This paper develops an advertising model in which goodwill affected by advertising effort has a positive effect on reference price and market demand. In a finite planning horizon, the optimal advertising strategy is provided by solving the optimization problem on the basis of Pontryagin’s maximum principle, then the optimal sales price is obtained through one time pricing strategy. Furthermore, we extend this problem to an infinite planning horizon and present the corresponding optimal strategies. In addition, the relationships between system parameters and optimal solutions are analyzed. Numerical examples are employed to illustrate the effectiveness of the theoretical results, and to assess the sensitivity analysis of system parameters on the optimal strategies.
Accepté le :
DOI : 10.1051/ro/2014063
Mots-clés : Advertising, reference price, Goodwill, maximum principle
@article{RO_2015__49_4_669_0,
author = {Zhang, Qiao and Zhang, Jianxiong and Tang, Wansheng},
title = {A dynamic advertising model with reference price effect},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {669--688},
publisher = {EDP-Sciences},
volume = {49},
number = {4},
year = {2015},
doi = {10.1051/ro/2014063},
zbl = {1327.90087},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ro/2014063/}
}
TY - JOUR AU - Zhang, Qiao AU - Zhang, Jianxiong AU - Tang, Wansheng TI - A dynamic advertising model with reference price effect JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2015 SP - 669 EP - 688 VL - 49 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ro/2014063/ DO - 10.1051/ro/2014063 LA - en ID - RO_2015__49_4_669_0 ER -
%0 Journal Article %A Zhang, Qiao %A Zhang, Jianxiong %A Tang, Wansheng %T A dynamic advertising model with reference price effect %J RAIRO - Operations Research - Recherche Opérationnelle %D 2015 %P 669-688 %V 49 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ro/2014063/ %R 10.1051/ro/2014063 %G en %F RO_2015__49_4_669_0
Zhang, Qiao; Zhang, Jianxiong; Tang, Wansheng. A dynamic advertising model with reference price effect. RAIRO - Operations Research - Recherche Opérationnelle, Tome 49 (2015) no. 4, pp. 669-688. doi : 10.1051/ro/2014063. http://www.numdam.org/articles/10.1051/ro/2014063/
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