# An Algorithm for Part Input Sequencing of Flexible Manufacturing Systems with Machine Disruption
## 3 Proposed Algorithm
The absolute improvement and relative improvement of Algorithm 1 versus Algorithm A1 for all performance measures TP, MF, and RU are also in Table 2.

It can be seen from the table that the averages of TP, MF, and RU by the proposed Algorithm 1 are 1254.9 parts, 86.4 min, and 71.03%, respectively. The averages of TP, MF, and RU by the comparative Algorithm A1 are 1251.8 parts, 87.4 min, and 70.87%, respectively. Algorithm 1 has better performance than Algorithm A1 for all performance measures of TP, MF, and RU as shown in the table. In the table, the absolute improvements \(\omega\) of TP, MF, and RU by Algorithm 1 versus Algorithm A1 are 3.1 parts, 0.98 min, and 0.16%, respectively. The relative improvements \(\varpi\) of TP, MF, and RU for Algorithm 1 versus Algorithm A1 are 0.25 parts, 1.12 min, and 0.23%, respectively. The absolute and relative improvements in the table display the improvements of all the performance measures: TP, MF, and RU. The values in the table display that all performance measures obtained by Algorithm 1 are better than those obtained by Algorithm A1. Significance tests are applied. The paired \(t\)-tests are conducted. The significance level is 0.1. The \(t\)-test statistic has the critical value of 1.37 at a significance level of 0.1. The test statistics obtained for the relative improvements by Algorithm 1 are 1.4, 2.44, and 1.17 for TP, MF, and RU, respectively, as illustrated in Table 2. The results show that TP and MF are improved significantly. Because MF improves, parts are produced faster with more parts \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Measure** & **TP** & **MF** & **RU** \\  & **(Parts)** & **(Minutes)** & **(\%)** \\ \hline Algorithm 1 & **1254.9** & **86.38** & **71.03** \\ Algorithm A1 & 1251.8 & 87.36 & 70.87 \\ \(\omega\) & **3.1** & **0.98** & **0.16** \\ \(\varpi\) (\%) & **0.25** & **1.12** & **0.23** \\ Test statistic & 1.4 * & 2.44 * & 1.17 \\ \hline \hline \end{tabular} Note: A bold number indicates the improvement of a performance measure. * indicates significant improvement of a performance measure.

\end{table} 
Table 2: Comparison of Algorithm 1 to Algorithm A1. produced. That TP and MF are significantly improved indicates a significant production increase. The results indicate that production is significantly increased by Algorithm 1 in comparison to Algorithm A1. In summary, the comparative results show significant production increase by Algorithm 1 compared to Algorithm A1. All performance measures of TP, MF, and RU obtained by Algorithm 1 show improvements in comparison to the comparative Algorithm A1. The comparative results indicate that the performance of Algorithm 1 is improved compared to Algorithm A1. That is, Algorithm 1 is superior to Algorithm A1 from the literature in the situation with no machine breakage. ## 5 Conclusions and Future Work

Disruption happens in the real world in supply chain and production environments. This paper studies disruption handling of machine breakage in FMS part input sequencing. The MDH Algorithm is proposed for part input sequencing of FMSs with machine breakage. The proposed algorithm is based on reactive scheduling. Because of the difficulty in simulating FMS machine breakage and repair in real-world production environments, the proposed algorithm is evaluated in a situation with no machine breakage. The proposed algorithm is compared to an existing FMS part input sequencing algorithm from the literature, the state-dependent part input algorithm. The comparative results indicate that the proposed MDH Algorithm improves the performance significantly, generating the significant increase in total parts produced and mean flowtime decrease in the situation with no machine breakage. The evaluation results indicate the superiority of the MDH Algorithm in comparison to the state-dependent part input algorithm in terms of total parts produced, mean flowtime, and robot utilization in the situation with no machine breakage.