Optimal pest-control through the introduction of a predator

A Markov decision model is considered for the control of a simple immigration process, which represents a pest population, by the introduction of a predator. The optimality criterion is that of minimising the long-run average cost per unit time. Firstly, an optimal policy is found within a restricted class of stationary policies which take controlling action if and only if the population size of the pests is greater than or equal to some critical value. The optimality of this policy within the wider class of all stationary policies is then proved.