## 5 Results of Computational Experiences  
In order to evaluate its performance, our methodology and our computer program were used to solve different instances of multi-model/mixed-model assembly lines that we found in the literature. Valid examples for our purposes are those that include task times, precedencies, scheduled production and available time, especially if the authors were interested in assigning tasks to constant workstations--although, in most cases, their objective functions are different from ours. First, original task times are transformed into unit workloads following the algorithm described in Section 4 on an electronic spreadsheet. Then, our computer program captures input data from the spreadsheet and finds the optimal solution according to our objective function.  
The first instance [11] includes 15 tasks and 3 models. Four specific tasks (2, 6, 8, 13) should be assigned to the same workstation for each model. The problem was solved on a PC with an Intel(r)Core(tm) i7-8700 processor at 3.2 GHz with 8 GB of RAM for \(\beta_{1}=\beta_{2}=1\) and the computer needed 0.06 s to find the optimal solution (Table 11). This instance was solved again for \(\beta_{1}=1\) and \(\beta_{2}=4\) (Table 11) with the same computer processor (CPU) time.  
In the second instance, [PERSON] presents a line with 19 tasks where three models are to be assembled for a production schedule of 120, 60 and 40 units of each model, respectively, during each shift [29]. The available time is not mentioned in the paper but [PERSON] assumes that the line has three workstations. For a theoretical minimum number of workstations equal to three and taking into account the amount of assembly work to be performed, the available time must be at least 414 min (this value is also mentioned in [29]). For this reason, we have repeated the same problem for values of assembly time between 414 and 480 min (one shift) for \(\beta_{1}=\beta_{2}=1\), as shown in Table 12.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Model (\(k\)):** & \multicolumn{2}{c}{**Alpha**} & \multicolumn{2}{c}{**Beta**} & \multicolumn{2}{c}{**Gamma**} \\
**Workstation** & **Tasks** & **Unit Load** & **Tasks** & **Unit Load** & **Tasks** & **Unit Load** \\
**(\(j\))** & **(\(i\))** & \(\[PERSON]^{*}\)\({}_{ik}\) & **(\(i\))** & \(\[PERSON]^{*}\)\({}_{ik}\) & **(\(i\))** & \(\[PERSON]^{*}\)\({}_{ik}\) \\ \hline
1 & 2 & 0.60 & 2 & 0.99 & 2 & 1.00 \\
2 & 1–4 & 0.94 & 1–4 & 0.90 & 1–4 & 0.65 \\
3 & 3–5–6 & 0.94 & 3–5–6 & 0.90 & 5–6 & 0.46 \\
4 & 8 & 0.60 & 8 & 0.36 & 8 & 1.00 \\
5 & 7–9–10 & 0.68 & 7–9–10 & 0.54 & 7–9–10 & 0.38 \\
6 & 11–12 & 0.94 & 11 & 0.99 & 11–12 & 0.85 \\ \hline \hline \end{tabular}
\end{table}
Table 10: Optimal assignment of tasks to workstations.  
The third instance involves 35 tasks and 6 models [49]. The problem was solved twenty times for \(\beta_{1}=1\) and \(\beta_{2}=7\) and the solver found different solutions (one example is Table 13) but all solutions were of the same quality because all required 14 workstations and in all cases, 34 of the 35 tasks could be assigned to the same workstations for the six models. Task 3240 has incompatible different precedencies for different models, and, in consequence, it behaves as two different tasks. Thus, we can consider that task 3240 was correctly assigned too.