Production, preventive and corrective maintenance planning in manufacturing systems under imperfect repairs

This paper deals with the joint analysis of the optimal production and maintenance planning problems for a manufacturing system subject to random failures and repairs. When a machine fails down, 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, 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) is proposed. 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 failure rate of the machine depends on the number of failures; hence, the control policies of the considered planning problems depend on the number of failures. A numerical example and a sensitivity analysis will illustrate the structure of the optimal control policies and the usefulness on the proposed approach.