## 3 Results  
The purpose of the computational experiment performed in this section was two-fold. One aim was to show the effectiveness of our approach compared to the solutions already reported in the literature under the same restrictions as the reference approaches with regard to the number of cells \(p\) and cell size \(U\); the other was to provide solutions that can be used as benchmarks for comparative testing with different CF solution approaches by finding better alternative solutions that have not been reported in the literature under different values of \(p\) and \(U\). The proposed PMP-based hard computing approach has been implemented and tested with two groups of GCF incidences: 26 small to intermediate-sized problem sets available in the literature and three expanded large-sized ones. The large-sized incidences are expanded with values of \(p\) which are different from the original ones. Tables 3 and 4 show a total of 39 test incidences for 26 small to intermediate-sized original problems and a total of five expanded test incidences for three large-sized original problems, respectively. \begin{table}
\begin{tabular}{l c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Problem**} & \multicolumn{6}{c}{**Problem Size**} & \multicolumn{6}{c}{**Reference Algorithm**} & \multicolumn{6}{c}{**Proposed Approach**} \\ \cline{2-13}  & \(n\)**(\(q\))** & \(m\) & \(t\) & \(p\) & \(U\) & \(e\) & EEs & **Voids** & **GE (\%)** & \(e\) & EEs & **Voids** & **GE (\%)** & **CPU (s)** \\ \hline
1. [33] & 4 & 5 & 11 & 2 & 2 & 9 & 0 & 1 & **90.00** & 9 & 0 & 1 & **90.00** & 0.05 a + 0.044 b \\ \hline
2. [38] & 6 & 10 & 20 & 2 & 4 & 28 & 2 & 8 & **72.22** & 28 & 2 & 8 & **72.22** & 0.05 + 0.047 \\  & 6(7) & 10 & 20 & 2 & 4 & 27 & 0 & 10 & 72.97 & 31 & 0 & 8 & **79.49** & 0.09 + 0.054 \\ \hline
3. [65] & 20 & 20 & 51 & 5 & 5 & 66 & 1 & 17 & **78.31** & 67 & 6 & 16 & 73.49 & 0.09 + 0.189 \\ \hline
4. [66] & 6 & 6 & 13 & 2 & 3 & 15 & 0 & 3 & **83.33** & 15 & 0 & 3 & **83.33** & 0.05 + 0.044 \\ \hline
5. [67] & 10 & 10 & 27 & 3 & 5 & 47 & 10 & 17 & 57.81 & 49 & 12 & 12 & **60.66** & 0.08 + 0.062 \\  & 10(13) & 15 & 27 & 3 & 5 & 49 & 5 & 20 & 63.77 c & 49 & 4 & 21 & **64.29** & 0.08 + 0.050 \\ \hline
6. [68] & 7 & 14 & 32 & 3 & 3 & 31 & 5 & 6 & **70.27 d** & 29 & 5 & 6 & 68.57 & 0.06 + 0.048 \\ \hline
7. [69] & 10 & 10 & 24 & 3 & 5 & 31 & 1 & 3 & **88.24** & 31 & 1 & 3 & **88.24** & 0.08 + 0.050 \\  & 10(11) & 10 & 24 & 3 & 5 & 33 & 3 & 10 & 69.77 & 33 & 1 & 3 & **88.89** & 0.06 + 0.049 \\ \hline
8. [70] & 8 & 13 & 26 & 3 & 3 & 33 & 2 & 5 & **81.58** & 33 & 3 & 4 & 81.08 & 0.09 + 0.049 \\
9. [70] & 30 & 30 & 89 & 6 & 7 & 151 & 1 & 48 & 75.38 & 150 & 1 & 46 & **76.02** & 0.11 + 0.065 \\ \hline  & 4 & 4 & 8 & 2 & 8 & 0 & 0 & **100.00** & 8 & 0 & **100.00** & 0.05 + 0.040 \\
10. [59] & 7 & 10 & 23 & 3 & 3 & 25 & 3 & 2 & **81.48** & 23 & 4 & 5 & 67.86 & 0.06 + 0.045 \\  & 11 & 10 & 22 & 4 & 3 & 28 & 3 & 3 & **80.65** & 27 & 3 & 4 & 77.42 & 0.08 + 0.041 \\  & 26 & 28 & 71 & 6 & 7 & 124 & 16 & 25 & **72.48** & 121 & 15 & 27 & 71.62 & 0.10 + 0.059 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Computational results with small to intermediate-sized original incidences. GE: grouping efficacy. Figure 5: Block diagonal solution to the hypothetical example. The former incidences are used for comparative purposes along with the results obtained by the reference approaches; the latter incidences are used to show the effectiveness of our approach in solving large-sized GCF incidences. The double-expanded large-size incidences have been produced by following [PERSON] et al. 's data expansion scheme [80], which duplicates rows and columns of an existing intermediate-sized binary PMIM instead of using randomly generated data sets. For the original problems 6, 11, 22, 23, and 24 in Table 3, extra incidences have been tested for values of \(p\) and \(U\) different from those used the in the original problems. Some of the original data sets include information on the operation sequences and/or production volumes of parts.