Abstract
We bring some concepts from market segmentation, which is a fundamental topic of marketing theory and practice, into the statement of an advertising and production problem for a seasonal product with Nerlove–Arrow’s linear goodwill dynamics. We consider two kinds of situations. In the first one, the advertising process can reach selectively each segment. In the second one, one advertising medium is available which has a known effectiveness spectrum for a non-trivial set of segments. In both cases we solve, using the Pontryagin’s Maximum Principle conditions, the optimal control problems in which goodwill productivity of advertising is concave and good production cost is convex. Two special cases are discussed in detail.
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References
Buratto A, Grosset L, Viscolani B (2006a) Advertising a new product in a segmented market. Eur J Oper Res 175: 1262–1267
Buratto A, Grosset L, Viscolani B (2006b) Advertising channel selection in a segmented market. Automatica 42: 1343–1347
Favaretto D, Mazzega P, Mezzaroba A, Viscolani B (1996) Optimal control of advertising and production of a seasonal product with nondifferentiable demand. Dyn Control 6: 91–104
Favaretto D, Viscolani B (1997) Determining optimal production and advertising policies for a seasonal product. Optimization 42: 359–378
Favaretto D, Viscolani B (1999) A multiperiod production and advertising problem for a seasonal product. Ann Oper Res 88: 31–45
Favaretto D, Viscolani B (2004) A general model for the marketing of seasonal products. J Interdiscipl Math 7(3): 349–366
Feichtinger G, Hartl RF, Sethi SP (1994) Dynamic optimal control models in advertising: recent developments. Manage Sci 40(2): 195–226
Grosset L, Viscolani B (2008) Advertising in a segmented market: comparison of media choices. IMA J Manage Math 19: 219–226
Jørgensen S (1982) A differential games solution to a logarithmic advertising model. J Oper Res Soc 33: 425–432
Jørgensen S, Kort PM, Zaccour G (2006) Advertising an event. Automatica 42(8): 1349–1355
Jørgensen S, Taboubi S, Zaccour G (2001) Cooperative advertising in a marketing channel. J Optim Theory Appl 110(1): 145–158
Jørgensen S, Zaccour G (2004) Differential games in marketing. Kluwer, Boston
Kotler P (2003) Marketing management, 11th edn. Prentice-Hall, Upper Saddle River
Kotler P, Trias de Bes F (2003) Lateral marketing: new techniques for finding breakthrough ideas. Wiley, Hoboken
Naik PA, Raman K (2003) Understanding the impact of synergy on multimedia communications. J Market Res 40(4): 375–388
Naik PA, Raman K, Winer RS (2005) Planning marketing-mix strategies in the presence of interactions. Market Sci 24(1): 25–34
Nerlove M, Arrow KJ (1962) Optimal advertising policy under dynamic conditions. Economica 29(2): 129–142
Seierstad A, Sydsaeter K (1987) Optimal control theory with economic applications. North-Holland, Amsterdam
Sethi SP (1975) Optimal control of a logarithmic advertising model. Oper Res Q 26: 317–319
Weber TA (2005) Infinite-horizon optimal advertising in a market for durable goods. Optim Control Appl Methods 26(6): 307–336
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The authors were supported by the Italian Ministry of University and Research, the University of Padua and the University of Venice.
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Favaretto, D., Viscolani, B. Advertising and production of a seasonal good for a heterogeneous market. 4OR-Q J Oper Res 8, 141–153 (2010). https://doi.org/10.1007/s10288-009-0103-2
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DOI: https://doi.org/10.1007/s10288-009-0103-2