# An Algorithm for Part Input Sequencing of Flexible Manufacturing Systems with Machine Disruption
## 3 Proposed Algorithm
\(\xi_{u}=-5K\) for \(A_{u}(t),\xi_{v}=-3K\) for \(A_{v}(t),\xi_{m}=-K\) for \(A_{m}(t),\xi_{v}=0\) for \(A_{n}(t)\). \(K=0.55\). Obtain the weight function \(\widetilde{\lambda}\) applying Equations (15) and (18). Obtain the overall function \(\widetilde{\lambda}\) by Equations (16), (17) and (20). Step 9. Obtain the minimal value of \(\tilde{\lambda}\), \(\tilde{\lambda}(t)=\min_{b_{ii}\in A_{x}(t)}\{\tilde{\lambda}_{q}(t,b_{hi}),q =u,v,m,n\}\). Obtain the input part \(b^{*}=\left\{b_{hi}|b_{hi}\in A_{x}(t)\wedge a_{hi}=\min_{b_{hi}\in A_{x}(t)}\{ \left.a_{hi}|\tilde{\lambda}_{q}(t,b_{hi})=\tilde{\lambda}(t),q=u,v,m,n\right\} \right\}\), \(\delta(t)=0\). \(u(t)=m_{hi1}+t\), \(t=u(t)\). Step 10. If \(\rho(t)=1\), \(u(t)=f_{b_{hi}k}(t)\), \(t=u(.)\). Obtain \(m_{b_{hi}k}(t)\), \(g=m_{b_{hi}k}(t)\), \(\rho(t)=0\), Obtain machine queue set \(A_{g}(t)=\left\{b_{hi}|g_{h,gg}(t)=1\right\}\), else go to Step 2. Step 11. Identify the part to be processed in the following. \(p^{*}=\left\{b_{hi}|b_{hi}\in A_{g}(t)\wedge a_{hi}=\min_{b_{hi}\in A_{\lambda _{g}(t)}}\{\left.a_{hi}|d_{hi}=\min_{b_{hi}\in A_{g}(t)}d_{hi}\right\}\right\} \right\}\), \(g_{h,gg}(t)=0\), go to Step 2. ```
**Algorithm 1**_Cont._ \begin{table}
\begin{tabular}{c l l} \hline \hline
**Notation** & \multicolumn{2}{c}{**Explanation**} \\ \hline  & & Indices and Sets \\ \(g\) & Machine queue set indicator & \\ \(J\) & Machine set, \(J=\{1,2,\cdots,M\}\) & \\ \(q\) & Part set indicator & Parameters \\ \(a_{hi}\) & Arrival time of \(b_{hi}\) & \\ \(d_{hi}\) & Due date of \(b_{hi}\) & \\ \(K\) & Constant & \\ \(M\) & Number of machines & \\ \(m_{hik}\) & Robot move time for \(k\) of \(b_{hi}\) & \\ \(S\) & Size of preprocess area & \\ \(T\) & Production cycle & \\ \(t_{0}\) & Initial time & \\ \(\xi_{q}\) & Weight of \(A_{q}(t)\) & \\ \(A_{c}(t)\) & Part set for processing at \(BM(t)\) & \\ \(A_{e}(t)\) & Part set needs repairing at \(t\) & \\ \(A_{g}(t)\) & Machine queue set \(g\) at \(t\) & \\ \(A_{o}(t)\) & Part set for not processing at \(BM(t)\) & \\ \(A_{q}(t)\) & Part set \(q\) at \(t\) & \\ \(A_{y}(t)\) & Part set \(y\) at \(t\) & \\ \(b^{*}\) & Part for inputting & \\ \(BM(t)\) & Broken machine at \(t\) & \\ \(c_{hi}\) & Completion time of \(b_{hi}\) & \\ \(f_{b_{hi}k}(t)\) & Completion time of \(k\) of \(b_{hi}\) at \(t\) & \\ \(g_{h_{hi}g}(t)\) & \(g_{h_{hi}g}(t)=\left\{\begin{array}{ll}1,&b_{hi}&\text{is in }A_{g}(t);\\ 0,&\text{otherwise.}\\ 1,&b_{hi}&\text{is in }A_{g}(t);\\ 0,&\text{otherwise.}\\ m_{b_{hi}k}(t)\) & Machine finishing \(k\) of \(b_{hi}\) at \(t\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Additional symbols utilized in Algorithm 1. The proposed MDH Algorithm (Algorithm 1) is a dynamic algorithm. It utilizes the information of the dynamic workload to make an input decision. The dynamic workload is described in [5]. When a part completes operations, Algorithm 1 then inputs a part dynamically. The proposed algorithm identifies a broken machine on an FMS shop floor. It also identifies part processing at a broken machine. The algorithm handles machine breakage according to a different part processing status at a broken machine to identify parts for inputting. Advanced information technology like RFID can be applied for the implementation of a shop floor monitoring system. The shop floor monitoring system collects and processes dynamic information on an FMS shop floor. The proposed algorithm runs with the shop floor monitoring system that applies RFID to identify and handle machine breakage. ## 4 Evaluation with Result Analyses

The evaluation of the proposed algorithm is based on a simulation. It is difficult to simulate machine breakage and repair in flexible manufacturing systems in real-world production environments. Therefore, the proposed Algorithm 1 is evaluated by simulation experiments and statistical analyses in the situation with no machine breakage. The proposed algorithm is compared to an FMS part input sequencing algorithm, the state-dependent part input algorithm (SPI algorithm) in the literature [31].