## 2 Materials and Methods
### Input Parameters  
The input parameters define the framework of the model and determine the production and maintenance tasks. They include key variables for planning machine capacity, maintenance intervals and production orders. The data used are fictitious due to confidentiality constraints and the complexity of obtaining comprehensive real-world datasets. However, to ensure a realistic representation of production conditions, the input parameters were carefully derived using best practices and expert judgment. To validate the accuracy and relevance of the data, a joint session was conducted with a production manager from a single- and small-batch production environment. The selection of influencing indicators for maintenance planning in the proposed model was based on a structured literature review. The aim was to derive selected indicators that are both theoretically sound and practically relevant. Three main categories of influence indicators were identified from the literature and form the basis for the following discussion. Machine-specific characteristics are integrated into the model, such as the age of the machines, which is modelled using operating hours, as well as their failure history, which was included as part of an expert interview using experience-based knowledge. Other theoretically relevant variables such as the mean time between failures or the criticality of individual machines are emphasised as important in the literature [22; 23], but are deliberately abstracted in the model in order to ensure feasibility in a dynamic production environment. Production-related aspects, including machine utilisation, order deadlines and planning flexibility, are directly taken into account in the model, as they represent key influencing variables for the interaction between production and maintenance [24; 25]. Organisational and strategic elements, such as the chosen maintenance strategy, are integrated into the model. However, aspects such as \"availability of personnel and spare parts\" and \"quality of the data basis\" will be discussed in the context of future extensions, as they are highly company-specific and are currently not systematically recorded in the application environment under consideration [26; 27; 28]. This reduced set of indicators was deliberately chosen to balance completeness and simplicity. It was confirmed in the expert session to be practically sufficient for operational maintenance decision-making. During this session, both the input parameters and the overall model structure were reviewed and confirmed to align with practical manufacturing scenarios. The expert assessment ensured that the selected values accurately reflected typical operating constraints, machine wear rates, and maintenance scheduling practices. Furthermore, the expert confirmed that no data elements critical for the model to effectively represent real-world production dynamics were missing. This validation ensures that the optimisation approach accounts for real-world constraints and operational requirements, making both the dataset and the model suitable for practical production planning. Maintenance tasks are defined with explicit durations, which serve as input parameters for the optimisation model. These durations are considered in the scheduling logic to ensure that maintenance activities can only be assigned to time windows of sufficient length. * Machine capacities determine the number of available machines and their specific properties. * Task priorities determine the urgency and importance of production orders. These priorities influence the scheduling by narrowing time windows and indirectly shaping the objective function. As a result, high-priority jobs are preferentially completed within their due dates, while delays are more acceptable for low-priority tasks. Order priorities are currently modelled by penalties and weighting in the objective function, which indirectly influence the schedule. However, dynamic reprioritisation based on real-time system states or evolving constraints is not yet implemented.