Optimal control of a simple immigration–emigration process through total catastrophes

Abstract

This paper is concerned with the problem of controlling a simple immigration–emigration process, which represents a pest population, by the introduction of total catastrophes which, when they occur, reduce the population size to zero. The optimality criterion is that of minimizing the expected long-run average cost per unit time. The optimality of a control-limit policy is obtained using the method of successive approximations. An efficient Markov decision algorithm that generates a sequence of strictly improved control-limit policies is developed. There is strong numerical evidence that the algorithm converges to the overall optimal policy.