## 7 Results and Discussion
### Results  
The case study previously presented is solved by applying the customized SA procedure proposed in this paper. The obtained results are analyzed in this sub-section. The optimal objective function value (Equation (5)) found is equal to 1.74. This indicator represents the overall goodness of the solution summarizing three of its main aspects. One of these is the line efficiency (LE, Equation (2)), equal to 89.85%. Strictly related with this, the number of workers of the line amounts to 20, while its lower bound is 18. This theoretical number is determined assuming that there are no constraints of any type to complete all assembly tasks. Another key feature is the line length (LN, Equation (3)), which is equal to 10 workstations. The lower bound of this indicator is seven since the maximum worker concentration per workstation is three. The third purpose of the proposed model is the minimization of the workload variation among assembly line workers, which is represented by the smoothness index (SI, Equation (4)). In the obtained solution, it is equal to 168 s and corresponds to 3% of the average workload of an individual worker, which is 5338 s. Table 3 summarizes the main features of the presented solution for the MALSP case study. The optimal solution for the considered case study indicates that the number of workers ranges from one to three at each multi-manned workstation. The possibility of assigning a variable worker number to workstations ensures high flexibility to the proposed synchronization. Moreover, the equipment needed at each multi-manned workstation is valuable information for the considered case study. The proposed procedure determines the equipment to install in each individual workstation. Furthermore, it manages its utilization by the workers during the cycle time to avoid any possible simultaneous adoption through the synchronization of their employment with task execution. In the obtained solution, just four pieces of equipment out of 20 (F, D, H, and I) are duplicated in two different workstations, and no equipment is assigned to more than two workstations. Figure 10 illustrates the workers to stations assignment, their saturation, and the equipment provided to each workstation. Moreover, even if the synchronization required for ensuring the solution feasibility tends to increase the idle time among tasks and reduce workers saturation, it averages 89.7% and it is high for all workers as its minimum is 77%, which is representative of the last worker on the line (Figure 10). Workbooks providing all the information that workers need to complete their assembly assignments over a cycle time could be valuable and useful tools in manufacturing companies. The proposed procedure is designed to automatically define for each worker the optimal sequence of tasks to perform, along with the equipment to use, the mounting position to adopt, and whether cooperation with other workers is required for every instant of the cycle time. Indeed, the start and end processing times of each task are specified to \begin{table}
\begin{tabular}{c c} \hline \hline
**Performance Indicator** & **Value** \\ \hline Objective function & 1.74 \\ Number of workers & 20 \\ Number of workstations & 10 \\ Line efficiency & 89.85\% \\ Smoothness index & 168 [s] \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Main features of the proposed optimal solution. ensure scheduling feasibility. Table 4 illustrates the workbook recommended for Worker 1 at Workstation II as an example. Using it as a support, the worker knows in detail what he is expected to do at every instant of the cycle time. Moreover, all the task sequences assigned to workers are provided in the Supplementary Materials. If some cooperation between workers is involved, a certain amount of idle time may arise between tasks when workers do not simultaneously complete the tasks previously assigned to them.