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.