## 4 Experiment Results
### Experiments  
In this section, we outline different experiments that were conducted to evaluate the performance of the \(QM\) and the proposed algorithm. In all experiments, Central Processing Unit time (\(CPUt\)) represents the time in seconds required to find the optimal or best feasible solution. Tables 5 and 6 show the results obtained by \(QP\) and \(MA\) for small and large job processing times, respectively. Table 5 clearly shows that the proposed algorithm was generating optimal solutions with a \(CPU\) time of less than 1 second for all problem instances. Quadratic model \(QM\) was also able to provide optimal schedules in a reasonable time. By considering much longer processing times than in the previous data series, we still obtained optimal solutions in reasonable \(CPU\) time even though the quadratic model became slower than in the first batch of problem instances. The proposed algorithm outperformed the quadratic model in terms of computational time that was still less than 1 second. Table 6 confirms these observations. \begin{table}
\begin{tabular}{l l} \hline Number of machines (\(m\)) & \(m\in\{30,31,32,\ldots,...,80\}\) \\ Number of jobs (\(n\)) & \(n=2m+1\) \\ Machine speed (\(s_{i}\)) & \(s_{i}\in U(1,5)\) \\ Job processing time (\(p_{j}\)) & \(p_{j}\in U(1,100)\) \\ Number of unavailability periods (\(n_{i}\)) & \(n_{i}=2\;\forall i=1,\ldots,m\) \\ Duration of an unavailability period on machine \(i\) (\(t_{i}\)) & \(t_{i}=10\;\forall i=1,\ldots,m\) \\ Length of time interval between two consecutive unavailability periods on machine \(i\) (\(T_{i}\)) & \(Ti=20i\) \\ \hline \end{tabular}
\end{table} 
Table 4: \(DS2\) parameters. \begin{table}
\begin{tabular}{l l} \hline Number of machines (\(m\)) & \(m\in\{2,3,5\}\) \\ Number of jobs (\(n\)) & \(n\in\{20,30,40,50,60,70,80\}\) \\ Machine speed (\(t_{i}\)) & \(s_{i}\in U(1,5)\) \\ Job processing time (\(p_{j}\)) & \(p_{j}\in U(5,50)\) and \(p_{j}\in U(50,100)\) \\ Number of unavailability periods (\(n_{i}\)) & \(n_{i}=\;m\;\forall i=1,\ldots,m\) \\ Duration of an unavailability period on machine \(i\) (\(t_{i}\)) & \(t_{i}=10,\;if\;p_{j}\in U(5,50)\) and \(t_{i}=15,\;if\;p_{j}\in U(50,100)\;\forall i=1,\ldots,m\) \\ Length of time interval between two consecutive unavailability periods on machine \(i\) (\(T_{i}\)) & \(Ti=25i,\;if\;p_{j}\in U(5,50)\) and \(T_{i}=50i,\;if\;p_{j}\in U(50,100)\) \\ \hline \end{tabular}
\end{table} 
Table 3: \(DS1\) parameters. In order to investigate the limitations of the proposed quadratic model, a second dataset series, namely, \(DS2\) was considered. Table 7 reports the computational results for both \(QM\) and \(MA\). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(m\) & \(n\) & \(C_{max}(QM)\) & \(C_{max}(MA)\) & \(CPUtt(QP)\) & \(CPUtt(MA)\) \\ \hline  
\hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of \(QM\) and \(MA\) for datasets \(DS1\) with \(s_{i}\in U(1,5)\) and \(p_{j}\in U(50,100)\). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(m\) & \(n\) & \(C_{max}(QM)\) & \(C_{max}(MA)\) & \(CPUtt(QM)\) & \(CPUtt(MA)\) \\ \hline  
\hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of \(QM\) and \(MA\) for datasets \(DS1\) with \(s_{i}\in U(1,5)\) and \(p_{j}\in U(5,50)\). The computational results displayed in Table 7 show that quadratic model \(QM\) was able to generate an optimal solution within a time limit for problems with up to 73 machines. On the basis of the computational results shown in Table 7, the quadratic model was not able to generate optimal solutions in a reasonable time and for bigger problems. Therefore, proposed procedure \(MA\) was tested for large-sized problems and compared to an adapted form of \(MLPT\), proposed earlier by the author of this paper in [7]. Table 8 reports the obtained results for problem instances with \(m\in\{100,200,300,400,500,600,.,700,800,1000\}\) and \(n=2m+1\). Table 8 shows that \(MA\) outperformed \(MLPT\) for all problem instances with slightly higher \(CPU\) time than the time of \(MLPT\)\(CPU\) for most instances.