## 4 Numerical Experiments
### Results of the Proposed Method
Negative values of average and best gaps mean that the method can find better solutions than that found by using Gurobi optimizer 9.1.1 within 12 h. (**a**) \(\alpha=200\), \(\beta=2000\). (**b**) \(\alpha=1000\), \(\beta=10,000\). \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{**(a)**} \\ \hline
**No. ** & **Ave.** & **Best** & **Worst** & **\# of Feasible** \\ \hline
1 & 2.40 & 0.00 * & 5.89 & 21 \\
2 & 0.79 & 0.00 & 4.68 & 41 \\
4 & 0.82 & 0.00 * & 2.46 & 3 \\
5 & 1.48 & 0.40 & 4.05 & 9 \\
7 & - & - & - & 0 \\
8 & 1.17 & 0.00 * & 4.41 & 23 \\
9 & - & - & - & 0 \\
10 & 1.16 & 0 \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{**(a)**} \\ \hline
**No.** & **Ave.** & **Best** & **Worst** & **\# of Feasible** \\ \hline
1 & 2.03 & 0.00 * & 5.74 & 48 \\
2 & 1.08 & 0.00 & 4.13 & 48 \\
4 & 0.43 & 0.00 * & 3.21 & 50 \\
5 & 1.75 & 0.00 * & 6.18 & 35 \\
7 & 5.19 & 0.40 & 10.18 & 41 \\
8 & 0.38 & 0.00 * & 3.51 & 50 \\
9 & 1.22 & 0.00 * & 5.33 & 50 \\
10 & 3.44 & 0.00 * & 12.36 & 50 \\ \hline \multicolumn{4}{c}{**(b)**} \\ \hline
**No.** & **Ave.** & **Best** & **Worst** & **\# of Feasible** \\ \hline
1 & 0.83 & 0.00 * & 3.56 & 50 \\
2 & 0.56 & 0.00 & 3.53 & 49 \\
4 & 0.20 & 0.00 * & 5.07 & 50 \\
5 & 1.64 & 0.00 * & 4.47 & 48 \\
7 & 3.09 & 0.00 * & 6.68 & 50 \\
8 & 0.84 & 0.00 * & 5.95 & 48 \\
9 & 0.22 & 0.00 * & 0.67 & 48 \\
10 & 1.03 & 0.00 * & 12.33 & 46 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Results of gaps in the method that adjust weight dynamically for \(n=50\). Negative values of average and best gaps mean that the methods can find better solutions than that found using the Gurobi optimizer 9.1.1 within 12 h. (**a**) Method 1 (Equations (20) and (21)). (**b**) Method 2 (Equations (22) and (23)). \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{**(a)**} \\ \hline
**No.** & **Ave.** & **Best** & **Worst** & **\# of feasible** \\ \hline
1 & 0.26 & \(-1.60\) & 2.51 & 50 \\
2 & 0.57 & \(-0.41\) & 3.15 & 50 \\
3 & 1.55 & \(-2.11\) & 8.49 & 50 \\
4 & 0.89 & \(-0.33\) & 6.49 & 50 \\
5 & \(-0.09\) & \(-3.30\) & 3.43 & 50 \\
6 & 1.73 & \(-0.31\) & 5.94 & 50 \\
7 & 0.90 & \(-0.69\) & 6.56 & 50 \\
9 & 2.02 & \(-0.10\) & 4.87 & 50 \\
10 & \(-1.32\) & \(-3.40\) & 2.19 & 50 \\ \hline \multicolumn{4}{c}{**(b)**} \\ \hline
**No.** & **Ave.** & **Best** & **Worst** & **\# of feasible** \\ \hline
1 & 1.47 & \(-1.66\) & 5.47 & 50 \\
2 & 2.24 & \(-0.50\) & 8.51 & 49 \\
3 & 2.99 & \(-2.11\) & 11.48 & 49 \\
4 & 2.20 & \(-0.33\) & 22.49 & 50 \\
5 & 0.80 & \(-3.61\) & 7.60 & 50 \\
6 & 3.60 & \(-0.69\) & 9.28 & 44 \\
7 & 1.54 & \(-0.69\) & 6.89 & 48 \\
9 & 3.23 & \(-0.15\) & 11.40 & 50 \\
10 & 0.59 & \(-3.39\) & 10.78 & 38 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Results of gaps in the method that dynamically adjusts weights for \(n=30\). Feasible solutions of instances 3 and 6 cannot be obtained by the latest version of the Gurobi optimizer 9.1.1 within 12 h. Symbol \({}^{***}\) means that an optimal solution can be obtained using the Gurobi optimizer 9.1.1 within 12 h. (**a**) Method 1 (Equations (20) and (21)). (**b**) Method 2 (Equations (22) and (23)).