## 2 Materials and Methods
### Pseudocode
A red border around a production step indicates that the completion date has been exceeded. The model is designed in such a way that delays occur preferentially for low-priority orders, while high-priority orders are completed on time wherever possible. ### Machine Status and Wear Progression

The wear curves (see Figures 2 and 3) illustrate the condition of the machines over the planning period. Each machine has a wear reserve that describes its remaining planned operational capability [29]. This reserve decreases with each use, with the rate of wear depending on the type of production order and the specific utilisation of the machine. Each

Figure 1: Machine allocation schedule with overtime, setup times and maintenance tasks. order is assigned an individual wear level for the machine. In addition, the planner can assign a stress level to each order, which accounts for other influencing factors. Together, these two parameters determine how much a job contributes to the wear of a machine. To further enhance the accuracy of wear assessment, the model accounts for varying stress levels associated with different production tasks. Each job type has a distinct impact on machine wear, depending on factors such as processing intensity, material properties and operating conditions. By assigning specific wear coefficients to different task categories,

Figure 3: Wear curves of the machines over the planning period including planned maintenance and recommended maintenance with regard to wear. Figure 2: Wear curves of the machines over the planning period including planned maintenance. the model provides a more refined evaluation of machine degradation over time. Future extensions incorporate advanced predictive analytics to further improve wear estimation and optimise maintenance planning. The model thus supports three types of maintenance strategies to meet different operational needs and levels of flexibility:

* As shown in Table 2, this variant follows fixed schedules, such as weekly, monthly or after a specific number of operating hours. Since these are planned independently of actual machine utilisation, they offer limited flexibility but enable regular maintenance that can be scheduled automatically. * This approach monitors machine wear continuously instead of merely tracking operating hours. Maintenance planners assess task impact in advance by evaluating workload and stress levels. When critical thresholds are reached, the model automatically suggests maintenance windows during idle periods in the production schedule. Compared to the first variant, this method dynamically integrates maintenance activities into available time slots based on real-time machine conditions. * The model also allows planners to schedule maintenance manually at any time, regardless of predefined intervals or wear levels. This offers full decision-making freedom and allows maintenance to be performed on demand. This multi-tiered approach ensures that maintenance planning remains adaptable to real-world conditions--balancing predictability and optimisation-driven efficiency, as well as manual control for exceptional cases. The input parameters of all maintenance tasks include defined durations, which are considered within the optimisation model. These durations are explicitly used in the scheduling logic to ensure that maintenance is only assigned when a time window of sufficient length is available. For dynamically scheduled maintenance, users can specify the expected duration manually or select predefined types. This guarantees that both static and reactive maintenance activities are realistically integrated into the production plan. To ensure this flexibility, the model combines different approaches. Maintenance measures can be adjusted to reduce machine wear while simultaneously increasing overall availability. The model continuously monitors machine wear levels and dynamically schedules maintenance when predefined usage thresholds are exceeded.