# A Network-Based Method for the EMU Train High-Level Maintenance Planning Problem
## 5 Empirical Case Study and Sensitivity Analysis
### Sensitivity Analysis  
Sensitivity analysis was performed to evaluate the effects of the variation in three parameters: (1) the average daily operating mileage of train-sets for calculating; (2) HM capacity at the depot; (3) the assumed minimum value of cumulative mileage.  
The average daily operating mileage is a key factor determining the deadline for delivering train-sets to the workshop. Because it is an estimated value based on historical data, we evaluate the impact of reducing 100 or increasing 100 in this analysis.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **z (km)** & **Improved Effects** & **Time Consumption** & **Improved Effects** \\ \hline I & 3,212,769 & - & 502s & - \\ II & 3,212,769 & 0 & 87s & 82.67\% \\ \hline \hline \end{tabular}
\end{table}
Table 6: Numerical comparison results.  
Figure 6: The number of train-sets be maintained for different periods within the year of 2017.  
The available HM capacity limits the train-sets such that not all undergo the HM at the maximum cumulative mileage. This can be adjusted by reallocating human and infrastructure resources. The maintenance capacity includes the maximal number of standard set that can be maintained simultaneously and the receiving capability per day. We analysis the scenarios with 10 standard sets of simultaneously maintenance capacity and two nature sets of receiving capacity at depot per day in this section. The interval of receiving train-sets for depot remains the same.  
The purpose of setting the assumed minimum value of cumulative mileage is to control the solution space. If it is too small, there will be no feasible solution existed; if it is too large, much time for solving will be took. Meanwhile, the smaller assumed value, the more date options for delivering train-set to workshop. We set \(p=80\), 90 and 100 respectively to analysis its sensitivity of calculating time.  
According to the variation in the three important parameters, 18 scenarios were created (see as in Table 7). The second, third and fourth column are the amplitude of variation for average daily operating mileage, maintenance capacity (including simultaneously maintenance capacity and receiving capacity) and \(p\) respectively. For each scenario, we compare the performance in mileage loss and time consumption under the proposed method. The \"+\" presents an increase and \"\(-\)\" represents decrease.  
In Table 7, we can see that the variation of average daily operating mileage will has no impact on the optimal objective value, but the result of the HMP will be completely reconstructed; the greater maintenance capability, the less mileage loss and time consumption; variation in the assumed minimum value of cumulative mileage has significant impact on the time consumption. The smaller the assumed value, the longer the time consumption. If the model is infeasible, we can increase the time options to obtain an optimal solution, i.e., increase the value of \(p\).  
The developed method performed very well in all scenarios. The maximum time consumption (129 s) is from scenario 15, with a greater average daily operating mileage and looser time options. The minimum time consumption (78 s) is from scenario 4 with greater maintenance capacity and tighter time options. However, for any one scenario above, it will take several days to obtain a solution by the manual process. In addition, the manual process is usually infeasible for the whole planning horizon, which needs frequency modification. It can generate a new plan that is efficiently based on our developed method when the condition changes.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Scenario** & \(I\) **(km)** & \(B_{2}N_{2}\) & \(p\) & \(z\) **(km)** & **Improved Effects** & \multicolumn{2}{c}{**Time Consumption (s)**} & **Improved Effects** \\ \hline
1 & 0 & 0,0 & 0 & 3,212,769 & - & 87 & - \\  
\hline \hline \end{tabular}
\end{table}
Table 7: Sensitivity analysis comparison results.