# Mixed-Integer Optimization Modeling for the Simultaneous Scheduling of Component Replacement and Repair Doctoral thesis, 2023

Maintenance is a critical aspect of many industries, playing an indispensable role in ensuring the optimal functionality, reliability, and longevity of various assets, equipment, and infrastructure. For a system to remain operational, maintenance of its components is required, and for the industry to optimize its operations, establishment of good maintenance policies and practices is vital.

This thesis concerns the simultaneous scheduling of preventive maintenance for a fleet of aircraft and their common components along with the maintenance workshop, to which the components are sent for repair. The problem arises from an industrial project with the Swedish aerospace and defence company Saab. In the four papers underlying this thesis, we develop mathematical models  based on a mixed-binary linear optimization model of a preventive maintenance scheduling problem with so-called interval costs over a finite and discretized time horizon. We extend this scheduling model with the flow of components through the repair workshop, including stocks of spare components as well as of damaged components to be repaired.
The components are modeled either individually, aggregated, or as jobs in the workshop, whose scheduling is considered to be preemptive or non-preemptive. Along with the scheduling, we address and analyze two contracting forms between the stakeholders---the aircraft operator and the repair workshop; namely, an availability of repaired components contract and a repair turn--around time contract of components sent to the repair workshop, leading to a bi-objective optimization problem for each of the two contracting forms. To handle the computational complexity of the problems at hand, we use Lagrangean relaxation and subgradient optimization to find lower bounding functions---in the objective space---of the set of non-dominated solutions, complemented with math-heuristics to identify good feasible solutions. Our modeling enables capturing important properties of the results from the contracting forms and it can be utilized for obtaining a lower limit on the optimal performance of a contracted collaboration between the stakeholders.

Mathematical Modeling

Workshop Scheduling

Maintenance Optimization

Simultaneous Scheduling

Mixed-Integer Linear Optimization

Multi-Objective Optimization

Contracting Forms

Pascal, Chalmers Tvärgata 3, Göteborg
Opponent: Prof. Dr Stefan Nickel, Karlsruhe Institute of Technology, Karlsruhe, Germany

## Author

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

### Obradović, G., Strömberg, A. -B., , Held F., Lundberg, K. Approximating the Pareto frontier for bi-objective preventive maintenance and workshop scheduling. A Lagrangean lower bounding methodology for evaluating contracting forms.

Establishing good maintenance policies and practices within industrial operations is essential as it has implications on productivity, efficiency, safety, and cost-effectiveness. Although maintenance costs represent, on average, a significant portion of the total operating budget, they are often underestimated since hidden costs are not accounted for. Hence, inferior maintenance policies lead to large increases in operational costs as well as to inefficient operations.

One of the main goals in military aviation is to optimize operational readiness, which is influenced by aircraft downtime due to (planned or unplanned) maintenance. Moreover, safety is vital as a failure can be fatal, making regular maintenance of the aircraft and its components nonnegotiable.

This thesis concerns the simultaneous scheduling of preventive maintenance of a fleet of aircraft and their common components and of the component repair workshop. The problem arises from an industrial project with the Swedish aerospace and defence company Saab AB. The mathematical models developed within the thesis are formulated with the goal of optimizing the integrated and circular supply chain and maintenance operations, such that the operational schedules are undisturbed (or minimally disturbed). Additionally, for some models that prove to be computationally demanding, mathematical solution methods are developed that enable obtaining approximate solutions within reasonable time.

### Effect based aircraft maintenance planning and operations support

VINNOVA (2017-04879), 2017-12-01 -- 2021-02-28.

### Subject Categories

Mathematics

Computational Mathematics

### ISBN

978-91-7905-908-8

Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 5374

### Publisher

Chalmers

Pascal, Chalmers Tvärgata 3, Göteborg

Opponent: Prof. Dr Stefan Nickel, Karlsruhe Institute of Technology, Karlsruhe, Germany