eudml.org/doc/105264>.

@article{Bykadorov2010,
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. },
author = {Bykadorov, Igor, Ellero, Andrea, Moretti, Elena},
journal = {RAIRO - Operations Research},
keywords = {Optimal control; advertising; sales promotions; seasonal products.; optimal control; sales promotions; seasonal products},
language = {eng},
month = {3},
number = {2},
pages = {109-127},
publisher = {EDP Sciences},
title = {Minimization of communication expenditure for seasonal products},
url = {http://eudml.org/doc/105264},
volume = {36},
year = {2010},
}

TY - JOUR
AU - Bykadorov, Igor
AU - Ellero, Andrea
AU - Moretti, Elena
TI - Minimization of communication expenditure for seasonal products
JO - RAIRO - Operations Research
DA - 2010/3//
PB - EDP Sciences
VL - 36
IS - 2
SP - 109
EP - 127
AB - 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.
LA - eng
KW - Optimal control; advertising; sales promotions; seasonal products.; optimal control; sales promotions; seasonal products
UR - http://eudml.org/doc/105264
ER -

References

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  10. L.S. Pontryagin, V.G. Boltyanskii, R.V. Gamkrelidze and E.F. Mishchenko, The Matematical Theory of Optimal Processes. Pergamon Press, London (1964).  
  11. A. Seierstad and K. Sydsaeter, Optimal Control Theory with Economic Applications. North-Holland, Amsterdam (1987).  
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