## 4 Sensitivity Analysis  
The sensitivity analysis is applied to the sample problem to analyze parts demands, worker capacities, machine capacities, and tool capacities for the optimal objective function value. Figure 2 illustrates the effects of the demands of all parts on the optimal objective value. With the increase in demands, the increase in optimum value is seen in the figure. These changes seen in Figure 2 result from the changes in the routings and the values of the objective function items. In this analysis, there are changes in the demand for each part type by decreasing or increasing 10 units at specific intervals. The demand value for Part 1 is 100, which is higher than the demands for the other parts. As a result, the sensitivity analysis ranges from 50 to 150 and has a different starting point on the graph compared to the other parts in Figure 2. For instance, when the demand for Part 1 increases from 100 to 150, the total objective function increases by approximately 5.52%. This means that the current situation for the demand for Part 1 performs better than such an increase. In Figure 3, the worker capacities' effects on the objective function value are presented. As shown in this figure, generally, an increase in worker capacities can increase the optimum objective function value. \begin{table}
\begin{tabular}{l l l l l} \hline \hline \multirow{2}{*}{**Part**} & \multirow{2}{*}{**Optimal Route**} & \multicolumn{3}{l}{**Machine Operation Sequence and Total**} \\  & & & **Number and Types of Tools Used** \\ \hline
1 & Route 2 & M1-J1(2), J2(3)-M3-J1(3)-M4-J2(3), J5(2) \\
2 & Route 1 & M2-J1(3), J2(3)-M4-J2(3), J5(2) \\
3 & Route 3 & M2-J3(3)-M4-J5(2)-M5-J1(3)-M6-J1(4) \\
4 & Route 1 & M3-J1(7)-M5-J3(3) \\ \hline \hline \end{tabular}
\end{table} 
Table 10: The optimal routing, machine operation sequence, and tools of the sample problem. \begin{table}
\begin{tabular}{l l l l l l l} \hline \hline  & \multicolumn{2}{l}{**Cell 1**} & \multicolumn{4}{c}{**Cell 2**} \\ \hline
**Machine** & M1 & M2 & M3 & M4 & M5 & M6 \\ \hline Utilization rate & 0.181 & 0.355 & 0.540 & 0.616 & 0.360 & 0.133 \\ \hline
**Worker** & I1 & I2 & & I3 & I4 & \\ \hline Utilization rate & 0.857 & 0.468 & & 0.909 & 0.730 & \\ \hline \hline \end{tabular}
\end{table} 
Table 11: The machine and worker utilization rate in cells. Figure 2: Effects of part demands. In this analysis, there are changes in the capacities of workers by decreasing or increasing 10 units at specific intervals. The capacity value of Worker 1 is 385, which is higher than the capacities of other workers. Consequently, the sensitivity analysis for Worker 1 is changed within the range of 345-425, and it indicates a distinct starting point on the graph compared to the other workers in Figure 3.  
The effects of machine capacities on objective function values are presented in Figure 4. The changes in the capacity of Machine 5 in Cell 2 do not affect the objective function value. It is also seen in Figure 4 that an increase in the capacities of Machines 3 and 4 leads to a simultaneous reduction in the objective function value. As a specific example, when the capacity of Machine 3 decreases from 1000 to 900, the total objective function value increases by approximately 0.14%. In Figure 5, it is shown how the changes in tool capacities affect the objective function values. An increase or decrease in the capacity value of Tool 2 of Machine 6, located in Cell 2, does not change the objective function value. For this analysis, as a specific example, decreasing the capacity of Tool 2 in Machine 4 from 17 to 5 results in an increase in the total objective function value of approximately 5.44%. Figure 4: Effects of machine capacities. Figure 3: Effects of worker capacities. In this study, sensitivity analysis evaluates the effect of changes in part demands, machine capacities, tool capacities, and workforce capacities on the objective function.