# A Network-Based Method for the EMU Train High-Level Maintenance Planning Problem
## 2 HMP Problem at CR
### Maintenance  
The maintenance requirement sets the limit on how much distance and time a train-set can operate before the next mandatory maintenance. Table 1 shows the HM requirement for the \"CRH1\" series EMU train-set in terms of cumulative operating mileage and cumulative operating days. For example, a train-set, CRH1B, should undergo the third-level maintenance after operating for 1,200,000 km or for three years before it can be assigned to the next operation utilization path with actual train trips. Furthermore, the HM requirement has a floating range. For example, cumulative operating mileage of the third-level maintenance for CRH1B is [1,100,000 km, 1,300,000 km], i.e., a CRH1B train-set will undergoes the procedures of third-level maintenance when its accumulated operating mileage is greater than 1,100,000 km and less than 1,300,000 km from the last HM. As seen in Table 1, the threshold of fourth-level and fifth-level are twice and four times, respectively, greater than the threshold of third-level. The interval between two consecutive HMs should be less than the third-level requirements according to CR [23]. Therefore, we can draw the conclusion that the HM requirements are equal to third-level requirements, and the train-set undergoes two consecutive HMs at different levels accordingly. On the basis of this rule, the HM cyclic graph could be drawn, as shown in Figure 2. Based on the sequence of HM cyclic graph and the HM requirement, the train-set accepts the different levels of HMs in turn until they are scrapped. Moreover, the maintenance procedures of higher-level maintenance include all maintenance procedures in lower-level maintenance. Thus, after one class of maintenance process, all cumulative operating mileage and days associated with that class and the corresponding lower-level classes of maintenance are all set to zero. Such as, all associated cumulative operating mileage and days for fourth-level and third-level should be set to zero after fourth-level. According to the CR, the HM requirements depends on the cumulative operating mileage mainly and the cumulative operating days as a supplement, and whichever comes first. The average daily operating mileage of CRH1B and CRH1E is 1600 km and 1500 km respectively. As the simple mathematical calculation based on the data in Table 1, we can conclude that the cumulative operating mileage for any train-set will fulfill firstly, such as a CRH1E EMU train-set, (1,200,000 km)/(1500 km/day) = 800 days < 3 years. Therefore, we could only take into account the cumulative operating mileage requirement and ignore the cumulative operating days in this paper. \begin{table}
\begin{tabular}{c c c c} \hline
**Type** & **Third-Level** & **Fourth-Level** & **Fifth-Level** \\ \hline CRH1B & \((120\pm 10)\times 10^{4}\) km & \((240\pm 10)\times 10^{4}\) km & \((480\pm 10)\times 10^{4}\) km \\ CRH1E & or 3 years & or 6 years & or 12 years \\ \hline \end{tabular}
\end{table} 
Table 1: Maintenance regulations for CRH1 series in China Railway. The average daily operating mileage is an estimated value based on historical data to calculate the eta (estimated time of arrival) of HM. This is a reasonable assumption, because at the operational level, we can assign itineraries to train-sets on each day so as to ensure that the true average number of operating mileage per day is close to the average daily operating mileage during the long planning horizon. When the train-set needed HM, it would be sent to a workshop. In order to keep away from the peak season of travel, some train-sets may choose to undergo the HM before the rush, and others may conduct maintenance after the rush. However, too much postponing will be bad for operation safety, and too much time ahead of the estimated time of arrival (ETA) will waste the operating mileage. In addition, as the HM is costly, frequent maintenance will lead to a great waste of resources. Therefore, under the premise of safety operation, the start time of HM should be postponed as soon as possible.