# Development of a Multiscenario Planning Approach for Urban Drainage Systems
## 3 Application Results
### Multi-Scenario-Based Planning Solution Based on Component-Wise Regret Cost (Phase II)  
This analysis utilized lower constraints than a predefined RC (expected RC obtained from Phase I in Table 3) obtained from scenario-optimal planning solutions. Table 4 shows the RC analysis of the multi-scenario-based planning solution based on component-wise RC. RC analyses of the compromise solution obtained in the proposed model revealed decreased values (in terms of the RC) as compared with the scenario-optimal solutions (Phase I). It was confirmed that properly adjusting the pipe sizes and manhole depths based on the common elements from scenario-optimal solutions (Phase I) decreased the RC for all scenarios. D2 had the lowest RC of USD 0.318 million, whereas D3 had the highest RC of 0.502 million USD; the difference between these values is USD 0.184 million. In the compromise solution, supplementary payments showed a more pronounced decreasing trend than overpayments. In addition, in terms of the total RC, a more pronounced decreasing trend was observed as compared with the scenario-optimal solutions obtained from Phase I. Figure 9 shows a comparison between the scenario-optimal solutions (Phase I) and the compromise solution obtained from the multi-scenario-based planning solution (Phase II) based on component-wise RC. The total system cost included the pipe construction, manhole depth, and penalty costs. The total system cost for the compromise solution in each scenario involved a higher investment than those for the scenario-optimal planning solutions, because the compromise solution considered alternative scenarios to minimize RC while reflecting the common elements. In addition, the total system cost of the compromise solution showed a decreasing trend from S1 to S3. Likewise, a decreasing tendency was observed for the total system cost from S4 to S6. It was confirmed that this tendency was related to the impact of the inflow distribution, that is, the close proximity of the critical nodes (double inflows) to the outlet significantly improved and decreased system performance, along with impact on the total system cost. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **Cost Categories** & **S1** & **S2** & **S3** & **S4** & **S5** & **S6** \\ \hline \multirow{3}{*}{\begin{tabular}{c} Pipe construction \\ cost \\ \end{tabular} } & Overpayment & 0.346 & 0.274 & 0.440 & 0.365 & 0.144 & 0.368 \\ \cline{2-7}  & Supplementary payment & 0.087 & 0.011 & 0.032 & 0.010 & 0.242 & 0.000 \\ \cline{2-7}  & Regret costs & 0.433 & 0.285 & 0.472 & 0.375 & 0.386 & 0.368 \\ \hline \multirow{3}{*}{\
\begin{tabular}{c} Manhole depth \\ cost \\ \end{tabular} } & Overpayment & 0.009 & 0.018 & 0.010 & 0.006 & 0.012 & 0.034 \\ \cline{2-7}  & Supplementary payment & 0.021 & 0.015 & 0.020 & 0.008 & 0.013 & 0.003 \\ \cline{2-7}  & Regret costs & 0.030 & 0.033 & 0.030 & 0.014 & 0.025 & 0.037 \\ \hline \multirow{3}{*}{
\begin{tabular}{c} Total regret cost \\ \end{tabular} } & Overpayment & 0.355 & 0.292 & 0.450 & 0.370 & 0.156 & 0.402 \\ \cline{2-7}  & Supplementary payment & 0.108 & 0.026 & 0.052 & 0.019 & 0.255 & 0.003 \\ \cline{1-1} \cline{2-7}  & Regret costs & 0.463 & 0.318 & 0.502 & 0.389 & 0.411 & 0.405 \\ \hline \hline \end{tabular} Note: Units of each cost are million U.S. dollars (USS million).  
\end{table} 
Table 4: RC analysis of the multi-scenario-based planning solutions (Phase II). Figure 10 illustrates a comparison of the system performance between the scenario-optimal solutions (Phase I) and the compromise solution obtained from the proposed model (Phase II). Generally, the compromise solution across future scenarios achieved better performance than the scenario-optimal solutions did. However, in S3 and S5, the multi-scenario-based planning solution exhibited a lower performance than the equivalent scenario-optimal planning solution. A compromise solution could exhibit lower performances than scenario-optimal planning solutions because the compromise solution considered all scenarios.