Preventive maintenance scheduling of multi-component systems with interval costs
Artikel i vetenskaplig tidskrift, 2014

We introduce the preventive maintenance scheduling problem with interval costs (PMSPIC), which is to schedule preventive maintenance (PM) of the components of a system over a finite and 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; the model is identical to that presented by Joneja (1990) for the joint replenishment problem within inventory management. We study this model from a polyhedral and exact solutions’ point of view, as opposed to previously studied heuristics (e.g. Boctor, Laporte, & Renaud, 2004; Federgruen & Tzur, 1994; Levi, Roundy, & Shmoys, 2006; Joneja, 1990).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 further relate the PMSPIC to the opportunistic replacement problem, for which detailed polyhedral studies were performed by Almgren et al. (2012a). The PMSPIC can be used as a building block to model several types of maintenance planning problems possessing deterioration costs. By a careful modeling of these costs, a polyhedrally sound 0–1 ILP model is used to find optimal solutions to realistic-sized multi-component maintenance planning problems. The PMSPIC is thus easily extended by side constraints or to multiple tiers, which is demonstrated through three applications; these are chosen to span several levels of unmodeled randomness requiring fundamentally different maintenance policies, which are all handled by variations of our basic model. Our first application considers rail grinding. Rail cracks increase with increasing intervals between grinding occasions, implying that more grinding passes must be performed—thus generating higher costs. We optimize the grinding schedule for a set of track sections presuming a deterministic model for crack growth; hence, no corrective maintenance (CM) will occur between the grinding occasions scheduled. The second application concerns two approaches for scheduling component replacements in aircraft engines. The first approach is bi-objective, simultaneously minimizing the cost for the scheduled PM and the probability of unexpected stops. In the second approach the sum of costs for PM and expected CM—without rescheduling—is minimized. When rescheduling is allowed, the 0–1 ILP model is used as a policy by re-optimizing the schedule at a component failure, which then constitutes an opportunity for PM. The policy manages the trade-off between costs for PM and unplanned CM and is evaluated in a simulation of the engine. The third application considers components’ replacement in wind mills in a wind farm, extending the PMSPIC to comprise multiple tiers with joint set-up costs. Due to the large number of components unexpected stops occur frequently, thus calling for a dynamic rescheduling, which is evaluated through a simulation of the system. In each of the three applications, the use of the 0-1 ILP model is compared with age or constant-interval policies; the maintenance costs are reduced by up to 16% as compared with the respective best simple policy. The results are strongest for the first two applications, possessing low levels of unmodeled randomness.

case studies

integer optimization

dynamic grouping

finite horizon

maintenance scheduling

polyhedral analysis


[Person 38002bc7-0e60-4072-9e87-93d9891c8485 not found]

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

[Person 91cdbf51-bbbe-405b-8efc-2a642b60c0eb not found]

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

[Person ca407630-5ed8-4c7e-9137-bac6d420d41d not found]

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

[Person 373c1513-f247-4373-8415-fcb3be985e79 not found]

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

[Person 9383ad41-b6f6-4bb7-9eeb-5ec2ee1e7fe1 not found]

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Computers and Industrial Engineering

0360-8352 (ISSN)

Vol. 76 390-400


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