## 5 Experiments
### Results  
The computer that was used in the experiments is powered by an i7 CPU running at 2.6 GHz. First, to validate the quality of our method, we compared its results to those of the mathematical model. The solver used to solve the mathematical model is CPLEX 12.6.3. Table 3 summarizes results obtained by both methods. Results represent tardiness. Computational times are also given. In case the solver does not find any solution in a reasonable computational time, the upper and lower bounds are reported.  
As we can see in Table 3, for the 10 and 15 jobs instances, our method finds an optimal solution in less time than the solver. For larger instances, the solver does not reach any optimal solution for hours while our method finds a good solution (actually the upper bound found by the solver) in a few seconds. Since the CPLEX solver ran for more than 30 h without finding a solution for the 32 jobs instance, we decided not to continue the exact resolution for larger instances, for which we propose a comparison between our method and the scheduling heuristic currently used by the company.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline Instance number & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 \\ \hline Machines & & 2 & & & 3 & & & 5 & & 10 \\ \hline Molds & 3 & 6 & 12 & 16 & 18 & 20 & 26 & 26 & 25 & 59 & 63 \\ \hline Jobs & 10 & 15 & 32 & 47 & 53 & 57 & 79 & 80 & 81 & 177 & 191 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Generated instances.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**Solver**} & \multicolumn{3}{c}{**Our Method**} \\ \hline
**Instance** & **Number of Jobs** & **Time** & **Tardiness** & **Time** & **Tardiness** \\ \hline
1 & 10 & 19 s & 38.00 & 19 s & 38.00 \\
2 & 15 & 12 min & 18.21 & 7 s & 18.21 \\
3 & 32 & 30 h & [37.65, 80.76] & 96 s & 80.76 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison of results between the solver and the hybrid method.  
Table 4 presents the results obtained for the big-sized instances with this benchmark heuristic and with our method. The comparison considers the tardiness and the number of setups. Over several replication, the shortest time needed to find one best solution is reported in the last column of the table.  
The results show that besides being easy to develop, the proposed method is effective, giving good results in reasonable computational time. In comparison with the benchmark method proposed by [30], an average reduction of 35% is achieved in tardiness. For some instances, the reduction of tardiness is as high as 65%. This can be explained by the fact that the proposed method is less constraining, as the molds are not fixed and can switch from a machine to another throughout the scheduling. Nevertheless, the proposed method leads to an increase in the number of setups. It is important to note that, since the main objective of the company was to reduce the tardiness, the number of setups was not considered in the objective function of the proposed method but for other problems or future studies, an objective function considering tardiness and number of setups, with different weights, can be considered.  
From the experimental study conducted in this section, we can thus conclude that our proposed approach brings a significant improvement in terms of tardiness when compared to the company current approach. Therefore, it is expected that the proposed approach will be implemented by the company as part of their production planning and scheduling system.