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Optimal Control of a Truncated General Immigration Process through Total Catastrophes

E. G. Kyriakidis
Journal of Applied Probability
Vol. 36, No. 2 (Jun., 1999), pp. 461-472
Stable URL: http://www.jstor.org/stable/3215468
Page Count: 12
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Optimal Control of a Truncated General Immigration Process through Total Catastrophes
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Abstract

A Markov decision model is considered for the control of a truncated general immigration process, which represents a pest population, by the introduction of total catastrophes. The optimality criterion is that of minimizing the expected long-run average cost per unit time. Firstly, a necessary and sufficient condition is found under which the policy of never controlling is optimal. If this condition fails, a parametric analysis, in which a fictitious parameter is varied over the entire real line, is used to establish the optimality of a control-limit policy. Furthermore, an efficient Markov decision algorithm operating on the class of control-limit policies is developed for the computation of the optimal policy.

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