# The Role of Industry 4.0 and Circular Economy for Sustainable Operations: The Case of Bike Industry
## 3 Model Formulation
### Sensitivity Analysis

I4.0 is identified as one of the main determinants to drive the application towards a more sustainable production through an economy that reuses, reduces, and recycles resources. The numerical examples in the above subsection are considered to study the effects of changes in the system parameters (\(p_{1}\), \(h_{f}\), \(h_{e}\), \(h_{g}\delta_{1}\), \(\theta_{2}\), \(\theta_{f}\), \(c_{pf}\), \(c_{pe}\), \(e_{r}\), \(g_{g}\), \(\alpha\), \(\beta\) and \(\gamma\)) on the optimal values of \(p^{*}\), \(t_{1}^{*}\), \(t_{4}^{*}\) and \(AC(p^{*}\), \(t_{1}^{*}\), \(t_{4}^{*})\). Therefore, the effects of changes in the parameters of a model are determined by solving the model and comparing the results with respect to changes made with parameters by +50%, +25%, -25%, and -50%, taking one parameter at a time and keeping the remaining parameters unchanged. The analytical results are shown in Tables 3 and 4. Other detailed results are tabulated in Table 5 to illustrate some managerial insights for bike company. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multirow{2}{*}{**Change (\%)**} & \multicolumn{5}{c}{**Optimal Solutions**} \\ \cline{3-6}  & & \(\mathbf{p^{*}}\) & \(\mathbf{t_{1}^{*}}\) & \(\mathbf{t_{4}^{*}}\) & \(\mathbf{AC(p^{*},t_{1}^{*},t_{2}^{*})}\) \\ \hline \multirow{4}{*}{\(p_{1}\)} & 50\% & 436.98 & 1.0686 & 3.7668 & 4020.82 \\  & 25\% & 419.47 & 1.1776 & 3.1692 & 3916.01 \\  & \(-\)25\% & 362.76 & 1.8736 & 3.0194 & 2706.39 \\  & \(-\)50\% & 278.78 & 2.6666 & 2.7895 & 2601.58 \\ \hline \multirow{4}{*}{\(h_{f}\)} & 50\% & 337.439 & 1.9686 & 3.3733 & 3903.41 \\  & 25\% & 344.952 & 1.8761 & 3.1449 & 3857.31 \\  & \(-\)25\% & 446.238 & 0.8659 & 3.0315 & 2765.10 \\  & \(-\)50\% & 451.165 & 0.8567 & 3.0256 & 2719.00 \\ \hline \multirow{4}{*}{\(h_{e}\)} & 50\% & 394.441 & 1.1452 & 2.7618 & 3284.07 \\  & 25\% & 394.957 & 1.1561 & 2.7758 & 3256.24 \\  & \(-\)25\% & 399.771 & 1.6601 & 3.8019 & 2972.56 \\  & \(-\)50\% & 399.592 & 1.6898 & 3.8199 & 2900.73 \\ \hline \multirow{4}{*}{\(h_{g}\)} & 50\% & 383.598 & 1.1781 & 3.9862 & 2917.13 \\  & 25\% & 386.711 & 1.1949 & 3.3030 & 2972.77 \\  & \(-\)25\% & 425.238 & 1.6743 & 2.4454 & 3384.04 \\  & \(-\)50\% & 430.651 & 1.7204 & 2.3511 & 3539.67 \\ \hline \multirow{4}{*}{\(c_{pf}\)} & 50\% & 402.703 & 1.1912 & 3.3701 & 3817.24 \\  & 25\% & 399.703 & 1.2012 & 3.1701 & 3814.22 \\  & \(-\)25\% & 391.703 & 1.2212 & 2.9701 & 3808.18 \\  & \(-\)50\% & 382.703 & 1.2312 & 2.8701 & 3805.16 \\ \hline \multirow{4}{*}{\(c_{pg}\)} & 50\% & 502.322 & 1.2312 & 5.1512 & 2969.65 \\  & 25\% & 457.434 & 1.2212 & 4.1232 & 2966.42 \\  & \(-\)25\% & 348.447 & 1.1912 & 2.9871 & 2960.98 \\  & \(-\)50\% & 300.512 & 1.1812 & 2.5678 & 2957.75 \\ \hline \multirow{4}{*}{\(c_{pe}\)} & 50\% & 406.568 & 2.1664 & 3.2438 & 3135.37 \\  & 25\% & 401.717 & 1.3311 & 3.2384 & 2973.28 \\  & \(-\)25\% & 379.631 & 0.9036 & 1.1935 & 2649.12 \\  & \(-\)50\% & 344.729 & 0.6090 & 1.1775 & 2487.04 \\ \hline \multirow{4}{*}{\(\theta_{1}\)} & 50\% & 401.325 & 1.2071 & 3.9700 & 2963.24 \\  & 25\% & 399.172 & 1.2092 & 3.7712 & 2963.24 \\  & \(-\)25\% & 396.091 & 1.2112 & 2.9189 & 2962.02 \\  & \(-\)50\% & 392.858 & 1.2134 & 2.8650 & 2961.84 \\ \hline \multirow{4}{*}{\(\theta_{2}\)} & 50\% & 398.501 & 1.2108 & 3.0691 & 2963.24 \\  & 25\% & 398.603 & 1.2111 & 3.0698 & 2963.14 \\ \cline{1-1}  & \(-\)25\% & 398.901 & 1.2115 & 3.0710 & 2963.03 \\ \cline{1-1}  & \(-\)50\% & 398.921 & 1.2118 & 3.0720 & 2963.02 \\ \hline \end{tabular}
\end{table} 
Table 3: Effect of changes in various parameters of the model for example 1.