Preventive maintenance scheduling of multi-component systems with deterioration costs

Preprint, 2012

We introduce the preventive maintenance scheduling problem with interval costs (PMSPIC), which is to schedule preventive maintenance of components of a system over a finite discretized time horizon, given a common set-up cost and component costs dependent on the lengths of the maintenance intervals. We present a 0-1 integer linear programming (0-1 ILP) model for the PMSPIC which was originally presented by Joneja (1990) to model the joint replenishment problem. We show that most of the integrality constraints can be relaxed and that the linear inequality constraints define facets of the convex hull of the feasible set. We present three applications demonstrating that the PMSPIC can be used to model several types of maintenance problems with deterioration costs. The first considers rail grinding. If the interval between the grinding occasions increases, then the sizes of the rail cracks increase, which implies that more grinding passes must be performed, generating a higher maintenance cost. We presume a deterministic model for crack growth and optimize the scheduling of the rail grinding on a set of track sections. Our second application concerns two approaches for the scheduling of component replacements in aircraft engines. In the first approach a bi-objective problem, simultaneously minimizing the cost for the scheduled preventive maintenance and the probability of unexpected stops, is formulated. The second approach considers the minimization of the sum of costs of preventive and expected corrective maintenance, without rescheduling. We also demonstrate that if rescheduling is allowed, then the 0-1 ILP model can be used as a policy by re-optimizing the schedule at a component failure, thus utilizing the opportunity for preventive maintenance. We evaluate the use of such a strategy in a simulation of the engine. The third approach considers components’ replacement in wind mills in a wind farm, extending the PMSPIC to consider several systems with a joint set-up cost. As for the aircraft engine application, we use the 0-1 ILP model as a policy for deciding upon replacement decisions allowing for rescheduling, and evaluate it by simulating the joint system. In each of the three applications, the use of the 0-1 ILP model is compared with age or constantinterval policies, resulting in a reduction of maintenance costs by up to 15% compared with the respective best simple policy.