# Aggregate overhaul and supply chain planning for rotables

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## Abstract

We consider the problem of planning preventive maintenance and overhaul for modules that are used in a fleet of assets such as trains or airplanes. Each type of module, or rotable, has its own maintenance program in which a maximum amount of time/usage between overhauls of a module is stipulated. Overhauls are performed in an overhaul workshop with limited capacity. The problem we study is to determine aggregate workforce levels, turn-around stock levels of modules, and overhaul and replacement quantities per period so as to minimize the sum of labor costs, material costs of overhaul, and turn-around stock investments over the entire life-cycle of the maintained asset. We prove that this planning problem is strongly \(\mathcal{NP}\)-hard, but we also provide computational evidence that the mixed integer programming formulation can be solved within reasonable time for real-life instances. Furthermore, we show that the linear programming relaxation can be used to aid decision making. We apply the model in a case study and provide computational results for randomly generated instances.

## Keywords

Maintenance Aggregate planning Life cycle costs \(\mathcal{NP}\)-hard Repairable parts Reverse logistics## Notes

### Acknowledgements

The authors would like to thank Bob Huisman of NedTrain for introducing this research topic to the authors and many stimulating discussions. The authors also thank Karin Vernooij who conducted an initial study in this subject, and who collected some of the data that we use. The authors also thank anonymous referees, Geert-Jan van Houtum and Matthew Reindorp for their constructive feedback.

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