# Development of a Multiscenario Planning Approach for Urban Drainage Systems
## 3 Application Results
### RC Computation  
Table 2 presents and summarizes the system material cost, RC, and the total cost of D1 under six scenarios (S1 to S6). The RCs in Table 2 represent overpayments or supplementary payments that were incurred when unanticipated future events unfolded. For alternative scenarios (S2 to S6), the pipes and manholes determined in D1 should be reconstructed and reinforced at least partially through additional investments (e.g., supplementary payments), or a scenario-optimal solution can be  
Figure 6: Flooding hydrograph in scenario-optimal solutions under corresponding individual scenarios. (**a**) Second quartile and (**b**) third quartile. Figure 7: Optimal component dimensions obtained from the scenario-optimal solutions. (**a**) pipe size and (**b**) manhole depth. excessively redundant for certain different scenarios from which the overpayment of RC is computed. D1 from S1 exhibits the highest RC, USD 0.757 million. The penalty costs for S1 and S6 were similar, USD 0.602 and 0.655 million, respectively. The final total cost (optimal + penalty + RC) for S1 and S6 were USD 2.272 and 3.083 million, respectively; their cost difference was USD 0.811 million (approximately 35% more that the final total cost of D1). The range of the total RC for the alternative scenarios (S2 to S6) which is generally indicated high cost, was between USD 0.500 and 0.757 million. Similar RC analyses were performed for all designs (D1 to D6) to obtain the total cost (optimal + regret costs) for the scenario-optimal planning solutions (D1 to D6) under alternative scenarios; the data are listed in Table 3. The scenario-optimal total costs are in the grey cells in Table 3. The cost statistics include: (1) expected cost, (2) cost standard deviation, and (3) expected RC. The expected cost was estimated as the probability-weighted mean value of the total cost (optimal and RC) for all scenarios, and the standard deviation was calculated as the variability of the total cost under all scenarios. The expected RC is the probability-weighted mean value of the RC (sum of the overpayments and supplementary payments), quantifying the mean cost difference between the optimal and total costs. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Scenarios**} & \multicolumn{3}{c}{**Cost Statistics**} \\ \hline
**Designs** & **S1** & **S2** & **S3** & **S4** & **S5** & **  
D1 and D5 exhibited the largest cost variability, which indicates decreasing system performance (greater probability of flooding because of flow congestion) in the alternative scenarios. In contrast, D3 had the highest value for the expected RC from the expected costs as compared with the other designs. Furthermore, D3 had a relatively high expected RC and the smallest cost variability under the alternative scenarios. However, in the event that an alternative scenario occurs, because of the higher expected RC, it would be relatively expensive to expand infrastructures (e.g., increasing pipe sizes, pump stations, and detention reservoir) in D3. Among the six scenario-optimal planning solutions, D1 performed poorly across all cost parameters and had the highest expected cost and RC. In contrast, D2 exhibited lower values for both expected cost and RC than that of the other designs. Thus, D2 could be preferable, because of the moderate cost variability without the other two non-biased cost statistics (i.e., expected cost and RC). Figure 8 depicts a visualization of the data in Table 3, presenting the cost variability for each scenario-optimal solution under each alternative scenario. The bar plots show the system-material cost, penalty cost (system performance), and RC, which is the sum of the overpayments and supplementary payments. The trends of expected cost for D1 and D3 clearly show contrary results (represent Table 3). While D3 had the lowest cost of USD 1.893 million, if S1 occurred, it would incur the highest potential cost, of USD 2.418 million; the difference between these cost values is USD 0.525 million.