IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v330y2018icp42-55.html
   My bibliography  Save this article

Optimal control of the customer dynamics based on marketing policy

Author

Listed:
  • Rosa, S.
  • Rebelo, P.
  • Silva, C.M.
  • Alves, H.
  • Carvalho, P.G.

Abstract

We consider an optimal control problem for a non-autonomous model of ODEs that describes the evolution of the number of customers in some firm. Namely we study the best marketing strategy. Considering a L2 cost functional, we establish the existence and uniqueness of optimal solutions, using an inductive argument to obtain uniqueness on the whole interval from local uniqueness. We also present some simulation results, based on our model, and compare them with results we obtain for an L1 cost functional. For the L1 cost functional the optimal solutions are of bang-bang type and thus easier to implement, because at every moment possible actions are chosen from a finite set of possibilities. For the autonomous case of L2 problem, we show the effectiveness of the optimal control strategy against other formulations of the problem with simpler controls.

Suggested Citation

  • Rosa, S. & Rebelo, P. & Silva, C.M. & Alves, H. & Carvalho, P.G., 2018. "Optimal control of the customer dynamics based on marketing policy," Applied Mathematics and Computation, Elsevier, vol. 330(C), pages 42-55.
    • Handle: RePEc:eee:apmaco:v:330:y:2018:i:c:p:42-55
    DOI: 10.1016/j.amc.2018.02.027
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300318301292
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2018.02.027?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. Silva, César M. & Rosa, Silvério & Alves, Helena & Carvalho, Pedro G., 2016. "A mathematical model for the customer dynamics based on marketing policy," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 42-53.
    2. Berman, Barry, 2016. "Referral marketing: Harnessing the power of your customers," Business Horizons, Elsevier, vol. 59(1), pages 19-28.
    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. Piotr Hadrian & František Milichovský & Pavel Mráček, 2021. "The Concept of Strategic Control in Marketing Management in Connection to Measuring Marketing Performance," Sustainability, MDPI, vol. 13(7), pages 1-21, April.

    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. Elias Carroni & Paolo Pin & Simone Righi, 2020. "Bring a Friend! Privately or Publicly?," Management Science, INFORMS, vol. 66(5), pages 2269-2290, May.
    2. Rae Yule Kim, 2020. "The influx of skeptics: an investigation of the diffusion cycle effect on online review," Electronic Markets, Springer;IIM University of St. Gallen, vol. 30(4), pages 821-835, December.
    3. Eggers, Fabian & Risselada, Hans & Niemand, Thomas & Robledo, Sebastian, 2022. "Referral campaigns for software startups: The impact of network characteristics on product adoption," Journal of Business Research, Elsevier, vol. 145(C), pages 309-324.
    4. Simona Cicognani & Sebastian Stein & Mirco Tonin & Michael Vlassopoulos, 2023. "Symbolic incentives and the recruitment of volunteers for citizen science projects," Oxford Economic Papers, Oxford University Press, vol. 75(4), pages 923-940.
    5. Mark Legg & Murat Hancer, 2020. "How patrons value casino promotional offers: A conjoint study," Tourism Economics, , vol. 26(4), pages 640-657, June.
    6. David Gligor & Christopher Newman & Saim Kashmiri, 2021. "Does your skin color matter in buyer–seller negotiations? The implications of being a Black salesperson," Journal of the Academy of Marketing Science, Springer, vol. 49(5), pages 969-993, September.
    7. Ioanna Karantza & Michael Chrissos Anestis & Sotirios Vlachakis, 2022. "Crisis mapping in the “senses” arena narratives," International Review on Public and Nonprofit Marketing, Springer;International Association of Public and Non-Profit Marketing, vol. 19(4), pages 649-673, December.
    8. Joseph Kolawole Abon & Rufus O. Adebayo, 2020. "The Use of Marketing as a Tool for Competitive Advantage among Potential and Professional Football Clubs in KZN, South Africa," Eurasian Journal of Business and Management, Eurasian Publications, vol. 8(4), pages 319-335.
    9. Kuang, Di & Ma, Baolong & Wang, Hong, 2022. "The relative impact of advertising and referral reward programs on the post-consumption evaluations in the context of service failure," Journal of Retailing and Consumer Services, Elsevier, vol. 65(C).
    10. Ghouri, Arsalan Mujahid & Akhtar, Pervaiz & Haq, Mirza A. & Mani, Venkatesh & Arsenyan, Gayane & Meyer, Martin, 2021. "Real-time information sharing, customer orientation, and the exploration of intra-service industry differences: Malaysia as an emerging market," Technological Forecasting and Social Change, Elsevier, vol. 167(C).

    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:apmaco:v:330:y:2018:i:c:p:42-55. 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.