IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v137y2008i3d10.1007_s10957-007-9350-6.html
   My bibliography  Save this article

Optimal Distributed Dynamic Advertising

Author

Listed:
  • C. Marinelli

    (Universität Bonn)

  • S. Savin

    (Columbia University)

Abstract

We propose a novel approach to modeling advertising dynamics for a firm operating over a distributed market domain based on controlled partial differential equations of the diffusion type. Using our model, we consider a general type of finite-horizon profit maximization problem in a monopoly setting. By reformulating this profit maximization problem as an optimal control problem in infinite dimensions, we derive sufficient conditions for the existence of its optimal solutions under general profit functions, as well as state and control constraints, and provide a general characterization of the optimal solutions. Sharper, feedback-form characterizations of the optimal solutions are obtained for two variants of the general problem.

Suggested Citation

  • C. Marinelli & S. Savin, 2008. "Optimal Distributed Dynamic Advertising," Journal of Optimization Theory and Applications, Springer, vol. 137(3), pages 569-591, June.
    • Handle: RePEc:spr:joptap:v:137:y:2008:i:3:d:10.1007_s10957-007-9350-6
    DOI: 10.1007/s10957-007-9350-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-007-9350-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-007-9350-6?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. Eric Bradlow & Bart Bronnenberg & Gary Russell & Neeraj Arora & David Bell & Sri Duvvuri & Frankel Hofstede & Catarina Sismeiro & Raphael Thomadsen & Sha Yang, 2005. "Spatial Models in Marketing," Marketing Letters, Springer, vol. 16(3), pages 267-278, December.
    2. Jean-Pierre Dubé & Puneet Manchanda, 2005. "Differences in Dynamic Brand Competition Across Markets: An Empirical Analysis," Marketing Science, INFORMS, vol. 24(1), pages 81-95, September.
    3. Gustav Feichtinger & Richard F. Hartl & Suresh P. Sethi, 1994. "Dynamic Optimal Control Models in Advertising: Recent Developments," Management Science, INFORMS, vol. 40(2), pages 195-226, February.
    4. Bart J. Bronnenberg & Vijay Mahajan, 2001. "Unobserved Retailer Behavior in Multimarket Data: Joint Spatial Dependence in Market Shares and Promotion Variables," Marketing Science, INFORMS, vol. 20(3), pages 284-299, October.
    5. Muller, Eitan, 1983. "Trial/awareness advertising decisions : A control problem with phase diagrams with non-stationary boundaries," Journal of Economic Dynamics and Control, Elsevier, vol. 6(1), pages 333-350, September.
    6. Luca Grosset & Bruno Viscolani, 2004. "Advertising for a new product introduction: A stochastic approach," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 12(1), pages 149-167, June.
    7. Naufel J. Vilcassim & Vrinda Kadiyali & Pradeep K. Chintagunta, 1999. "Investigating Dynamic Multifirm Market Interactions in Price and Advertising," Management Science, INFORMS, vol. 45(4), pages 499-518, April.
    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. Silvia Faggian & Luca Grosset, 2009. "Optimal investment in age-structured goodwill," Working Papers 194, Department of Applied Mathematics, Università Ca' Foscari Venezia.
    2. Giorgio Fabbri & Fausto Gozzi & Andrzej Swiech, 2017. "Stochastic Optimal Control in Infinite Dimensions - Dynamic Programming and HJB Equations," Post-Print hal-01505767, HAL.
    3. Silvia Faggian & Luca Grosset, 2013. "Optimal advertising strategies with age-structured goodwill," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(2), pages 259-284, October.
    4. 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.
    5. Dominika Bogusz & Mariusz Gorajski, 2014. "Optimal Goodwill Model with Consumer Recommendations and Market Segmentation," Lodz Economics Working Papers 1/2014, University of Lodz, Faculty of Economics and Sociology, revised Oct 2014.

