Optimal production and maintenance policy for imperfect production systems

A joint optimization of the production run length and preventive maintenance (PM) policy is studied for a deteriorating production system where the in-control period follows a general probability distribution with non-decreasing failure rate. In the literature, the sufficient conditions for the optimality of the equal-interval PM schedule are explored to derive an optimal production run length and an optimal number of PM actions. Nevertheless, an exhaustive search may arise. In this study, based on the assumption that the conditions for the optimality of the equal-interval PM schedule hold, we derive some structural properties for the optimal production/PM policy, which increases the efficiency of the solution procedure. These analyses have implications for the practical application of the production/PM model to be more available in practice. A numerical example of gamma shift distribution with non-decreasing failure rates is used to illustrate the solution procedure, leading to some insight into the management process.