## 6 Experimental Tests
### Model Validation and Comparison Results
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{\(i=j\)} & **Demand** & \multirow{2}{*}{\(p_{[T]}\)} & \multicolumn{3}{c}{**HCLP**} & \multicolumn{3}{c}{**MCLP–MCLP**} & \multicolumn{3}{c}{**MCLP–SCLP**} & \multicolumn{3}{c}{**SCLP–SCLP**} \\  & & & **\%** & **Z** & **Y** & **T** & **\%** & **Z** & **Y** & **T** & **\%** & **Z** & **Y** & **T** & **\%** & **Z** & **Y** & **T** \\ \hline \multirow{4}{*}{50} & Low & 4 & 82 & 4.5 & 5.2 & 6 & 82 & 3.5 & 4.7 & 10 & & NS & & 0 & 5 & 7.5 & 1 \\  & Low & 5 & - & - & - & - & 89 & 4.5 & 5 & 8 & 76 & 5 & 8.1 & 3 & - & - & - & - \\  & High & 4 & 76 & 4.5 & 5.5 & 3 & 76 & 3.5 & 5.4 & 10 & & NS & & 0 & 5 & 7.25 & 2 \\  & High & 5 & - & - & - & - & 82 & 4.5 & 5 & 11 & 70 & 5 & 8.5 & 3 & - & - & - & - \\ \hline \multirow{4}{*}{100} & Low & 5 & 68 & 5.5 & 6.3 & 84 & 63 & 3.7 & 5.2 & 98 & 25 & 5 & 11.4 & 397 & 21 & 6 & 12.9 & 292 \\  & Low & 6 & - & - & - & - & 68 & 4.5 & 6.3 & 100 & 27 & 6 & 11 & 584 & - & - & - & - \\  & High & 5 & 62 & 5.7 & 6.5 & 53 & 61 & 4.2 & 6.6 & 45 & & NS & & 30 & 7 & 15.8 & 485 \\  & High & 6 & - & - & - & - & 60 & 4.2 & 6.1 & 32 & & NS & & - & - & - \\ \hline \multirow{4}{*}{150} & Low & 7 & 83 & 7.5 & 10 & 499 & 76 & 5.7 & 8.5 & 1020 & & NS & & 28 & 21.7 & 26.4 & 1023 \\  & Low & 8 & - & - & - & - & 72 & 4.7 & 8.1 & 1015 & & NS & & - & - & - & - \\ \cline{1-1}  & High & 7 & 76 & 8 & 10.1 & 672 & 62 & 4.7 & 8.5 & 1025 & & NS & & 28 & 150 & 301 & 1029 \\ \cline{1-1}  & Low & 8 & - & - & - & - & 48 & 3.7 & 6.3 & 1022 & 28 & 24 & 1020 & - & - & - & - \\ \hline \multirow{4}{*}{200} & Low & 14 & 55 & 14 & 11.6 & 1083 & & & & & & & & & & & & \\ \cline{1-1}  & High & 14 & 46 & 14 & 11.7 & 1076 & & & & & & & & & & & & \\ \hline \multirow{4}{*}{250} & Low & 21 & 52 & 21.7 & 15.1 & 1115 & & & & & & & & & & & & & \\ \cline{1-1}  & High & 21 & 43 & 21.7 & 15.1 & 1757 & & & & & & & & & & & & & \\ \hline \hline \end{tabular}  
* RE: resource exceeded and NS: no solution.  
\end{table} 
Table 7: Computational results to compare different variants for four regions. The number of variables is the same in all variant problems, but the number of constraints is different, which has an influence on the efficiency of the results. As the Constraints of (8)-(11), (13)-(15), and (19) are the same in all problems, we name this set of constraints \(\Delta\), and our comparison takes into account the rest of the constraints in each problem. The number of constraints and an example of the problem with 50 demand points studied as the first problem in Table 3 is included in Table 8. In our test problems, the number of modules and strategic and tactical periods do not take large values, but it is the number of demand points that has a considerable impact by augmenting the size of problems. Therefore, it can be concluded that SCLP-SCLP has the largest number of constraints, and the order after SCLP-SCLP is MCLP-SCLP, HCLP, and MCLP-MCLP. However, the computational times of problems and the fact that MCLP-MCLP/MCLP-SCLP exceeded resources/no solution results for most of the test problems, the difference in the number of constraints does not have a significant impact on the quality of the results or computational time.