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A Discrete-Time Population-Control Model with Setup Cost

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  • David L. Jaquette

    (The Rand Corporation, Santa Monica, California)

Abstract

A discrete-time stochastic model is often used to describe a natural animal, pest, or epidemic population. Control action, representing harvesting, exterminating, etc., can be taken periodically to reduce the current population level, and so modify its future growth. Dynamic programming can be used to determine optimal control policies for models where growth and control produce economically measurable benefits and/or costs. When controlling action incurs a setup charge plus a cost component linear in the amount of state reduction produced, the optimal policy is found to be characterized by a pair ( s n , S n ), where reduction is made in period n to state s n if the native population is found to be above state S n . Analogy with inventory theory is exploited in proving the result.

Suggested Citation

  • David L. Jaquette, 1974. "A Discrete-Time Population-Control Model with Setup Cost," Operations Research, INFORMS, vol. 22(2), pages 298-303, April.
    • Handle: RePEc:inm:oropre:v:22:y:1974:i:2:p:298-303
    DOI: 10.1287/opre.22.2.298
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    Cited by:

    1. Dawid, Herbert & Kopel, Michael, 1997. "On the Economically Optimal Exploitation of a Renewable Resource: The Case of a Convex Environment and a Convex Return Function," Journal of Economic Theory, Elsevier, vol. 76(2), pages 272-297, October.
    2. Thomas, Timothy S., 1999. "Transformation Of Fallow Systems Under Population Pressure," 1999 Annual meeting, August 8-11, Nashville, TN 21603, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    3. Sadeh, Arye & Griffin, Wade L., 1997. "Value of feedback in agricultural decisions," Agricultural Systems, Elsevier, vol. 53(2-3), pages 285-301.
    4. Evangelos Toumasatos & Stein Ivar Steinshamn, 2018. "Coalition Formation with Externalities: The Case of the Northeast Atlantic Mackerel Fishery in a Pre- and Post-Brexit Context," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 20(02), pages 1-48, June.
    5. Toumasatos, Evangelos & Steinshamn, Stein Ivar, 2017. "Coalition Formation with Externalities: The Case of the Northeast Atlantic Mackerel Fishery in a Pre and Post Brexit Context," Discussion Papers 2017/11, Norwegian School of Economics, Department of Business and Management Science.

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