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/
, and , Pricing and advertising of private and national brands in a dynamic marketing channel. J. Optim. Theor. Appl. 137 (2008) 465–483. | DOI | Zbl
H. Arslan and S. Kachani, Dynamic pricing under consumer reference-price effects. Wiley, EORMS (2011).
and , Looking for loss aversion in scanner panel data: the confounding effect of price response heterogeneity. Marketing Sci. 19 (2000) 185–200. | DOI
, and , Could myopic pricing be a strategic choice in marketing channels? A game theoretic analysis. J. Econ. Dyn. Control. 33 (2009) 1699–1718. | DOI | Zbl
, , and , A comparative analysis of reference price models. J. Consumer Res. 24 (1997) 202–214. | DOI
, and , Minimization of communication expenditure for seasonal products. RAIRO-Oper. Res. 36 (2002) 109–127. | DOI | Numdam | Zbl
and , Monopolistic competition and optimum product diversity. Amer. Econ. Rev. 67 (1977) 297–308.
and , Advertising and production of a seasonal good for a heterogeneous market. 4OR-Q. J. Oper. Res. 8 (2010) 141–153. | DOI | Zbl
, and , Explicit solutions of optimization models and differential games with nonsmooth (asymmetric) reference-price effect. Oper. Res. 51 (2003) 721–734. | DOI | Zbl
, and , Optimal price promotions in the presence of asymmetric reference-price effects. Manag. Decis. Econ. 28 (2007) 569–577. | DOI
, Signaling quality: dynamic price-advertising model. J. Optim. Theor. Appl. 143 (2009) 479–496. | DOI | Zbl
, and , On controlled linear diffusions with delay in a model of optimal advertising under uncertainty with memory effects. J. Optim. Theor. Appl. 142 (2009) 291–321. | DOI | Zbl
, The impact of reference price effects on the profitability of price promotions. Marketing Sci. 14 (1995) 82–104. | DOI
and , Advertising events in a competitive framework. J. Optim. Theor. Appl. 146 (2010) 375–385. | DOI | Zbl
H. Helson, Adaptation-level Theory. Harper and Row Publishers Inc. New York (1964).
, and , Recent developments in dynamic advertising research. Eur. J. Oper. Res. 220 (2012) 591–609. | DOI | Zbl
and , To influence or not to influence: external reference price strategies in pay-what-you-want pricing. J. Bus. Res. 66 (2013) 275–281. | DOI
, and , Cooperative advertising in a marketing channel. J. Optim. Theor. Appl. 110 (2001) 145–158. | DOI | Zbl
, and , Retail promotions with negative brand image effects: Is cooperation possible? Eur. J. Oper. Res. 150 (2003) 395–405. | DOI | Zbl
and , Prospect theory: an analysis of decision under risk. Econometrica 47 (1979) 263-291. | DOI | Zbl
and , A dynamic model for advertising and pricing competition between national and store brands. Eur. J. Oper. Res. 193 (2009) 451–467. | DOI | Zbl
and , The impact of external reference price on consumer price expectations. J. Retail. 79 (2003) 223–236. | DOI
and , A dynamic model of reference price and expected quality. Marketing Lett. 7 (1996) 41–52. | DOI
and , Reference effects of price and promotion on brand choice behavior. J. Marketing Res. 26 (1989) 299–310. | DOI
, and , Dual role of price and myopia in a marketing channel. Eur. J. Oper. Res. 219 (2012) 284–295. | DOI | Zbl
and , Price coordination in distribution channels: A dynamic perspective [J]. Eur. J. Oper. Res. 240 (2015) 401–414. | DOI | Zbl
and , An empirical analysis of internal and external reference prices using scanner data. J. Consumer Res. 19 (1992) 62–70. | DOI
, and , Reference price research: review and propositions. J. Marketing 69 (2005) 84–102. | DOI
and , Dynamic pricing with loss averse consumers and peak-end anchoring. Oper. Res. 59 (2011) 1361–1368. | DOI | Zbl
and , Dynamic pricing strategies with reference effects. Oper. Res. 55 (2007) 413–429. | DOI | Zbl
, Incorporating reference price effects into a theory of consumer choice. Marketing Sci. 11 (1992) 287–309. | DOI
, Why are consumers less loss averse in internal than external reference prices? J. Retail. 89 (2013) 62–71. | DOI
S.P. Sethi and G.L. Thompson, optimal control theory: Applications to management science and economics. Kluwer, Dordrecht, Netherlands (2000). | Zbl
and , Advertising strategies in a franchise system. Eur. J. Oper. Res. 198 (2009) 655–665. | DOI | Zbl
, Coordinating pricing and inventory decisions under reference price effects. Int. J. Manuf. Technol. Manage. 13 (2008) 78–94. | DOI
, , and , Supply chain coordination through cooperative advertising with reference price effect. Omega-Int. J. Manage. S. 41 (2013) 345–353. | DOI
, and , Strategic pricing with reference effects in a competitive supply chain. Omega-Int. J. Manage. S. 44 (2014) 126–135. | DOI
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