Optimal production, maintenance and lockout/tagout control policies in manufacturing systems

We consider a production control problem for a manufacturing system subject to random failures and repairs. This paper differs from similar research projects in that it considers preventive maintenance activities and differentiates two types of repairs: repairs with lockout/tagout, associated with accident prevention, and repairs without lockout/tagout. Its goal is to find the optimal production rate, preventive maintenance rates and repair rates in order to minimize operating costs, backlog costs, inventory costs and unforeseen costs (accidents). The optimization criterion is that of minimizing the total expected infinite horizon discount cost. In order to solve this problem, a more realistic analysis model is proposed in this paper to consider the effects of machine age-dependent preventive and corrective maintenance policies on optimal safety stock levels. Hence, a unified framework is developed, allowing production, preventive and corrective maintenance to be jointly considered. Optimality conditions are provided for the manufacturing systems considered, and numerical methods are used to obtain machine age-dependent optimal control policies (production, preventive and corrective maintenance rates). Numerical examples and sensitivity analyses are included to illustrate the importance and effectiveness of the proposed methodology.