IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v229y2013i2p433-443.html
   My bibliography  Save this article

Optimal advertising and pricing in a class of general new-product adoption models

Author

Listed:
  • Helmes, Kurt
  • Schlosser, Rainer
  • Weber, Martin

Abstract

In [21], Sethi et al. introduced a particular new-product adoption model. They determine optimal advertising and pricing policies of an associated deterministic infinite horizon discounted control problem. Their analysis is based on the fact that the corresponding Hamilton–Jacobi–Bellman (HJB) equation is an ordinary non-linear differential equation which has an analytical solution. In this paper, generalizations of their model are considered. We take arbitrary adoption and saturation effects into account, and solve finite and infinite horizon discounted variations of associated control problems. If the horizon is finite, the HJB-equation is a 1st order non-linear partial differential equation with specific boundary conditions. For a fairly general class of models we show that these partial differential equations have analytical solutions. Explicit formulas of the value function and the optimal policies are derived. The controlled Bass model with isoelastic demand is a special example of the class of controlled adoption models to be examined and will be analyzed in some detail.

Suggested Citation

  • Helmes, Kurt & Schlosser, Rainer & Weber, Martin, 2013. "Optimal advertising and pricing in a class of general new-product adoption models," European Journal of Operational Research, Elsevier, vol. 229(2), pages 433-443.
    • Handle: RePEc:eee:ejores:v:229:y:2013:i:2:p:433-443
    DOI: 10.1016/j.ejor.2013.02.035
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221713001689
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2013.02.035?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Trichy V. Krishnan & Dipak C. Jain, 2006. "Optimal Dynamic Advertising Policy for New Products," Management Science, INFORMS, vol. 52(12), pages 1957-1969, December.
    2. Horsky, Dan, 1980. "Comments on "The Relationship between Diffusion Rates, Experience Curves, and Demand Elasticities for Consumer Durable Technological Innovations."," The Journal of Business, University of Chicago Press, vol. 53(3), pages 75-78, July.
    3. Frank M. Bass & Trichy V. Krishnan & Dipak C. Jain, 1994. "Why the Bass Model Fits without Decision Variables," Marketing Science, INFORMS, vol. 13(3), pages 203-223.
    4. Bernard Pras & Gilles Laurent & Gary L. Lilien, 1994. "Research Traditions in Marketing," Post-Print halshs-00150675, HAL.
    5. Huang, Jian & Leng, Mingming & Liang, Liping, 2012. "Recent developments in dynamic advertising research," European Journal of Operational Research, Elsevier, vol. 220(3), pages 591-609.
    6. repec:dau:papers:123456789/3445 is not listed on IDEAS
    7. Kumar, Subodha & Sethi, Suresh P., 2009. "Dynamic pricing and advertising for web content providers," European Journal of Operational Research, Elsevier, vol. 197(3), pages 924-944, September.
    8. Bass, Frank M, 1980. "The Relationship between Diffusion Rates, Experience Curves, and Demand Elasticities for Consumer Durable Technological Innovations," The Journal of Business, University of Chicago Press, vol. 53(3), pages 51-67, July.
    9. S. P. Sethi & A. Prasad & X. He, 2008. "Optimal Advertising and Pricing in a New-Product Adoption Model," Journal of Optimization Theory and Applications, Springer, vol. 139(2), pages 351-360, November.
    10. Russell, Thomas, 1980. "Comments on "The Relationship between Diffusion Rates, Experience Curves, and Demand Elasticities for Consumer Durable Technological Innovations."," The Journal of Business, University of Chicago Press, vol. 53(3), pages 69-73, July.
    11. Fruchter, Gila E. & Van den Bulte, Christophe, 2011. "Why the Generalized Bass Model leads to odd optimal advertising policies," International Journal of Research in Marketing, Elsevier, vol. 28(3), pages 218-230.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Régis Chenavaz & Corina Paraschiv & Gabriel Turinici, 2017. "Dynamic Pricing of New Products in Competitive Markets: A Mean-Field Game Approach," Working Papers hal-01592958, HAL.
    2. Schlosser, Rainer & Chenavaz, Régis Y. & Dimitrov, Stanko, 2021. "Circular economy: Joint dynamic pricing and recycling investments," International Journal of Production Economics, Elsevier, vol. 236(C).
    3. Ghobadi, Somayeh Najafi- & Bagherinejad, Jafar & Taleizadeh, Ata Allah, 2021. "A two-generation new product model by considering forward-looking customers: Dynamic pricing and advertising optimization," Journal of Retailing and Consumer Services, Elsevier, vol. 63(C).
    4. Karray, Salma & Martín-Herrán, Guiomar, 2022. "The impact of a store brand introduction in a supply chain with competing manufacturers: The strategic role of pricing and advertising decision timing," International Journal of Production Economics, Elsevier, vol. 244(C).
    5. Chenavaz, Régis Y. & Eynan, Amit, 2021. "Advertising, goodwill, and the Veblen effect," European Journal of Operational Research, Elsevier, vol. 289(2), pages 676-682.
    6. Régis Chenavaz & Corina Paraschiv & Gabriel Turinici, 2021. "Dynamic Pricing of New Products in Competitive Markets: A Mean-Field Game Approach," Dynamic Games and Applications, Springer, vol. 11(3), pages 463-490, September.
    7. Chenavaz, Régis Y. & Feichtinger, Gustav & Hartl, Richard F. & Kort, Peter M., 2020. "Modeling the impact of product quality on dynamic pricing and advertising policies," European Journal of Operational Research, Elsevier, vol. 284(3), pages 990-1001.
