Minimization of communication expenditure for seasonal products
RAIRO - Operations Research - Recherche Opérationnelle, Tome 36 (2002) no. 2, pp. 109-127.

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.

DOI : 10.1051/ro:2002012
Mots-clés : optimal control, advertising, sales promotions, seasonal products 
@article{RO_2002__36_2_109_0,
     author = {Bykadorov, Igor and Ellero, Andrea and Moretti, Elena},
     title = {Minimization of communication expenditure for seasonal products},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {109--127},
     publisher = {EDP-Sciences},
     volume = {36},
     number = {2},
     year = {2002},
     doi = {10.1051/ro:2002012},
     mrnumber = {1957983},
     zbl = {1062.90022},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ro:2002012/}
}
TY  - JOUR
AU  - Bykadorov, Igor
AU  - Ellero, Andrea
AU  - Moretti, Elena
TI  - Minimization of communication expenditure for seasonal products
JO  - RAIRO - Operations Research - Recherche Opérationnelle
PY  - 2002
SP  - 109
EP  - 127
VL  - 36
IS  - 2
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/ro:2002012/
DO  - 10.1051/ro:2002012
LA  - en
ID  - RO_2002__36_2_109_0
ER  - 
%0 Journal Article
%A Bykadorov, Igor
%A Ellero, Andrea
%A Moretti, Elena
%T Minimization of communication expenditure for seasonal products
%J RAIRO - Operations Research - Recherche Opérationnelle
%D 2002
%P 109-127
%V 36
%N 2
%I EDP-Sciences
%U http://www.numdam.org/articles/10.1051/ro:2002012/
%R 10.1051/ro:2002012
%G en
%F RO_2002__36_2_109_0
Bykadorov, Igor; Ellero, Andrea; Moretti, Elena. Minimization of communication expenditure for seasonal products. RAIRO - Operations Research - Recherche Opérationnelle, Tome 36 (2002) no. 2, pp. 109-127. doi : 10.1051/ro:2002012. http://www.numdam.org/articles/10.1051/ro:2002012/

[1] M.M. Abraham and L.M. Lodish, Fact-Based Strategies for Managing Advertising and Promotion Dollars: Lessons from Single Source Data, Working Paper #89-006. Marketing Department, The Wharton School of the University of Pennsylvania (1989).

[2] A. Buratto and D. Favaretto, Optimal communication mix to maximize brand image, Rapporto No. 95/2001. Dipartimento di Matematica Applicata, Università di Venezia (2001).

[3] D. Favaretto and B. Viscolani, A single production and advertising control problem with bounded final goodwill. J. Inform. Optim. Sci. 21 (2000) 337-357. | MR | Zbl

[4] G. Feichtinger, R.F. Hartl and S.P. Sethi, Dynamic optimal control models in advertising: Recent developments. Management Sci. 40 (1994) 195-226. | Zbl

[5] S. Funari and B. Viscolani, Advertising and congestion management for a museum temporary exhibition. Central Eur. J. Oper. Res. (to appear). | MR | Zbl

[6] G.L. Lilien, P. Kotler and K.S. Moorthy, Marketing models. Prentice Hall Int., Englewood Cliffs (1992).

[7] J.D.C. Little, Aggregate advertising models: The state of the art. Oper. Res. 27 (1979) 629-667. | Zbl

[8] P.A. Naik, M.K. Mantrala and A.G. Sawyer, Planning media schedules in the presence of dynamic advertising quality. Marketing Sci. 17 (1998) 214-235.

[9] M. Nerlove and K.-J. Arrow, Optimal advertising policy under dynamic conditions. Economica 29 (1962) 129-142.

[10] L.S. Pontryagin, V.G. Boltyanskii, R.V. Gamkrelidze and E.F. Mishchenko, The Matematical Theory of Optimal Processes. Pergamon Press, London (1964). | MR | Zbl

[11] A. Seierstad and K. Sydsaeter, Optimal Control Theory with Economic Applications. North-Holland, Amsterdam (1987). | Zbl

[12] K. Spremann, The signaling of quality by reputation, in Optimal Control Theory and Economic Analysis 2, edited by G. Feichtinger. North-Holland, Amsterdam (1985) 235-252.

[13] M.L. Vidale and H.B. Wolfe, An operations research study for sales response to advertising. Oper. Res. 5 (1957) 370-381. | MR

Cité par Sources :