# 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 (\%) \({}^{\dagger}\)** & **CPLEX** & **Heuristic** \\ \hline
10 & 31 & 99,938 & 103,679 & 3.61 & 54.43 & 0.02 \\  & 32 & 100,048 & 103,625 & 3.45 & 83.15 & 0.02 \\  & 33 & 98,220 & 99,221 & 1.01 & 337.07 & 0.02 \\  & 34 & 96,713 & 97,831 & 1.14 & 65.65 & 0.02 \\  & 35 & 99,205 & 103,530 & 4.18 & 82.81 & 0.02 \\  & 36 & 97,558 & 100,409 & 2.84 & 5.59 & 0.02 \\  & 37 & 92,685 & 93,386 & 0.75 & 199.40 & 0.01 \\  & 38 & 97,727 & 98,997 & 1.28 & 17.76 & 0.01 \\  & 39 & 98,465 & 98,477 & 0.01 & 48.02 & 0.01 \\  & 40 & 95,509 & 99,563 & 4.07 & 51.15 & 0.01 \\ \cline{2-7}  & \multicolumn{1}{c}{average} & \multicolumn{3}{c}{2.27} & 94.50 & 0.02 \\ \hline
12 & 41 & 99,004 & 102,985 & 3.87 & 138.18 & 0.02 \\  & 42 & 95,393 & 99,588 & 4.21 & 94.93 & 0.02 \\  & 43 & 95,428 & 96,940 & 1.56 & 316.49 & 0.02 \\  & 44 & 100,728 & 102,010 & 1.26 & 4005.74 & 0.02 \\  & 45 & 92,420 & 93,997 & 1.68 & 394.93 & 0.02 \\  & 46 & 96,613 & 98,264 & 1.68 & 895.34 & 0.02 \\  & 47 & 96,676 & 101,203 & 4.47 & 167.93 & 0.02 \\  & 48 & 92,614 & 93,242 & 0.67 & 486.23 & 0.01 \\  & 49 & 91,582 & 92,525 & 1.02 & 575.96 & 0.01 \\  & 50 & 92,176 & 94,345 & 2.30 & 525.38 & 0.02 \\ \cline{2-7}  & \multicolumn{1}{c}{average} & \multicolumn{3}{c}{2.30} & 760.11 & 0.02 \\ \hline
14 & 51 & 115,364 & 119,444 & 3.42 & 8736.24 & 0.02 \\  & 52 & 111,140 & 113,723 & 2.27 & \textgreater{}15,000 \({}^{\ddagger}\) & 0.02 \\  & 53 & 117,477 & 118,300 & 0.70 & \textgreater{}15,000 \({}^{\ddagger}\) & 0.02 \\  & 54 & 110,723 & 113,863 & 2.76 & 12,163.61 & 0.01 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results of the test on 8-period instances. \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 (\%) \({}^{\dagger}\)** & **CPLEX** & **Heuristic** \\ \hline
14 & 69,480 & 70,481 & 1.42 & 11.13 & \textless{}0.01 \\  & 15 & 66,838 & 69,198 & 3.41 & 18.30 & \textless{}0.01 \\  & 16 & 63,811 & 66,202 & 3.61 & 10.19 & \textless{}0.01 \\  & 17 & 68,788 & 71,314 & 3.54 & 10.58 & \textless{}0.01 \\  & 18 & 66,745 & 67,238 & 0.73 & 20.91 & \textless{}0.01 \\  & 19 & 69,016 & 70,455 & 2.04 & 36.71 & \textless{}0.01 \\  & 20 & 66,568 & 68,379 & 2.65 & 5.08 & 0.01 \\ \cline{2-7}  & \multicolumn{1}{c}{average} & \multicolumn{3}{c}{2.88} & 14.99 & \textless{}0.01 \\ \hline
14 & 21 & 67,916 & 70,694 & 3.93 & 8.09 & 0.01 \\  & 22 & 61,201 & 62,444 & 1.99 & 15.28 & 0.01 \\  & 23 & 60,641 & 63,014 & 3.77 & 16.34 & 0.02 \\  & 24 & 60,307 & 61,645 & 2.17 & 32.15 & 0.01 \\  & 25 & 64,082 & 66,033 & 2.95 & 16.37 & 0.02 \\  & 26 & 69,131 & 71,795 & 3.71 & 15.77 & 0.01 \\  & 27 & 66,336 & 67,238 & 1.34 & 16.75 & 0.01 \\  & 28 & 67,969 & 69,926 & 2.80 & 15.75 & 0.01 \\  & 29 & 68,762 & 70,799 & 2.88 & 64.61 & 0.01 \\  & 30 & 66,468 & 68,441 & 2.88 & 14.84 & 0.01 \\ \cline{2-7}  & \multicolumn{1}{c}{average} & \multicolumn{3}{c}{2.86} & 21.60 & 0.01 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: \(Cont.\)