# Development of a Multiscenario Planning Approach for Urban Drainage Systems
## 4 Summary and Conclusions  
In this study, the pipe design and layout that minimizes the total system cost for a given set of future scenarios was determined. The future scenarios included the following: (1) different spatial and temporal rainfall patterns and (2) specifications of manholes for drain-inflow distribution in the nodes of the network. The proposed model consists of a two-phase optimization model: (1) the scenario-optimal solution was obtained in the scenario-optimal planning approach (Phase I) and (2) the common elements across all scenarios were identified, and the total RC was computed  
Figure 10: Comparison of the system performance between scenario-optimal solutions and multi-scenario-based compromise solution. Figure 9: Comparison of the final total costs between scenario-optimal solutions and multi-scenario-based compromise solution. considering the individual component-wise RCs to determine a compromise solution (Phase 2). The multi-scenario-based planning model was demonstrated in the UDS planning of a simple grid network, i.e., the S-city drainage network. Finally, the scenario-optimal solution (Phase I) and the compromise solution (Phase II), considering both a reasonable planning investment and system performance, could be presented to decision makers and other stakeholders. The scenario-optimal planning model (Phase I) delivered a solution that was demonstrated to be cost effective only for its corresponding scenario; for all alternative scenarios, the system performance was poor (high penalty cost) and involved an excessive RC. In addition, in Phase I, the additional requirements for the critical information of the UDS to the inflow distribution, along with other uncertainty factors in future scenarios, were identified. Specifically, the close proximity of critical nodes (doubled inflows) to the outlets significantly enhanced the system performance. Cost analyses for the scenario-optimal planning solutions were also performed; the tradeoff was represented by the expected cost. In addition, the selection of any scenario-optimal planning solution resulted in overpayments and supplementary payments in RC. To seek a compromise solution, the proposed Phase II optimization model considered critical uncertainties in a multi-scenario-based planning solution approach, by simultaneously including multiple future scenarios. It was confirmed that the proposed model tended to remove the inherent uncertainties in the scenario-optimal planning approach (Phase I). Overall, the results of the compromise solution obtained in Phase II, presented trends of decreasing RC in all future scenarios. In addition, the system performance was considerably improved in the compromise solution as compared with the scenario-optimal solutions (Phase I), although the system material costs were greater than those of the Phase I solutions, because RC was properly decreased while accounting for all future scenarios. Thus, the multi-scenario-based optimization method focused on minimizing the initial construction cost with reasonable adaptability to different scenarios. Generally, the compromise solution across all scenarios achieved better performance than the scenario-optimal planning solutions. Thus, the compromise solution could respond to any alternative scenario and achieve a balance between robustness and flexibility. This study included certain limitations that could be addressed in future studies. First, the scenario generation, herein, focused only on spatiotemporal rainfall patterns having the same frequency; different design frequencies due to the rainfall patterns were not involved. Second, this study considered the same occurrence probability under different scenarios; an unequal occurrence probability of future scenarios should be considered in future studies. Third, only non-temporal scenarios were considered in this study. Planning or construction with the possibility for modification need to be conducted under various future conditions.