## 4 Application Analysis and Results
### Application Results
#### 4.2.2 Robustness and Sensitivity Analysis  
Moreover, the robustness of the SAA-derived solution was quantified and the sensitivity of the model to the weight of the scenarios was also analyzed. The solution of the SAA approach was robust but not optimal for all scenarios. For comparison, the GCA optimization model was optimized for each scenario. The average processing time, including the assembly time, the disassembly time, and the re-assembly time, for the robust solution obtained by the SAA approach and the solutions obtained by certain order optimization with a single scenario are shown in Table 4. Note that the weight of the scenarios was determined in the SAA approach, while in the model with certain order optimization with a single scenario, the weight of the exact scenario was changed to 1, with the others changed to 0. We report the average assembly time, disassembly time, re-assembly time, and total production time for all scenarios in rows AS, RD, RA, and Total. The variances of the disassembly time and re-assembly time instances are given in rows \(Var_{D}\) and \(Var_{A}\).  
The following can be observed in Table 4:  
1. The gap between the robust solution and the single scenario optimal solutions was 0.05%, implying that these costs are expected to be saved if orders are predicted  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Robust Solution** & **Scenario Optimal Solutions** & **Gap** \\ \hline AS (h) & 3023.00 & 3026.22 & \(-0.11\%\) \\ RD (h) & 9323.45 & 9315.89 & 0.08\% \\ RA (h) & 1196.66 & 1194.14 & 0.21\% \\ Total (h) & 13,543.11 & 13,536.25 & 0.05\% \\ \(Var_{D}\) & 1136.76 & 1391.05 & \(-18.28\%\) \\ \(Var_{A}\) & 4168.04 & 4202.06 & \(-0.81\%\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Average times needed for the robust solution and scenario optimal solutions.  
accurately or are known. This result confirms that the objective of the robust solution is very close to the optimal solutions of each scenario; thus, the robust solution is acceptable.
2. The variances of the disassembly time and re-assembly time for the robust solution were 18.28 and 0.81% less than that of the scenario optimal solutions, which was an expected trend. The robust solution obtained by the SAA approach could achieve higher production stability.  
The reworking time reveals that the scenario optimal solution is superior to the robust solution in most scenarios. The distribution of reworking time, including the disassembling and re-assembling times, in the two models is presented in Figure 6 for the 100 scenarios:  
It can be observed in Figure 6 that, due to the volatility of the scenarios, the results of the optimal solution exhibited significant differences. Thus, whatever the GCA decided, the re-assembly time was higher than for other scenarios that had similar orders. Moreover, the disassembly times for the robust solution were more concentrated on the average value, which indicates that applying the robust solution can achieve lower and more stable average disassembly times.  
The above results show the comparison of the three production strategies: MTO, the SAA approach, and an empirical method. The proposed SAA GCA optimization approach can save 33.08% of production time. Moreover, the robustness of the proposed approach was evaluated, and the results show that the GCA obtained by the proposed approach had low variances in the reworking time.