# Human Cognitive and Motor Abilities in the Aging Workforce: An Information-Based Model
## 5 A Case Study from the Automotive Industry
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & & \(\mathbf{I_{c}}\) & \(\mathbf{I_{m}}\) & \(\mathbf{I_{m,ID}}\) [bit] \\ \hline \multirow{2}{*}{**Sub-Tasks**} & \multirow{2}{*}{**WS1: Set the Thrust Ring into the Flange**} & \(\mathbf{I_{c}}\) [bit] & \(\mathbf{I_{m,ID}}\) [bit] & \(\mathbf{I_{m,MTM}}\) [bit] \\  & & **(Equation (1))** & **(Equation (8a))** & **(Equation (8b))** \\ \hline
1 & Grasp the flange & - & - & 2.66 \\
2 & Place the flange under the magnifying glass & - & 1.58 & - \\
3 & Verify the presence of the defect & 1.00 & - & - \\
4 & Put the flange in the scrap basket in the presence & - & - & 2.98 \\
4 & of the defect \({}^{*}\) & - & 1.32 & - \\
5 & Place the flange on the punching machine & - & 1.32 & - \\
6 & Grasp the thrust ring on the flange & - & - & 2.66 \\
7 & Place the thrust ring on the flange & - & 2.00 & - \\
8 & Verify the correct position of the thrust ring & 1.00 & - & - \\
9 & Push the button start on the punching machine & 2.00 & - & - \\
10 & Push the button “scrap” \({}^{*}\) on the punching & 1.00 & - & - \\  & machine(wrong punching) & 1.00 & - & - \\
11 & Grasp and put the flange in the basket (OK & - & - & 5.64 \\  & flange/NOK flange) & - & - & 5.64 \\ \hline \multirow{2}{*}{**Sub-Tasks**} & \multirow{2}{*}{**WS2: Set the Oil Seal into the Flange**} & \(\mathbf{I_{c}}\) [bit] & \(\mathbf{I_{m,ID}}\) [bit] & \(\mathbf{I_{m,MTM}}\) [bit] \\  & & **(Equation (1))** & **(Equation (8a))** & **(Equation (8b))** \\ \hline
1 & Grasp the flange & - & - & 2.66 \\
2 & Verify the punching (OK/NOK punching) & 1.00 & - & - \\
3 & Place the flange on the punching machine & - & 1.32 & - \\
4 & Verify that the oil seal side of the flange is facing & 1.00 & - & - \\
5 & Grasp the oil seal & - & - & 2.66 \\
6 & Place the oil seal on the flange & - & 2.81 & - \\
7 & Verify that the spring side of the oil seal is facing & 1.00 & - & - \\  & downwards & & 2.00 & - & - \\
8 & Push the button start on the punching machine & 2.00 & - & - \\
9 & Push the button “incorrect positioning” \({}^{*}\) (repeat & 2.00 & - & - \\
10 & Push the button “scrap” \({}^{*}\) (wrong punching) & 1.00 & - & - \\
11 & Grasp and put the flange in the basket (OK & - & - & 5.64 \\  & flange/NOK flange) & - & - & 5.64 \\ \hline \multirow{2}{*}{**Sub-Tasks**} & \multirow{2}{*}{**WS3: Set the Bushing into the Triangular Ring**} & \(\mathbf{I_{c}}\) [bit] & \(\mathbf{I_{m,ID}}\) [bit] & \(\mathbf{I_{m,MTM}}\) [bit] \\  & & **of the Flange** & **(Equation (1))** & **(Equation (8a))** & **(Equation (8b))** \\ \hline
1 & Grasp the triangular ring from the basket & - & - & 2.66 \\
2 & Place the triangular ring on the punching machine & - & 1.32 & - \\
3 & Verify the correct position of the triangular ring & 1.00 & - & - \\
4 & Grasp the bushing from the basket & - & - & 2.66 \\
5 & Place the bushing on the punching machine & - & 2.81 & - \\
6 & Verify the correct position of the bushing & 1.00 & - & - \\
7 & Push the button “punching” & 2.00 & - & - \\
8 & Verify the correct punching & 1.00 & - & - \\  & Grasp and put the flange in the basket (OK & - & - & 5.64 \\  & flange/NOK flange) & - & - & 5.64 \\ \hline \hline \end{tabular} \({}^{*}\) The corresponding time required to complete these sub-tasks is evaluated by considering 5% of scraps.  
\end{table} 
Table 8: Information content of sub-tasks performed in each workstation (WS). Being the cycle time equal to 15 (s), the operator-WS assignment that minimizes the idle time of the line can be obtained by solving the following optimization problem:  
\[\min_{[\kappa,k]}\sum_{i=1}^{5}\sum_{k=1}^{3}(T_{c}-T_{i,k})\times x_{i,k}\] (16a) subjected to: \[T_{c}-T_{i,k}\geq 0\ \forall\ i,k \tag{16b}\]  
where i = 1,...,5 is the i-th operator, k = 1,... 3 is the k-th WS, and \(x_{i,k}\) is a boolean variables of the assignment problem (\(x_{i,k}\) = 1 if the i-th operator is assigned to the k-th WS; \(x_{i,k}\) = 0 otherwise).