A dynamic advertising model with reference price effect

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.

[1]  Hasan Arslan,et al.  Dynamic Pricing Under Consumer Reference‐Price Effects , 2011 .

[2]  Guiomar Martín-Herrán,et al.  Could myopic pricing be a strategic choice in marketing channels? A game theoretic analysis , 2007 .

[3]  Bruno Viscolani,et al.  Advertising and production of a seasonal good for a heterogeneous market , 2007, 4OR.

[4]  Guiomar Martín-Herrán,et al.  A dynamic model for advertising and pricing competition between national and store brands , 2009, Eur. J. Oper. Res..

[5]  G. Thompson,et al.  Optimal Control Theory: Applications to Management Science and Economics , 2000 .

[6]  A. Dixit,et al.  Monopolistic competition and optimum product diversity , 1977 .

[7]  Andrea Ellero,et al.  Minimization of communication expenditure for seasonal products , 2002, RAIRO Oper. Res..

[8]  Russell S. Winer,et al.  An Empirical Analysis of Internal and External Reference Prices Using Scanner Data , 1992 .

[9]  S. Raj,et al.  Reference Price Research: Review and Propositions , 2005 .

[10]  Annie Peng Cui,et al.  To influence or not to influence: External reference price strategies in pay-what-you-want pricing , 2013 .

[11]  D. Bell,et al.  Looking for Loss Aversion in Scanner Panel Data: The Confounding Effect of Price Response Heterogeneity , 2000 .

[12]  Gadi Fibich,et al.  Explicit Solutions of Optimization Models and Differential Games with Nonsmooth (Asymmetric) Reference-Price Effects , 2003, Oper. Res..

[13]  Zhimin Huang,et al.  Supply chain coordination through cooperative advertising with reference price effect , 2013 .

[14]  O. Lowengart,et al.  Optimal price promotion in the presence of asymmetric reference-price effects , 2007 .

[15]  Gila E. Fruchter,et al.  Signaling Quality: Dynamic Price-Advertising Model , 2009 .

[16]  Jian Huang,et al.  Recent developments in dynamic advertising research , 2012, Eur. J. Oper. Res..

[17]  Lakshman Krishnamurthi,et al.  A comparative analysis of reference price models , 1997 .

[18]  A. Tversky,et al.  Prospect Theory : An Analysis of Decision under Risk Author ( s ) : , 2007 .

[19]  Bruno Viscolani,et al.  Advertising Events in a Competitive Framework , 2010 .

[20]  D. Putler.  Incorporating Reference Price Effects into a Theory of Consumer Choice , 1992 .

[21]  Georges Zaccour,et al.  Production, Manufacturing and Logistics Retail promotions with negative brand image effects: Is cooperation possible? , 2003 .

[22]  L. Liang,et al.  Strategic pricing with reference effects in a competitive supply chain , 2014 .

[23]  Guiomar Martín-Herrán,et al.  Price coordination in distribution channels: A dynamic perspective , 2015, Eur. J. Oper. Res..

[24]  Rutger van Oest,et al.  Why are Consumers Less Loss Averse in Internal than External Reference Prices , 2013 .

[25]  Timothy L. Urban.  Coordinating pricing and inventory decisions under reference price effects , 2008, Int. J. Manuf. Technol. Manag..

[26]  Praveen K. Kopalle,et al.  The impact of external reference price on consumer price expectations , 2003 .

[27]  G. Zaccour,et al.  Pricing and Advertising of Private and National Brands in a Dynamic Marketing Channel , 2008 .

[28]  R. Bucklin,et al.  Reference Effects of Price and Promotion on Brand Choice Behavior , 1989 .

[29]  Georges Zaccour,et al.  Dual role of price and myopia in a marketing channel , 2012, Eur. J. Oper. Res..

[30]  E. Greenleaf.  The Impact of Reference Price Effects on the Profitability of Price Promotions , 1995 .

[31]  Ioana Popescu,et al.  Dynamic Pricing with Loss Averse Consumers and Peak-End Anchoring , 2010, Oper. Res..

[32]  Pradeep Chintagunta,et al.  Advertising strategies in a franchise system , 2009, Eur. J. Oper. Res..

[33]  R. Winer,et al.  A dynamic model of reference price and expected quality , 1996 .

[34]  G. Zaccour,et al.  Cooperative Advertising in a Marketing Channel , 2000 .

[35]  Ioana Popescu,et al.  Dynamic Pricing Strategies with Reference Effects , 2007, Oper. Res..

[36]  Sergei Savin,et al.  On Controlled Linear Diffusions with Delay in a Model of Optimal Advertising under Uncertainty with Memory Effects , 2007, J. Optimization Theory and Applications.