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Numerical Solutions to Some Optimal Control Problems Arising from Innovation Diffusion

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  • Luigi De Cesare
  • Andrea Di Liddo
  • Stefania Ragni

Abstract

In this paper we propose a numerical approach for the solution of some optimalcontrol problems arising in the field of marketing decision models. Inparticular, we account for a specific innovation diffusion model. A numericalapproach may be useful to investigate some features of state variables andparameters of interest. The discrete problem is solved by the SimulatedAnnealing method and the resulting numerical scheme is applied to some testcases. Copyright Kluwer Academic Publishers 2003

Suggested Citation

  • Luigi De Cesare & Andrea Di Liddo & Stefania Ragni, 2003. "Numerical Solutions to Some Optimal Control Problems Arising from Innovation Diffusion," Computational Economics, Springer;Society for Computational Economics, vol. 22(2), pages 173-186, October.
    • Handle: RePEc:kap:compec:v:22:y:2003:i:2:p:173-186
    DOI: 10.1023/A:1026185814203
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    References listed on IDEAS

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    1. John A. Norton & Frank M. Bass, 1987. "A Diffusion Theory Model of Adoption and Substitution for Successive Generations of High-Technology Products," Management Science, INFORMS, vol. 33(9), pages 1069-1086, September.
    2. Vijay Mahajan & Robert A. Peterson, 1978. "Innovation Diffusion in a Dynamic Potential Adopter Population," Management Science, INFORMS, vol. 24(15), pages 1589-1597, November.
    3. Frank M. Bass, 1969. "A New Product Growth for Model Consumer Durables," Management Science, INFORMS, vol. 15(5), pages 215-227, January.
    4. Goffe, William L. & Ferrier, Gary D. & Rogers, John, 1994. "Global optimization of statistical functions with simulated annealing," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 65-99.
    5. Luigi De Cesare & Andrea Di Liddo, 2001. "A Stackelberg Game Of Innovation Diffusion: Pricing, Advertising And Subsidy Strategies," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 3(04), pages 325-339.
    6. Shlomo Kalish, 1985. "A New Product Adoption Model with Price, Advertising, and Uncertainty," Management Science, INFORMS, vol. 31(12), pages 1569-1585, December.
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