    8. Lotfi, Ali & Naoum-Sawaya, Joe & Lotfi, Aslan & Jiang, Zhengrui, 2024. "To Skim or not to Skim: Studying the Optimal Pricing Strategy for Technology Products," Omega, Elsevier, vol. 127(C).
    9. Schlosser, Rainer, 2015. "Dynamic pricing and advertising of perishable products with inventory holding costs," Journal of Economic Dynamics and Control, Elsevier, vol. 57(C), pages 163-181.
    10. Fuxiao Lu & Guowei Liu & Jianxiong Zhang & Wansheng Tang, 2016. "Benefits of partial myopia in a durable product supply chain considering pricing and advertising," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(10), pages 1309-1324, October.
    11. Régis Chenavaz & Sajjad M. Jasimuddin, 2017. "An analytical model of the relationship between product quality and advertising," Post-Print hal-01685892, HAL.
    12. Kurt Helmes & Rainer Schlosser, 2015. "Oligopoly Pricing and Advertising in Isoelastic Adoption Models," Dynamic Games and Applications, Springer, vol. 5(3), pages 334-360, September.
    13. Helmes, Kurt L. & Schlosser, Rainer, 2013. "Dynamic advertising and pricing with constant demand elasticities," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2814-2832.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Régis Chenavaz & Sajjad M. Jasimuddin, 2017. "An analytical model of the relationship between product quality and advertising," Post-Print hal-01685892, HAL.
    2. Meade, Nigel & Islam, Towhidul, 2006. "Modelling and forecasting the diffusion of innovation - A 25-year review," International Journal of Forecasting, Elsevier, vol. 22(3), pages 519-545.
    3. Hariharan, Vijay Ganesh & Talukdar, Debabrata & Kwon, Changhyun, 2015. "Optimal targeting of advertisement for new products with multiple consumer segments," International Journal of Research in Marketing, Elsevier, vol. 32(3), pages 263-271.
    4. Schlosser, Rainer, 2016. "Joint stochastic dynamic pricing and advertising with time-dependent demand," Journal of Economic Dynamics and Control, Elsevier, vol. 73(C), pages 439-452.
    5. Fouad El Ouardighi & Gustav Feichtinger & Gila E. Fruchter, 2018. "Accelerating the diffusion of innovations under mixed word of mouth through marketing–operations interaction," Annals of Operations Research, Springer, vol. 264(1), pages 435-458, May.
    6. Gila E. Fruchter & Ashutosh Prasad & Christophe Van den Bulte, 2022. "Too Popular, Too Fast: Optimal Advertising and Entry Timing in Markets with Peer Influence," Management Science, INFORMS, vol. 68(6), pages 4725-4741, June.
    7. Koray Cosguner & P. B. (Seethu) Seetharaman, 2022. "Dynamic Pricing for New Products Using a Utility-Based Generalization of the Bass Diffusion Model," Management Science, INFORMS, vol. 68(3), pages 1904-1922, March.
    8. Fruchter, Gila E. & Van den Bulte, Christophe, 2011. "Why the Generalized Bass Model leads to odd optimal advertising policies," International Journal of Research in Marketing, Elsevier, vol. 28(3), pages 218-230.
    9. Daekook Kang, 2021. "Box-office forecasting in Korea using search trend data: a modified generalized Bass diffusion model," Electronic Commerce Research, Springer, vol. 21(1), pages 41-72, March.
    10. Vahideh Sadat Abedi & Oded Berman & Fred M. Feinberg & Dmitry Krass, 2022. "Strategic new product media planning under emergent channel substitution and synergy," Production and Operations Management, Production and Operations Management Society, vol. 31(5), pages 2143-2166, May.
    11. Elmar Kiesling & Markus Günther & Christian Stummer & Lea Wakolbinger, 2012. "Agent-based simulation of innovation diffusion: a review," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 20(2), pages 183-230, June.
    12. Frank M. Bass, 2004. "Comments on "A New Product Growth for Model Consumer Durables The Bass Model"," Management Science, INFORMS, vol. 50(12_supple), pages 1833-1840, December.
    13. Yuri Peers & Dennis Fok & Philip Hans Franses, 2012. "Modeling Seasonality in New Product Diffusion," Marketing Science, INFORMS, vol. 31(2), pages 351-364, March.
    14. Rajshree Agarwal & Barry L. Bayus, 2002. "The Market Evolution and Sales Takeoff of Product Innovations," Management Science, INFORMS, vol. 48(8), pages 1024-1041, August.
    15. Peres, Renana & Muller, Eitan & Mahajan, Vijay, 2010. "Innovation diffusion and new product growth models: A critical review and research directions," International Journal of Research in Marketing, Elsevier, vol. 27(2), pages 91-106.
    16. Trichy V. Krishnan & Frank M. Bass & Dipak C. Jain, 1999. "Optimal Pricing Strategy for New Products," Management Science, INFORMS, vol. 45(12), pages 1650-1663, December.
    17. Peters, Kay & Albers, Sönke & Kumar, V., 2008. "Is there more to international Diffusion than Culture? An investigation on the Role of Marketing and Industry Variables," EconStor Preprints 27678, ZBW - Leibniz Information Centre for Economics.
    18. Guseo, Renato & Schuster, Reinhard, 2021. "Modelling dynamic market potential: Identifying hidden automata networks in the diffusion of pharmaceutical drugs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
    19. Abedi, Vahideh Sadat, 2019. "Compartmental diffusion modeling: Describing customer heterogeneity & communication network to support decisions for new product introductions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    20. Krishnamoorthy, Anand & Prasad, Ashutosh & Sethi, Suresh P., 2010. "Optimal pricing and advertising in a durable-good duopoly," European Journal of Operational Research, Elsevier, vol. 200(2), pages 486-497, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:229:y:2013:i:2:p:433-443. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.