Manufacturing production scheduling with preventive maintenance in random environments

Consider the optimal control of a manufacturing system consisting of k stages in which a single consumable good is produced in a random jump environment. At each stage of the manufacturing process there are n workstations that can fail and be repaired. The workstations are assumed to have different operating parameters for a given stage. The mean time to failure for a given workstation, on a given stage, is modeled as a function of the uptime of the workstation. The uptime of the workstations is a monotone increasing function, which can be reset to a lower level by preventive maintenance. This formulation combines features of flexible and multistage manufacturing systems. The goal is to schedule the production of the consumable good subject to random effects and preventive maintenance.