## 5 Proposed Methodology
### Process Modelling Methodology
#### 5.3.2 Model Synthesis and Operation Procedure
The individual models have to be linked according to the topology represented in stage 2. Connection points are created by the fusion of output buffers of preceding processes with the input buffers of the subsequent processes in common ones. * Definition of the characteristics of the jobs considered for process. The number of jobs plays a significant role in the complexity of the overall PN model, as different branches are considered for each process with its own quantitative characteristics. In addition, the way that jobs are operated must be defined (by part or by batch) if batches are split or if they are treated as a unity and many more decisions and assumptions concerning the execution and simulation of the model through the performance of events in it. * Once the structure of the overall model is confirmed, the quantitative parameters of the system have to be added. Typically, such parameters refer to time (delays) and quantities (e.g., resources participating in a process). In the case of controllable events, the time instants at which they will occur are specified (or the delays associated to their occurrence), while in the case of uncontrollable events, other parameters should be specified (e.g., the distribution followed, and consequences in specific entities). Once again, times should be calculated with respect to the way jobs are processed (by part or by batch) in order to have realistic results. In addition, in this step, certain variables that are necessary in order to represent the state of the system as well as to measure certain KPIs have to be defined. KPIs are not always common, as they have to do with areas of interest of the specific application and in many cases ways to calculate them or record them during the simulations must be specified, as this is not straightforward. This part is very important also for the performance evaluation of the system under the scenarios considered. Typical such indicators can be mean idleness time of the machines, percentage of the time a machine is operational, percentage of the time a machine produces, mean number of parts in buffers, maximum tardiness, mean tardiness, energy efficiency connected indicators and many more. * Representation of the initial state of the system. This refers to the initial inventory levels (raw materials, semi-processed parts and products),initial states of machines, resource availability, as well as to the orders that must be processed. Initial state of the system is very important, as it affects the complexity of the models constructed as well as their execution through simulation, since it defines the initial reachability state set. The set of initial parameter values is referred as a scenario, and the study of alternative scenarios is critical between others in order to forecast the behaviour of the model or even optimize it when no analytical optimisation tools can be considered (by comparative simulation and evaluation of results). In the case of Petri net models, the initial state is defined as a token distribution in the places of the model. * Initially, simulation of the base scenario and evaluation of the results obtained is performed. Comparison of these results with the realistic ones validates and justifies the practical use of the received model and enables its usage for the study of other cases. The base scenario typically describes a well-known production case whose results can be compared easily with the ones from the simulation. If the results are similar, then the model is considered accurate, validated and verified and can be used for studying alternative scenarios, realistic or planned. As described in [37], validation itself is viewed as a process and evidence for \"building the right model\". In addition, verification, which is also a process, is concerned with \"building the model right\". * The further use of the model can be offline for what-if analysis and evaluation of alternatives or online, in the context of a digital twin serving as a digital shadow of the real system.