Optimal joint preventive maintenance and production policies

We study joint preventive maintenance (PM) and production policies for an unreliable production–inventory system in which maintenance/repair times are non-negligible and stochastic. A joint policy decides (a) whether or not to perform PM and (b) if PM is not performed, then how much to produce. We consider a discrete-time system, formulating the problem as a Markov decision process (MDP) model. The focus of the work is on the structural properties of optimal joint policies, given the system state comprised of the system's age and the inventory level. Although our analysis indicates that the structure of optimal joint policies is very complex in general, we are able to characterize several properties regarding PM and production, including optimal production/maintenance actions under backlogging and high inventory levels, and conditions under which the PM portion of the joint policy has a control-limit structure. In further special cases, such as when PM set-up costs are negligible compared to PM times, we are able to establish some additional structural properties.