Optimal-control of a simple immigration – birth–death process through total catastrophes

This paper deals with the problem of controlling a simple immigration–birth–death process, which represents a pest population, by the introduction of total catastrophes. The optimality criterion is that of minimising the long-run average cost per unit time. A semi-Markov decision formulation with a finite set of decision epochs is obtained, provided that the birth, death and catastrophe rates satisfy a certain condition. The optimal policy is found to be of control-limit type by the standard policy iteration algorithm.