Skip to main content

Advertisement

Log in

A firm's control with price and investment

  • Published:
Zeitschrift für Operations Research Aims and scope Submit manuscript

Abstract

We consider a dynamic sales and output capacity model. The price function and the investment rate are control variables of a control model that can be solved by synthesis of optimal control paths. This model is similar to a differential game byLevine/Thepot. One of the extensions is that the investment effectiveness function is concave. Two possible optimal strategies can be derived beginning with a positive inventory level and ending with excess capacity, equal sales and output.

Zusammenfassung

Wir beschäftigen uns mit einem dynamischen Absatz- und Outputkapazitäts modell. Preis und Investitionsrate sind Steuervariable eines Kontrollmodells, das durch Verknüpfung von optimalen Pfaden gelöst werden kann. Dieses Modell baut auf einem Differentialspiel vonLevine/Thepot auf. Eine der Erweiterungen besteht darin, daß die Funktion der Investitions effektivität als konkav angenommen wird. Es können zwei mögliche optimale Strategien abgeleitet werden, die mit einem positiven Lagerstand beginnen und mit aufeinander abgestimmten Absatz- und Produktionskapazitäten enden.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Levine, J., andJ. Thepot: Open Loop and Closed Loop Equilibria in a Dynamic Duopoly. In: Optimal Control Theory and Economic Applications, ed. by: G. Feichtinger, North Holland, Amsterdam 1982, 143–156.

    Google Scholar 

  • Gould, JP.: Diffusion Processes and Optimal Advertising Policy. In: Microeconomic Foundations of Employment and Inflation Theory, ed. by: Phelps et al., WW Norton, London 1970, 338–368.

    Google Scholar 

  • Luptacik, M.: Optimal Price and Advertising Policy under Atomistic Competition. Journal of Economic Dynamics and Control4, 1982, 57–71.

    Google Scholar 

  • Feichtinger, B., andR. Hartl: Ein nichtlineares Kontrollproblem der Instandhaltung. OR Spektrum3, 1981, 49–58.

    Google Scholar 

  • Sethi, S.P., andG.L. Tompson: Applied Optimal Control and Management Science. Martinus Hijhoff, Boston 1981.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gaugusch, J. A firm's control with price and investment. Zeitschrift für Operations Research 29, B153–B165 (1985). https://doi.org/10.1007/BF01920575

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01920575

Keywords

Navigation