Stability of real-time lot scheduling policies for an unreliablemachine

A single-machine multiproduct manufacturing system with random breakdowns and random repair times is considered. Under a weak capacity condition on the system it is shown that the total work-in-progress (WIP) is a recurrent stochastic process. By replacing the stochastic model by a deterministic one with preventive maintenance activities scheduled on a regular basis or by strengthening the capacity condition, the boundaries of WIP and expected WIP, respectively, over time can be shown