## 2 Literature Review  
### Digital Models and Simulation-Based Approaches  
The digitalization of manufacturing systems today represents a great opportunity to reach significant levels of productivity and be competitive on the market. In this context, the Digital Twin is one of the most promising paradigms [16; 17; 18], with applications in several domains such as smart factory control [19; 20], fault diagnosis [21], additive manufacturing [22; 23], production optimization [24]. As pointed out by [PERSON] et al. [11], the term Digital Twin, in the sense of \"digital counterpart of physical object\", is often used as a synonym of Digital Model and Digital Shadow. Therefore, it is necessary to make a differentiation between these 3 concepts, based on the level of data integration between physical and digital world. The Digital Model does not presuppose any automated exchange of data between physical object and digital object. Then, there is no real-time synchronization. The Digital Shadow, on the other hand, is characterized by an automated one-way data flow from physical object to digital object. Basically, any change in the physical world implies a real-time change in the digital world, not vice versa. Finally, the Digital Twin is characterized by a real-time synchronization between the physical world and the digital world, with an automated exchange of data in both directions [11]. Through the digitalization of the real world, it is possible to perform simulations, which enable the optimization of the plans in the virtual world, which are then delivered to the real world with high probability of success. Basically, the analysis of different scenarios makes possible the identification of any errors in advance, to avoid their occurrence within the real manufacturing system, minimizing waste and maximizing returns. In this paper, the focus is on the Digital Model concept combined with simulation, following the paradigm of Modeling & Simulation for manufacturing [25]. There are several successful simulation-based approaches in the literature. Some examples are given below. [PERSON] et al. [26] present an approach where an ontology-based virtual factory is continuously integrated with the real plant. The digital object is used to conduct simulations, aimed at understanding in advance the impact of possible decisions on production and maintenance. [PERSON] et al. [27] develop a data-drivensimulation approach for remanufacturing operations, characterized by data coming from digital manufacturing systems. In this case, the simulation serves to support improvements in the real system, based on the results obtained in the digital counterpart. [PERSON] et al. [28] propose a scheduling method based on dynamic data-driven simulation to improve the performance of a manufacturing system. The designed approach is tested through a case study on numerical control machining in the domain of cloud manufacturing, and the results demonstrate its goodness. The reader is referred to some comprehensive literature reviews for other simulation-driven approaches [29; 30].  
In recent years, the areas of use of Digital Models are becoming more and more widespread, with different connotations. Specifically, the M&S approach can be integrated within a decision support system, which is defined as \"a specific class of computerized information system, enabling to manage decision-making activities\" [31]. [PERSON] et al. [32], through a digital twin architecture, have developed a decision support system with the aim of better scheduling preventive maintenance interventions. [PERSON] et al. [33] have adopted a digital replica as a basis for a decision support system, capable of providing improvements in terms of resource optimization in a smart city scenario. [PERSON] and [PERSON] [34] have recently integrated the Digital Twin paradigm into a decision support system to improve the order management process.