## 5 Case Study and Discussion
### Analysis of Results  
Table 3 shows the computational results in terms of the timetables and bus schedules. Compared to the MA, the rescheduling model (ISCR) and its variants, solved by various intelligent algorithms, consistently demonstrate a notable enhancement in solution quality, achieving at least a 12.94% cost reduction. Through the co \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & \multicolumn{2}{c}{**Timetable**} & \multicolumn{2}{c}{**Bus Schedule**} & \multicolumn{2}{c}{**Total Cost**} & **Compared** \\ \cline{3-10}  & & **CT** & \(\mathbf{z}_{Q}\) & \(\mathbf{z}_{H}\) & **RR** & \(\mathbf{z}_{P}\) & \(\mathbf{z}_{C}\) & \(\mathbf{z}\) & **with MA** \\ \hline  & MA & 5 & 10,000 & 2559.19 & 0.00\% & **0** & 1950 & 14,509.19 & - \\ \hline \multirow{3}{*}{WOT} & Greedy & 2 & 4000 & 2422.57 & 12.39\% & 7000 & 1950 & 15,372.57 & +5.95\% \\  & Greedy- & LNS & 2 & 4000 & 1681.30 & 8.85\% & 5000 & 1950 & 12,631.30 & \(-12.94\%\) \\  & DP-LNS & 2 & 4000 & 1807.62 & 6.19\% & 3500 & 1950 & 11,257.62 & \(-22.41\%\) \\ \hline \multirow{3}{*}{WT} & Greedy & 0 & 0 & 3285.93 & 13.04\% & 7500 & 1650 & 12,435.93 & \(-14.29\%\) \\  & Greedy- & LNS & 0 & 0 & 2512.72 & 13.91\% & 8000 & 950 & 11,462.72 & \(-21.00\%\) \\ \cline{1-1}  & DP-LNS & 0 & 0 & 2368.42 & 12.17\% & 7000 & 950 & 10,318.42 & \(-28.88\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Computational results in the breakdown scenario. buses, the number of CTs decreases from 5 to about 2. This indicates that even an experienced controller using the MA would struggle to accurately analyze problems and thus effectively coordinate buses. As the severity of disruptions increases, the application of the rescheduling model for comprehensive rescheduling becomes necessary. Notably, solving the WOT model using the greedy approach increases the total cost by 5.95%. This increment in cost occurs because the solution reduces the number of CTs but requires more reassignments compared to the MA. Controllers can evaluate the pros and cons of different schemes based on specific situational requirements. Comparing the results of the different models indicates that considering delay times allows trip cancellations to be significantly reduced. Thus, introducing delay times allows trips to be performed more flexibly, making it easier to obtain an optimal solution containing sufficient trips. However, we also find that modeling using delays changes the service frequency, increasing the corresponding cost \(z_{H}\) by about 35.64%. This additional cost is unavoidable and requires LNS algorithms for further optimization. The LNS algorithm is implemented based on the heuristic operator designed in this study, which is more effective in identifying irregular departure intervals for optimization. Thus, we can alleviate the imbalanced service frequency caused by introducing delayed trips. The results of WT modeling show that the cost \(z_{H}\) decreases by 23.53% using the proposed LNS algorithm. Moreover, dynamic programming can help obtain a beneficial long-term rescheduling scheme. The available information on trips and buses needs to be determined based on the scheme in the previous period. This means that the state of sub-stages will change according to the different schemes of the previous sub-stage, resulting in a distinct connection network. Dynamic programming can comprehensively evaluate the hysteresis effects of the sub-schemes and, therefore, obtain a comprehensively optimal solution. Significantly, the results also show that at most 13.91% of trips, including those with practical conflicts, need to be reassigned to mitigate the impact of disruptions in the current scenario, which provides a preliminary impact range. Based on the above analysis, the proposed DP-LNS algorithm can maintain sufficient service capability during different disruptions. However, it is difficult to ensure service regularity because of the variations in timetables caused by delays and cancellations.