# Linking Scheduling Criteria to Shop Floor Performance in Permutation Flowships
## 4 Computational Results
### Dominance Relationships among Scheduling Criteria
* From Table 2, it can be seen that makespan outperforms \(\sum ITH_{j}\) with respect to throughput, and, in general, with respect to \(ACT\) (with the exception of small problem instances for certain processing times' generation). Finally, regarding work in process, in general, makespan outperforms \(\sum ITH_{j}\) if \(n>m\), whereas the opposite occurs if \(m\geq n\). * Tables 3 and 4 show an interesting result: despite the problem size and/or the distribution of the processing times, makespan outperforms both \(\sum IT_{j}\) and \(CTV\) for all three shop floor performance measures considered. This result reveals that the minimisation of \(CTV\) or \(\sum IT_{j}\) are poorly linked to shop floor performance, as least compared to makespan minimisation. * Table 5 show that, regardless the generation of processing times and/or the problem size, completion time performs worse than \(\sum ITH_{j}\) for makespan, whereas it outperforms it in terms of average cycle time and work in process. * Table 6 show that, with few exception cases, the completion time outperforms \(\sum IT_{j}\) for all three SF indicators. * In Table 7, a peculiar pattern can be observed: while it can be that \(\sum C_{j}\) dominates \(CTV\) with respect to the three SF indicators, this is not the case for the random processing times, as in this case the makespan values obtained by \(CTV\) are higher than those observed for the total completion time. * In Tables 8 and 9 it can be seen that \(\sum ITH_{j}\) outperforms both \(\sum IT_{j}\) and \(CTV\) for all instance sizes and all generation of the processing times. Regarding considering the heads or not in the idle time function, this result makes clear that idle time minimisation including the heads is better with respect to all shop floor performance measures considered. * Finally, in Table 10 it can be seen that the relative performance of \(\sum IT_{j}\) and \(CTV\) with respect to the indicators depends on the type of testbed and on the problem instance size. However, in view of the scarce alignment of both scheduling criteria with any SF already detected in Tables 3, 4, 8 and 9, these results do not seem relevant for the purpose of our analysis. * If a trade-off between two shop floor performance measures is sought, for each pair of indicators it is possible to represent the set of _efficient_ scheduling criteria in a multi-objective manner, i.e., criteria for which no other criterion in the set obtains better results with respect to both two indicators considered. This set is represented in Table 11, and it can be seen that completion time minimisation is the only efficient criterion to minimise both \(WIP\) and \(ACT\). In contrast, if \(TH\) is involved in the trade-off, a better value for \(TH\) (and worse for \(ACT\) and \(WIP\)) can be obtained by minimising \(\sum ITH_{j}\), and a further better value for \(TH\) (at the expenses of worsening \(ACT\) and \(WIP\)) would be obtained by minimising \(C_{max}\). \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**LC**} & \multicolumn{3}{c}{**MC**} & \multicolumn{3}{c}{**HC**} & \multicolumn{3}{c}{**NC**} \\ \(n\) & \(m\) & **TH** & **ACT** & **WIP** & **TH** & **ACT** & **WIP** & **TH** & **ACT** & **WIP** & **TH** & **ACT** & **WIP** & **TH** & **ACT** & **WIP** \\ \hline
10 & 10 & **0.0** & **0.0** & **0.0** & **0.0** & **0.0** & **0.0** & **0.0** & **0.0** & **0.0** & **0.0** & **0.0** & **0.0** \\
20 & 50 & 100.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\
50 & 10 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\
50 & 20 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\
50 & 50 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\  & & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: \(p\)-values for rejecting the hypotheses \(H_{0}\) regarding the pair \((\sum C_{j}^{*},IT^{*})\) for different testbeds.