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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
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    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.
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    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.

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