Optimizing production and imperfect preventive maintenance planning׳s integration in failure-prone manufacturing systems

• Integration of production planning and imperfect preventive maintenance is explored.
• Imperfect maintenance is modeled using a fitting age reduction hybrid hazard rate.
• A practical approximate optimization model for this integration is proposed.
• The resulting naturally MINL optimization model is reformulated and solved as a MILP.
• An effective fix-and-optimize procedure is proposed for large instances of this MILP.

This paper investigates the issue of integrating production and maintenance planning in a failure-prone manufacturing system. It is assumed that the system׳s operating state is stochastically predictable, in terms of its operating age, and that it can accordingly be preventively maintained during preplanned periods. Preventive maintenance is assumed to be imperfect, that is when performed, it brings the manufacturing system to an operating state that lies between ‘as bad as old’ and ‘as good as new’. Only an overhauling of the system brings it to a ‘as good as new’ operating state again. A practical integrated production and preventive maintenance planning model, that takes into account the system׳s manufacturing capacity and its operational reliability state, is developed. The model is naturally formulated as a mixed-integer non-linear optimization problem, for which an extended mixed-integer linear reformulation is proposed. This reformulation, while it solves the proposed integrated planning problem to optimality, remains quite demanding in terms of computational time. A fix-and-optimize procedure, that takes advantage of some properties of the original model, is then proposed. The reformulation and the fix-and-optimize procedure are tested on some test instances adapted from those available in the literature. The results show that the proposed fix-and-optimize procedure performs quite well and opens new research direction for future improvements.