Optimal safety stocks and preventive maintenance periods in unreliable manufacturing systems

We consider a manufacturing system with preventive maintenance that produces a single part type. An inventory is maintained according to a machine-age-dependant hedging point policy. We conjecture that, for such a system, the failure frequencies can be reduced through preventive maintenance resulting in possible increase in system performance. Traditional preventive maintenance policies, such as age replacement, periodic replacement, are usually studied without finished goods inventories. In the cases where the finished goods inventories are considered, restrictive assumptions are used, such as not allowing breakdown during the stock build up period and during backlog situations due to the complexity of the mathematical model. In order to solve this problem, we develop a more realistic mathematical model of the system, and derive expressions of the overall incurred cost used as the basis for optimal determination of the jointly production and preventive maintenance policies (i.e. production rates and preventive maintenance frequency, depending on inventory levels of the produced parts). Such a cost consists of inventory, backlog, corrective and preventive maintenance costs. The work reported here has a significant practical application (no restriction on failures occurrence and backlog situations) in the context of production planning of manufacturing systems. Numerical examples are included to illustrate the importance and the effectiveness of the proposed methodology.