A semi-Markov decision algorithm for the maintenance of a production system with buffer capacity and continuous repair times

We consider a model consisting of a deteriorating installation (I) that transfers a raw material to a production unit and a buffer, which has been built between the I and the production unit to cope with unexpected failures of the I that may cause delays in production. The problem of the optimal preventive maintenance of the I is considered. It is assumed that the repair times follow some known continuous distributions. It seems intuitively reasonable that, for fixed buffer level, the optimal policy is of control-limit type, i.e. it initiates the preventive maintenance of the I if and only if the degree of its deterioration exceeds a critical level. An efficient semi-Markov decision algorithm, which operates on the class of control-limit policies, is developed. Numerical examples provide strong evidence that the algorithm converges to the optimal policy.