Optimal preventive maintenance of a production system with an intermediate buffer

In this paper we consider a model consisting of a deteriorating installation that transfers a raw material to a production unit and a buffer which has been built between the installation and the production unit. The deterioration process of the installation is considered to be nonstationary, i.e. the transition probabilities may depend not only on the working conditions of the installation but on its age as well. The problem of the optimal preventive maintenance of the installation is considered. Under a suitable cost structure it is shown that, for fixed age of the installation and fixed buffer level, the optimal policy is of control-limit type. When the deterioration process is stationary, an efficient Markov decision algorithm operating on the class of control-limit policies is developed. There is strong numerical evidence that the algorithm converges to the optimal policy. Two generalizations of this model are also discussed.