# Production Planning Problem of a Two-Level Supply Chain with Production-Time-Dependent Products
## 4 Computational Experiments
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**I**} & \multirow{2}{*}{**Instances**} & \multicolumn{3}{c}{**Solutions**} & \multicolumn{3}{c}{**CPU Time (s)**} \\ \cline{3-7}  & & **CPLEX** & **Heuristic** & **PE (\%) \({}^{\ddagger}\)** & **CPLEX** & **Heuristic** \\ \hline  & 55 & 112,605 & 117,975 & 4.55 & 4699.99 & 0.02 \\  & 56 & 115,180 & 116,935 & 1.50 & \textgreater{}15,000 \({}^{\ddagger}\) & 0.01 \\  & 57 & 119,450 & 123,219 & 3.06 & \textgreater{}15,000 \({}^{\ddagger}\) & 0.02 \\  & 58 & 123,667 & 127,613 & 3.09 & 8910.81 & 0.02 \\  & 59 & 114,046 & 116,018 & 1.70 & \textgreater{}15,000 \({}^{\ddagger}\) & 0.01 \\  & 60 & 115,386 & 118,936 & 2.98 & \textgreater{}15,000 \({}^{\ddagger}\) & 0.02 \\ \hline average & & & 2.60 & 12,451.06 \({}^{\#}\) & 0.02 \\ \hline overall & & & 2.39 & 4435.22 \({}^{\#}\) & 0.02 \\ \hline \hline \end{tabular} \({}^{\dagger}\) percentage error of the heuristic solution from the solution (or the best feasible solution in case where CPLEX could not solve the instance to optimality) obtained with CPLEX; \({}^{\ddagger}\) This shows that CPLEX could not solve the instance to optimality in 15,000 s. \({}^{\#}\) This is a lower bound on the computation time.  
\end{table} 
Table 2: _Cont._ \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**I**} & \multirow{2}{*}{**Instances**} & \multicolumn{3}{c}{**Solutions**} & \multicolumn{3}{c}{**CPU Time (s)**} \\ \cline{3-7}  & & **CPLEX** & **Heuristic** & **PE (\%) \({}^{\ddagger}\)** & **CPLEX** & **Heuristic** \\ \hline
10 & 61 & 169,759 & 173,114 & 1.94 & 173.61 & 0.03 \\  & 62 & 155,805 & 158,119 & 1.46 & 9513.37 & 0.03 \\  & 63 & 167,030 & 169,765 & 1.61 & 12,856.51 & 0.02 \\  & 64 & 165,533 & 165,721 & 0.11 & \textgreater{}15,000 \({}^{\ddagger}\) & 0.02 \\  & 65 & 166,244 & 170,480 & 2.48 & 11,773.90 & 0.02 \\  & 66 & 165,533 & 167,651 & 1.26 & \textgreater{}15,000 \({}^{\ddagger}\) & 0.02 \\  & 67 & 160,947 & 167,575 & 3.96 & 3900.53 & 0.26 \\  & 68 & 152,001 & 153,545 & 1.01 & 433.19 & 0.03 \\  & 69 & 164,455 & 168,434 & 2.36 & 543.02 & 0.02 \\  & 70 & 164,631 & 168,660 & 2.39 & 4205.11 & 0.02 \\ \cline{2-7}  & \multicolumn{3}{c}{average} & & 1.49 & 10,719.57 & 0.03 \\ \hline
12 & 71 & 167,634 & 169,971 & 1.37 & 10,465.67 & 0.02 \\  & 72 & 171,343 & 175,637 & 2.44 & \textgreater{}15,000 \({}^{\ddagger}\) & 0.02 \\  & 73 & 156,004 & 161,773 & 3.57 & \textgreater{}15,000 \({}^{\ddagger}\) & 0.02 \\  & 74 & 165,812 & 170,245 & 2.60 & 5367.22 & 0.02 \\  & 75 & 160,362 & 165,337 & 3.01 & \textgreater{}15,000 \({}^{\ddagger}\) & 0.02 \\  & 76 & 174,292 & 178,776 & 2.51 & \textgreater{}15,000 \({}^{\ddagger}\) & 0.02 \\  & 77 & 162,923 & 166,636 & 2.23 & \textgreater{}15,000 \({}^{\ddagger}\) & 0.02 \\  & 78 & 160,262 & 162,809 & 1.56 & 3284.66 & 0.02 \\  & 79 & 165,380 & 166,674 & 0.78 & \textgreater{}15,000 \({}^{\ddagger}\) & 0.12 \\  & 80 & 177,514 & 181,282 & 2.08 & 5342.69 & 0.02 \\ \cline{2-7}  & \multicolumn{3}{c}{average} & & 2.22 & 11786.71 & 0.03 \\ \hline
14 & 81 & 143,200 & 146,261 & 2.09 & 2292.85 & 0.03 \\  & 82 & 148,173 & 150,786 & 1.73 & \textgreater{}15,000 \({}^{\ddagger}\) & 0.03 \\  & 83 & 140,813 & 144,716 & 2.70 & \textgreater{}15,000 \({}^{\ddagger}\) & 0.02 \\  & 84 & 144,862 & 149,986 & 3.42 & \textgreater{}15,000 \({}^{\ddagger}\) & 0.02 \\  & 85 & 143,006 & 145,343 & 1.61 & 2278.75 & 0.03 \\  & 86 & 136,539 & 140,606 & 2.89 & \textgreater{}15,000 \({}^{\ddagger}\) & 0.02 \\  & 87 & 144,260 & 149,363 & 3.42 & \textgreater{}15,000 \({}^{\ddagger}\) & 0.02 \\  & 88 & 140,587 & 144,633 & 2.80 & \textgreater{}15,000 \({}^{\ddagger}\) & 0.02 \\  & 89 & 138,474 & 142,013 & 2.49 & 14,701.13 & 0.02 \\  & 90 & 145,716 & 146,730 & 0.69 & \textgreater{}15,000 \({}^{\ddagger}\) & 0.03 \\ \cline{2-7}  & \multicolumn{3}{c}{average} & & 2.38 & 11,927.26 \({}^{\#}\) & 0.02 \\ \hline overall & & & 2.03 & 11,477.85 \({}^{\#}\) & 0.03 \\ \hline \hline \end{tabular} \({}^{\dagger}\). I \({}^{\star}\) See the footnotes of Table 2.  
\end{table}