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• A challenging graduation project/internship in a high-tech result orientated work environment

• Weekly supervision and availability of the technical staff for support

• An internship allowance

• Working in an actual R&D project as part of the team

• Internship results to be used in the current and future projects

Royal NLR has been the ambitious research organisation with the will to keep innovating for over 100 years. With that drive, we make the world of transportation safer, more sustainable, more efficient and more effective. We are on the threshold of breakthrough innovations. Plans and ideas start to move when these are fed with the right energy. Over 800 driven professionals work on research and innovation, from aircraft engineers to psychologists and from mathematicians to application experts. Our colleagues are happy to tell you what it's like to work at NLR. This assignment will be managed by the Avionics Systems and Maintenance Engineering (ASAM) department.

Aircraft maintenance planning involves scheduling maintenance tasks and allocating the technicians, equipment, hangar slots and spare parts they require, under strict safety and availability constraints. In practice, schedules are still built from fixed intervals and static rules, and revised manually when conditions change: unexpected findings, delays, or a part that is not in stock. Prognostics and Health Management (PHM) now provides component-level health and remaining useful life estimates, which creates the opportunity to adapt maintenance and spare part decisions to the actual condition of the fleet. However, maintenance scheduling and spare part inventory are mostly optimised separately, despite their strong interdependence [1]. Joint, condition-driven formulations for multi-component aircraft systems with limited spares exist [2], and deep reinforcement learning has shown substantial cost reductions for engine maintenance [3], but such approaches remain far from the real-world scheduling systems used by operators.

The gap lies in dynamic scheduling: policies that update as the state of the aircraft and the operational context evolve. The literature is rich in mathematical frameworks for this purpose, from Markov decision processes and their contextual extensions [4] to stochastic programming and reinforcement learning, but implementing them in realistic setups and demonstrating their value against standard baselines is still a major challenge [5]. Three difficulties stand out. First, the action space is large and structured: executing a maintenance task requires preparatory actions, such as collecting equipment, securing the spare part and booking a technician, with precedence and resource constraints. Second, policies must be updated fast, which forces a trade-off between computationally expensive but precise models and lighter but approximate ones. Third, fair benchmarks against the rule-based practice are rarely reported. This project therefore formulates a mathematical framework for dynamic, joint maintenance scheduling and spare part management, starting from a small NLR use case and scaling up, and provides a comparative benchmark of several solution methods.

1.     Van Horenbeek, A., Buré, J., Cattrysse, D., Pintelon, L., Vansteenwegen, P. (2013). Joint maintenance and inventory optimization systems: A review. International Journal of Production Economics, 143(2), 499-508.

2.     de Pater, I., Mitici, M. (2021). Predictive maintenance for multi-component systems of repairables with Remaining-Useful-Life prognostics and a limited stock of spare components. Reliability Engineering & System Safety, 214, 107761.

3.     Lee, J., Mitici, M. (2023). Deep reinforcement learning for predictive aircraft maintenance using probabilistic Remaining-Useful-Life prognostics. Reliability Engineering & System Safety, 230, 108908.

4.     Hallak, A., Di Castro, D., Mannor, S. (2015). Contextual Markov Decision Processes. arXiv preprint arXiv:1502.02259.

5.     Pinciroli, L., Baraldi, P., Zio, E. (2023). Maintenance optimization in industry 4.0. Reliability Engineering & System Safety, 234, 109204.

The assignment will include the following tasks:

§  A literature study on dynamic maintenance scheduling and spare part management, covering sequential decision-making frameworks (e.g., Markov decision processes and their contextual extensions, stochastic programming, reinforcement learning) and their application to aircraft maintenance.

§  Selection of a use case provided by NLR, and formulation of a mathematical framework that jointly handles maintenance scheduling and spare part management, including preparatory actions and resource constraints.

§  Developing dynamic solution methods for the framework and analysing the trade-off between computational cost and solution quality when policies must be updated fast.

§  Applying the framework to the use case, starting small and scaling up, and providing a comparative benchmark of several methods against standard baselines.

The final outcomes of this assignment will be:

§  A structured assessment, as part of a literature study, of mathematical frameworks for dynamic maintenance scheduling and spare part management, together with a justified selection of the use case.

§  A mathematical formulation and implementation of a dynamic framework for joint maintenance scheduling and spare part management, with a comparative benchmark of several solution methods against standard baselines on the selected use case.

§  A technical report, either an MSc thesis following the guidelines of your faculty or an internship report, describing the approach, results, and conclusions of the work.

§  Optionally: a conference and/or journal publication.

Relevant datasets and tools for this research problem are:

§  A relevant use case from NLR, including maintenance task records, resource and technician availability, and spare part inventory information.

§  Public PHM datasets for condition and remaining useful life inputs, such as turbofan engine run-to-failure data (N-CMAPSS).

§  Optimisation solvers and modelling libraries, such as Gurobi, Google OR-Tools and Pyomo, for exact and heuristic baselines.

§  Reinforcement learning libraries and simulation environments, such as Gymnasium and Stable-Baselines3, for learning-based methods.

For an MSc thesis, the standard duration of a thesis at your faculty applies (typically 9 months). For an internship, the duration is 6 months.

§  You are an MSc student in Aerospace Engineering, Applied Mathematics, Operations Research, Computer Science or a similar master.

§  You have a strong background in optimisation, stochastic processes or sequential decision-making (e.g., Markov decision processes, reinforcement learning).

§  You have experience with programming in Python and with optimisation or machine learning libraries, for instance Pyomo, OR-Tools or PyTorch.

§  You have an affinity with aircraft maintenance, logistics or PHM, and are motivated to bring mathematical methods closer to real-world scheduling systems.

Submit your application via the NLR portal, together with your (i) Motivation letter and (ii) CV and we will contact you as soon as possible. For more information about the assignment contact Lisanne Visseren ([email protected]) or Lisandro Jimenez ([email protected]).