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Optimal pest control through catastrophes

Published online by Cambridge University Press:  14 July 2016

E.G. Kyriakidis  and
Andris Abakuks
E.G. Kyriakidis
Affiliation:
Birkbeck College
Andris Abakuks*
Affiliation:
Birkbeck College
*
∗ Postal address for both authors: Department of Statistics, Birkbeck College, University of London, Malet St, London WC1E 7HX, UK.
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Abstract

This paper is concerned with the problem of controlling a simple immigration–birth process, which represents a pest population, by the introduction of catastrophes which, when they occur, reduce the population size to zero. The optimality criterion is that of minimising the long-term average cost per unit time of the process. Firstly, an optimal policy is found within a restricted class of stationary policies, which introduce catastrophes if and only if the population size is greater than or equal to some critical value x. The optimality of this policy within the wider class of all stationary policies is then verified by applying the general results of Bather (1976).

Keywords

IMMIGRATION–BIRTH PROCESSCATASTROPHESMINIMUM AVERAGE COSTMARKOVIAN DECISION PROCESS
Type
Short Communications
Information
Journal of Applied Probability , Volume 26 , Issue 4 , December 1989 , pp. 873 - 879
Copyright
Copyright © Applied Probability Trust 1989 

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References

Bailey, N. T. J. (1964) The Elements of Stochastic Processes. Wiley, New York.Google Scholar
Bather, J. (1976) Optimal stationary policies for denumerable Markov chains in continuous time. Adv. Appl. Prob. 8, 144–158.Google Scholar
Brockwell, P. J. (1986) The extinction time of a general birth and death process with catastrophes. J. Appl. Prob. 23, 851–858.Google Scholar
Ross, S. M. (1970) Applied Probability Models with Optimization Applications. Holden-Day, San Francisco.Google Scholar