## 6 Discussion  
In our experiment in Section 4, we compare the solution of a multi-model assembly line balancing problem that we can achieve through our method with the solution reached with the creation of a combined model analyzed as a single-model line. We find that the classical approach of a combined model results in an inapplicable multi-model line. Furthermore, the results in Table 9 are better than those achieved with a combined model in Table 4 because fewer workstations are necessary and there is less idle time. The method computes the theoretical minimum number of workstations and the fraction of the production time that the line should be devoted to each model in order to achieve the desired output. As a drawback, this procedure computes the required capacity, but it does not assign tasks to workstations. This can be performed, for each model, using well-known heuristics or linear programming but by always replacing task times with workload and replacing cycle time with station capacity (typically, one operator). To go one step further, we have coded a piece of software in Python, which takes advantage of Google's solver, in order to assign tasks to workstations, with the same number of workstations for each model and even the same tasks performed at each station for each model, which gives stability to the line. The approach based on workload allows studying the three lines together, as shown in Section 4.5, leading to the solution in Table 10. This solution presents a line operated by a constant number of operators where tasks are consistently assigned to the same \begin{table}
\begin{tabular}{c c c} \hline \hline
**Workstation** & **Model 1, 2, 5 and 6** & **Model 3 and 4** \\ \hline
1 & 3230-3255-3265-3285 & 3230-3240-3255-3265-3285 \\
2 & 3245-3290-3335 & 3245-3290-3335 \\
3 & 3235-3305-3360 & 3235-3305-3360 \\
4 & 3275-3295-3300 & 3275-3295-3300 \\
5 & 3310-3315-3340 & 3310-3315-3340 \\
6 & 3250-3280-3365 & 3250-3280-3365 \\
7 & 3330-3370 & 3330-3370 \\
8 & 3345 & 3345 \\
9 & 3320-3375-3380 & 3320-3375-3380 \\
10 & 3385-3405 & 3385-3405 \\
11 & 3325-3390-3395 & 3325-3390-3395 \\
12 & 3350 & 3350 \\
13 & 3240-3270-3355 & 3270-3355 \\
14 & 3400 & 3400 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: A solution to problem from [49]. Figures represent tasks. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Available** & \begin{tabular}{c} **Theoretical** \\ **Minimum** \\ **Number** \\ **of Workstations** \\ \end{tabular} & \begin{tabular}{c} **Number of** \\ **Workstations in** \\ **Multi-Model Line** \\ \end{tabular} & \
\begin{tabular}{c} **Tasks** \\ **Assigned** \\ **to Constant** \\ **Workstations** \\ \end{tabular} &
\begin{tabular}{c} **Efficiency** \\ **Time** \\ **(s)** \\ \end{tabular} \\ \hline
480 & 2.59 & 3 & 19 & 0.86 & 0.09 \\
458 & 2.71 & 3 & 19 & 0.90 & 0.09 \\
436 & 2.85 & 3 & 18 & 0.95 & 0.12 \\
414 & 3.00 & 4 & 19 & 0.75 & 0.14 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Results of the computational experience with an instance from [29]. workstations across the different models. The resulting line can produce what was expected; it is flexible (different models, different quantities) and the resulting task distribution is directly applicable, with balanced workstations. All these characteristics agree with the principles of LM: JIT production, respect for people and reduced waste of resources. In our first additional instance, the original paper [11] was able to find, through a heuristic method (based on a procedure to balance robotic lines), a line operated by five people. For \(\beta_{1}=\beta_{2}=1\), our software found an optimal solution with five stations, where thirteen (out of fifteen) tasks--except tasks 3 and 5--were assigned to constant workstations for all the models. The solutions found in the original paper [11], although its objective function had a different purpose, correctly allocated tasks 2, 6, 8 and 13 to five workstations. Execution time cannot be compared since the paper searched for another objective.