    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. Marinelli, Carlo, 2007. "The stochastic goodwill problem," European Journal of Operational Research, Elsevier, vol. 176(1), pages 389-404, January.
    2. Chan, Tat Y. & Narasimhan, Chakravarthi & Yoon, Yeujun, 2017. "Advertising and price competition in a manufacturer-retailer channel," International Journal of Research in Marketing, Elsevier, vol. 34(3), pages 694-716.
    3. 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.
    4. P. Baecke & D. Van Den Poel, 2012. "Including Spatial Interdependence in Customer Acquisition Models: a Cross-Category Comparison," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 12/788, Ghent University, Faculty of Economics and Business Administration.
    5. Sylvia Hristakeva & Julie Holland Mortimer, 2023. "Price Dispersion and Legacy Discounts in the National Television Advertising Market," Marketing Science, INFORMS, vol. 42(6), pages 1162-1183, November.
    6. Awi Federgruen & Ming Hu, 2015. "Multi-Product Price and Assortment Competition," Operations Research, INFORMS, vol. 63(3), pages 572-584, June.
    7. Kamrad, Bardia & Lele, Shreevardhan S. & Siddique, Akhtar & Thomas, Robert J., 2005. "Innovation diffusion uncertainty, advertising and pricing policies," European Journal of Operational Research, Elsevier, vol. 164(3), pages 829-850, August.
    8. Jean-Pierre Dubé & Puneet Manchanda, 2005. "Differences in Dynamic Brand Competition Across Markets: An Empirical Analysis," Marketing Science, INFORMS, vol. 24(1), pages 81-95, September.
    9. Sheng, Li, 2010. "Competing or cooperating to host mega events: A simple model," Economic Modelling, Elsevier, vol. 27(1), pages 375-379, January.
    10. Liu, Zhuping & Duan, Jason A & Mahajan, Vijay, 2020. "Dynamics and peer effects of brand revenue in college sports," International Journal of Research in Marketing, Elsevier, vol. 37(4), pages 756-771.
    11. Awi Federgruen & Ming Hu, 2016. "Technical Note—Sequential Multiproduct Price Competition in Supply Chain Networks," Operations Research, INFORMS, vol. 64(1), pages 135-149, February.
    12. Vincent Nijs & Kanishka Misra & Eric T. Anderson & Karsten Hansen & Lakshman Krishnamurthi, 2010. "Channel Pass-Through of Trade Promotions," Marketing Science, INFORMS, vol. 29(2), pages 250-267, 03-04.
    13. Ouardighi, Fouad El & Tapiero, Charles S., 1998. "Quality and the diffusion of innovations," European Journal of Operational Research, Elsevier, vol. 106(1), pages 31-38, April.
    14. Amr Farahat & Georgia Perakis, 2011. "TECHNICAL NOTE---A Comparison of Bertrand and Cournot Profits in Oligopolies with Differentiated Products," Operations Research, INFORMS, vol. 59(2), pages 507-513, April.
    15. Alessandra Buratto & Luca Grosset, 2006. "A communication mix for an event planning: a linear quadratic approach," 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. 14(3), pages 247-259, September.
    16. Karray Salma & Martín-Herrán Guiomar, 2008. "Investigating the Relationship Between Advertising and Pricing in a Channel with Private Label Offering: A Theoretic Model," Review of Marketing Science, De Gruyter, vol. 6(1), pages 1-39, August.
    17. Richards, Timothy J. & Patterson, Paul M., 2006. "Firm-Level Competition in Price and Variety," Journal of Agricultural and Applied Economics, Southern Agricultural Economics Association, vol. 38(3), pages 1-22, December.
    18. Yan Chen & Youran Qi & Qing Liu & Peter Chien, 2018. "Sequential sampling enhanced composite likelihood approach to estimation of social intercorrelations in large-scale networks," Quantitative Marketing and Economics (QME), Springer, vol. 16(4), pages 409-440, December.
    19. H. Dharma Kwon & Hongzhong Zhang, 2015. "Game of Singular Stochastic Control and Strategic Exit," Mathematics of Operations Research, INFORMS, vol. 40(4), pages 869-887, October.
    20. 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.

    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:spr:joptap:v:137:y:2008:i:3:d:10.1007_s10957-007-9350-6. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.