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.

This paper investigates inspection strategies for a finite-state continuous-time Markovian deteriorating system. Two inspection strategies are considered: sequential inspection and continuous inspection. Unlike many previous efforts, the inspection times for the sequential inspection strategy are assumed to be non-negligible. The replacement times and costs for both strategies are non-negligible and state dependent. Our objective here is to minimize the expected long-run cost rate. Iterative algorithms are provided to derive the optimal policies for both strategies. The structures of these optimal policies and their corresponding optimal cost rates are discussed and compared.