A Markov decision algorithm for optimal pest control through uniform catastrophes

This paper is concerned with the problem of controlling the stochastic growth of a bounded pest population by the introduction of uniform catastrophes, whose rate is proportional to the population size. The optimality criterion is that of minimizing the long-run average cost per unit time. An appealing class of policies consists of the monotone policies, which introduce catastrophes if and only if the population size is equal to or exceed some critical value x. Firstly, a necessary and sufficient condition is found under which the policy of never controlling is optimal. If this condition fails, an efficient Markov decision algorithm that generates a sequence of strictly improved monotone policies is developed. There is strong numerical evidence that the algorithm converges to the optimal policy within the wider class of all stationary policies.