Production and maintenance planning for a failure-prone deteriorating manufacturing system: a hierarchical control approach

The work presented in this paper examines the joint analysis of the optimal production and maintenance planning policies for a manufacturing system subject to random failures and repairs. When a machine fails, an imperfect corrective maintenance is undertaken. The objective of this study is to minimize a discounted overall cost consisting of preventive and corrective maintenance costs, inventory holding cost, and backlog cost. A two-level hierarchical decision-making approach is proposed, based on the determination of the mean time to failure (first level) and the statement of a joint optimization of production, preventive, and corrective maintenance policies (second level). Hence, the production, preventive, and corrective maintenance rates are determined in the second level, given the failure rates obtained from the first level. In the proposed model, the machine's failure rate depends on the number of imperfect repairs, and as a result, the control policies of the considered planning problems therefore depend on the number of failures. The structure of the optimal control policies and the usefulness of the proposed approach are illustrated through a numerical example and a sensitivity analysis.