A Discrete Time Population Control Model with Set-Up Cost.
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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 the future growth of the population. 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] sub [n], [S] sub [n]), where reduction is made in period [n] to state [s] sub [n] if the native population is found to be above state [S] sub [n]. Analogy with inventory theory is exploited in proving the result. (Prepared for publication in [Operations Research] and presentation at the 44th National ORSA meeting in November 1973.) 13 pp. Ref.
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