## 5 Illustrative Example
### Design Planning  
For conceptualizing the reconfigurable machine tool, in this case, study, we selected a set of E-KPIs that come in front of the paradigms of industry 4.0 and circular economy. At this point, we want to highlight the fact that selecting the E-KPIs for this case study was influenced by the concept of \"waste\" applied in lean manufacturing; that is, to eliminate all activities that do not bring value-added to the system. In an eco-smart manufacturing system from the paradigm of industry 5.0, modules of machines come as independent cyber-physical systems, with plug-and-play capabilities, in a master-slave reconfigurable architecture. This type of solution has already been investigated by the authors of this paper and is published in [10]. Thus, in the design problem under investigation in this case study, we consider all modules embedding this capacity, which, in principle, is a key KPI of reconfigurability but not a dependent one from other KPIs. Therefore, it is not included in the optimization problem from this research.  
Considering the aspects mentioned above, we finally limited the optimization problem to five performance indicators (E-KPIs) for the conceptual design of the reconfigurable machine tool with adjustable functionality under the space of possibilities imposed by the family of parts described by the generic part from Figure 1:  
* Time for reconfiguring machine's functionality (code in the set: 1 (\(i=1\)); trend: minimize (\(k(1)=-1\)));
* Variety of available constructive modules of the machine (code in the set: 2 (\(i=2\)); trend: maximize (\(k(2)=1\)));
* Number of locations for the interfaces between modules (code in the set: 3 (\(i=3\)); trend: maximize (\(k(3)=1\)));
* Number of possible configurations (code in the set: 4 (\(i=4\)); trend: maximize (\(k(4)=1\)));
* Granularity level (code in the set: 5 (\(i=5\)); trend: maximize (\(k(5)=1\))).  
Based on expert judgments and applying a structured ranking tool (in this case the analytical hierarchy process [24; 25]), the following normalized-to \(-1\) value weights are assumed in this case study: \(\beta_{1}=0.11\); \(\beta_{2}=0.25\); \(\beta_{3}=0.26\); \(\beta_{4}=0.24\); \(\beta_{5}=0.14\). The target values for the performance indicators in this case study are: \(V_{T1}=120\) min; \(V_{T2}=10\) #; \(V_{T3}=2\) locations/module; \(V_{T4}=12\) #; \(V_{T5}=75\)%.  
To measure the effective values \(V_{Ei}\), \(i=1\),..., 5, while applying the SCV algorithm, the following aspects are considered:  
* If a certain module in the structure is of pure rotation or translation, the assumption is that it can be easily ordered from the producer, thus available when required.  
* If a certain module in the structure is of pure rotation or translation, it is assumed that it is no difficult to consider two locations on the module for joining with other modules.
* If it is denoted with \(g_{r}\) the granularity level of the structure, with \(n_{f}\) the number of functionalities of the structure, and with \(n_{m}\) the number of modules integrated into the structure to ensure the necessary functionalities for manufacturing the generic part, the following equation is established: \(g_{r}(n_{f}/n_{m})\cdot 100[\%]\).
* If it is denoted with \(t_{r}\) the time required for reconfiguration, with \(t_{m}\) the estimated average time for assembly /disassembly of a module (e.g., approx. 20 min), with \(m_{i}\) the number of modules that must be replaced or repositioned, with \(m_{a}\) the number of new modules that must be added in the system, and with \(t_{a}\) the time allocated for various adjustments (e.g., here, \(t_{a}\) could be considered as 20% from \(t_{m}\cdot(m_{i}+m_{a})\)), the following equation is established: \(t_{r}=t_{m}\cdot(m_{i}+m_{a})+t_{a}\).