## 5 Results
### Initial Parameters  
A general full factorial design [42] was implemented in order to select the initial parameters for the Tabu list-based algorithm. The selected response variable was the total planning cost and the experimental factors included three basic parameters: The number of iterations, the Tabu tenure, and the number of candidate solutions per iteration. Each experimental factor had three experimental levels (as shown in Table 5). The selected levels were defined according to prior tests with every group of instances and by considering the number of \begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value** \\ \hline \(i\) & 50, 100, or 200 SKU \\ \(i\)* & 15, 30, or 60 final products \\ \(t\) & 25, 50, or 75 planning periods \\ \(r\) & 5, 10, or 20 resources \\ \(k\) & 50, 100, or 200 strokes \\ \(D_{i,t}\) & Uniform [1000, 2000] \\ \(h_{i,t}\) & Uniform [10, 20] \\ \(\text{CO}_{k,t}\) & Uniform [5, 8] \\ \(CS_{k,t}\) & Uniform [5, 10] \\ \(SO_{i,k}\) & Uniform [35, 50] \\ \(SI_{i,k}\) & Uniform [4, 8] \\ \(LT_{k}\) & Uniform [1, 2] \\ \(KAP_{r,t}\) & Uniform [2000, 6000] \\  & Uniform [4000, 8000] \\  & Uniform [12,000, 14,000] \\ \(TO_{k,r}\) & Uniform [2, 5] \\ \(TS_{k,r}\) & Uniform [5, 10] \\ \hline \end{tabular}
\end{table} 
Table 4: Parameter settings for randomly-generated test cases [28]. Figure 2: The identification system for test instances [28]. SKU, Stock Keeping Unit. iterations where the solution improvement rate become smaller and stable. The response variables were the total planning cost and the total computational time. Two problem sizes were defined: TI1-SKU50-P15-T25-R10-K50 for small problems and TI7-SKU200-P60-T75-R30-K50 for large problems. The total computational time was measured and the total planning cost was calculated. Normality, homoscedasticity, and an independence test were performed, and the results of the analysis of variance (ANOVA) for both problem sizes are shown in Tables 6-9. \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Source** & **DF** & **Adj. MS** & **F** & \(\boldsymbol{p}\) \\ \hline Tabu\_Tenure & 2 & 5.68 \(\times\) 10\({}^{12}\) & 5.13 & 0.037 \\ Iterations & 2 & 1.65 \(\times\) 10\({}^{14}\) & 149.4 & 0.000 \\ Candidate\_Sol. & 2 & 3.99 \(\times\) 10\({}^{13}\) & 36.04 & 0.000 \\ Tabu\_Tenure *Iterations & 4 & 3.21 \(\times\) 10\({}^{12}\) & 2.9 & 0.094 \\ Tabu\_Tenure *Candidate Sol. & 4 & 8.33 \(\times\) 10\({}^{11}\) & 0.75 & 0.583 \\ Iterations *Candidate Sol. & 4 & 6.64 \(\times\) 10\({}^{12}\) & 6 & 0.016 \\ Error & 8 & 1.11 \(\times\) 10\({}^{12}\) & & \\ Total & 26 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: ANOVA for total planning cost in small problems. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Response Variables** & **Experimental Factor** & **Experimental Levels** \\ \hline \multirow{6}{*}{Total Planning Cost Total Computational Time} & \multirow{2}{*}{Number of Iterations} & 25 \\  & & 50 \\  & & 75 \\ \cline{1-1} \cline{2-3}  & & 1/4 of Number of Iterations \\ \cline{1-1} \cline{2-3}  & & 1/2 of Number of Iterations \\ \cline{1-1} \cline{2-3}  & & 3/4 of Number of Iterations \\ \cline{1-1} \cline{2-3}  & & 5 \\ \cline{1-1} \cline{2-3}  & & 10 \\ \cline{1-1} \cline{2-3}  & & 15 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Experimental factors and levels. \begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Source** & **DF** & **Adj. MS** & **F** & \(\boldsymbol{p}\) \\ \hline Tabu\_Tenure & 2 & 5.68 \(\times\) 10\({}^{12}\) & 5.13 & 0.037 \\ Iterations & 2 & 1.65 \(\times\) 10\({}^{14}\) & 149.4 & 0.000 \\ Candidate\_Sol. & 2 & 3.99 \(\times\) 10\({}^{13}\) & 36.04 & 0.000 \\ Tabu\_Tenure *Iterations & 4 & 3.21 \(\times\) 10\({}^{12}\) & 2.9 & 0.094 \\ Tabu\_Tenure *Candidate Sol. & 4 & 8.33 \(\times\) 10\({}^{11}\) & 0.75 & 0.583 \\ Iterations *Candidate Sol. & 4 & 6.64 \(\times\) 10\({}^{12}\) & 6 & 0.016 \\ Error & 8 & 1.11 \(\times\) 10\({}^{12}\) & & \\ Total & 26 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: ANOVA for total planning cost in small problems.