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Optimal Goodwill Path to Introduce a New Product

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  • S. Mosca

    (University of Padova)

  • B. Viscolani

    (University of Padova)

Abstract

We consider the problem of determining an optimal goodwill path for the introduction of a new product in a market, while looking for the maximum foreseen profit. The foreseen revenue depends on the product introduction time and on the goodwill level at the same time. We focus on the advertising costs associated with the goodwill evolution and assume that the cost function possesses some rather general features which are shared by the cost functions of the Nerlove-Arrow type models. The dynamic optimization problem is discussed in the calculus of variations framework. A few examples associated with special cost functions are discussed in detail.

Suggested Citation

  • S. Mosca & B. Viscolani, 2004. "Optimal Goodwill Path to Introduce a New Product," Journal of Optimization Theory and Applications, Springer, vol. 123(1), pages 149-162, October.
    • Handle: RePEc:spr:joptap:v:123:y:2004:i:1:d:10.1023_b:jota.0000043995.54900.1a
    DOI: 10.1023/B:JOTA.0000043995.54900.1a
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    References listed on IDEAS

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    1. S. Jørgensen & S. Taboubi & G. Zaccour, 2001. "Cooperative Advertising in a Marketing Channel," Journal of Optimization Theory and Applications, Springer, vol. 110(1), pages 145-158, July.
    2. 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.
    3. Alessandra Buratto & Bruno Viscolani, 2002. "New product introduction: goodwill, time and advertising cost," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 55(1), pages 55-68, March.
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    Cited by:

    1. Marc Artzrouni & Patrice Cassagnard, 2017. "Nerlove–Arrow: A New Solution to an Old Problem," Journal of Optimization Theory and Applications, Springer, vol. 172(1), pages 267-280, January.
    2. Mariusz Górajski & Dominika Machowska, 2017. "Optimal double control problem for a PDE model of goodwill dynamics," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 85(3), pages 425-452, June.
    3. 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.
    4. 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.

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