## Appendix B
### LCC of Vehicle  
The vehicles of urban rail transit are divided into motors with power units and trailers without power units, which are combined into trains according to the train formation plan. The LCC of vehicle \(LCC^{(vch)}\) consists of purchase costs, operating costs, maintenance costs, and the residual value at the end of the system LC of all vehicles. The operation cost mainly comes directly from the traction power consumption for operation. Maintenance cost refers to the expenses incurred by daily vehicle maintenance and periodic maintenance, including medium maintenance, regular maintenance, and renewal. These two items are affected by the train line plan and timetable. For example, express trains have low traction power consumption, wear, and other vehicle degradations caused by train accelerationand deceleration owing to low stopping times. For simplicity, we assume that the daily train timetables are the same, and the residual value rates of the motor and trailer are \(r_{j}^{(veh)},\forall j\in\{motor,trailer\}\). Thus, \(LCC^{(veh)}\) can be calculated using the vehicle average cost per unit time according to (A2),  
\[LCC^{(veh)}=\sum_{k\in\mathcal{K}}\sum_{i\in\{motor,trailer\}}\frac{N_{k}^{(veh) }m_{k}^{(i)}}{m_{k}}\cdot\frac{T_{i}^{(veh,P)}(1-r_{i}^{(veh)})}{T_{i}^{(veh)}}+ \frac{T}{t}\sum_{i\in I^{(veh)}(t)}\Big{(}c^{(ep)}E_{i}+C_{i}^{(veh,M)}\Big{)}\] (A2)  
where \(t\) denotes the operation time per day; the index set \(I^{(veh)}(t)\) denotes the set of operation lines of the daily train timetable; \(N_{k}^{(veh)}\) denotes the vehicle number of each type \(k\in\mathcal{K}\) train; \(m_{k}^{(i)},c_{i}^{(veh,P)}\), and \(T_{i}^{(veh)},\forall i\in\{motor,trailer\}\) denote the motor/trailer number, purchase cost, and design life of each type \(k\in\mathcal{K}\) train, respectively; \(c^{(ep)}\) denotes the electricity price; and \(C_{i}^{(veh,M)}\) denotes the maintenance cost. This model is universal, because we can use the weighted average cost of different train timetables to calculate the operation and maintenance cost per unit time if considering special train timetables on holidays.  
To quantitatively study the impact of the line plan on vehicle maintenance, we divide the maintenance cost into four parts according to the maintenance content: power-consumption-related cost, traction-based mechanical-work-related cost, resistance-based mechanical-work-related cost, and operation-time-related cost with per unit time costs \(c_{1}^{(veh,M)},c_{2}^{(veh,M)},c_{3}^{(veh,M)}\), and \(c_{4}^{(veh,M)}\), respectively. Thus, the maintenance cost in the vehicle LC can be calculated using (A3)-(A7), where \(C_{i}^{(j,M)}\) denotes the motor/trailer maintenance cost for train \(i\in I^{(veh)}(t)\).  
\[C_{i}^{(veh,M)}=\sum_{k\in\mathcal{K}}\sum_{j\in\{motor,trailer\}}\pi_{ik}m_{k} ^{(i)}C_{i}^{(j,M)},\forall i\in I^{(veh)}(t)\] (A3)  
\[C_{i}^{(motor,M)}=c_{1}^{(veh,M)}E_{i}+c_{2}^{(veh,M)}W_{i}^{(tra)}+c_{3}^{(veh,M)}W_{i}^{(tra)}+c_{4}^{(veh,M)}t,\forall i\in I^{(veh)}(t)\] (A4)  
\[C_{i}^{(trailer,M)}=c_{3}^{(veh,M)}W_{i}^{(bra)}+c_{4}^{(veh,M)}t,\forall i\in I ^{(veh)}(t)\] (A5)  
\[E_{i}=\eta^{(b)}\eta^{(j)}\eta^{(c)}W_{i}^{(bra)},\forall i\in I^{(veh)}(t)\] (A6)  
\[W_{i}^{(bra)}=W_{i}^{(tra)},\forall i\in I^{(veh)}(t)\] (A7)  
\(W_{i}^{(tra)}\) is calculated by (A8), where \(w^{(tra)}(l_{e},t_{e})\) is the unit mass traction work of the running segment \(e\in\mathcal{E}_{i}\) and was calculated by the approximation method with a segment length \(l_{e}\) and time \(t_{e}\) by [PERSON] et al. [52].  
\[W_{i}^{(tra)}=w^{(tra)}(l_{e},t_{e})\sum_{e\in\mathcal{E}_{i}}\left(v_{e}P^{(p )}+\sum_{k\in\mathcal{K}}\sum_{j\in\{motor,trailer\}}\pi_{ik}m_{k}^{(j)}P^{(j )}\right),\forall i\in I^{(veh)}(t)\] (A8)