**2. Methodology**

To clearly describe the evaluation method, the input and output variables and the operation process of the URT system are introduced first. Then, the SBM model is developed to measure the operational efficiency of URT lines. Furthermore, a measurement for energy efficiency is proposed.

#### *2.1. Input and Output Variables and Operation Process*

Generally, a URT system is invested in by enterprises to provide travel services for citizens. Its operation process is shown in Figure 1. According to previous studies, line mileage, station, train, and energy are indispensable resources for transportation services [19,26,29,38,39]. Hence, these four resources are considered input variables in the operation process. Passenger transport volume and revenue passenger kilometers are taken as the two desirable output variables, while energy-related CO2 emission is considered one undesirable output variable.

**Figure 1.** The operation process of a URT system.

#### *2.2. Efficiency Evaluation Model Based on SBM-DEA*

This study aims to measure the operational efficiency and energy efficiency of Chinese URT lines with the SBM model. As a non-radial DEA approach, the SBM model directly captures each "input excess" and "output shortfall" to identify the inefficiency of DMUs from an overall perspective [40]. Therefore, the SBM model has been widely used to evaluate the efficiency of public transportation systems, such as by Zhang et al. [41], Chu et al. [42], and Tavassoli et al. [43].

Suppose that there are *n* DMUs, which represent the URT lines, denoted by DMU*j* (*j* = 1, 2, ... , *n*). Each DMU utilizes line mileage (*XL*), station (*XD*), train (*XT*), and energy (*XE*) and then produces passenger transport volume (*YP*), revenue passenger kilometers (*YR*), and CO2 emissions (*YC*). The evaluation model for the operational efficiency of the URT line based on SBM can be expressed as follows:

$$\begin{aligned} \theta\_i &= \min \frac{-4\left(\frac{\hat{\lambda}\_i^T + \hat{\lambda}\_i^T + \hat{\lambda}\_i^T + \hat{\lambda}\_i^T\right)}{1 + \left(\frac{\hat{\lambda}\_i^T + \hat{\lambda}\_i^T + \hat{\lambda}\_i^T\right)} \\ \text{s.t.} &\quad \sum\_{j=1}^n \lambda\_j X L\_j + s\_i^- = X L\_i, \\ &\quad \sum\_{j=1}^n \lambda\_j X D\_j + s\_{\bar{\alpha}}^- = X D\_{i\bar{\nu}}, \\ &\quad \sum\_{j=1}^n \lambda\_j X T\_j + s\_{\bar{\alpha}}^- = X T\_{i\bar{\nu}}, \\ &\quad \sum\_{j=1}^n \lambda\_j X E\_j + s\_{\bar{\alpha}}^- = X E\_{i\bar{\nu}}, \\ &\quad \sum\_{j=1}^n \lambda\_j Y P\_j - s\_{\bar{\nu}}^+ = Y P\_{i\bar{\nu}}, \\ &\quad \sum\_{j=1}^n \lambda\_j Y R\_j - s\_{\bar{\nu}}^+ = Y R\_{i\bar{\nu}}, \\ &\quad \sum\_{j=1}^n \lambda\_j Y C\_j + s\_{\bar{\alpha}}^- = Y C\_{i\bar{\nu}}, \\ &\quad \sum\_{j=1}^n \lambda\_j = 1, \\ &\quad \lambda\_{\bar{\beta}} = 1, \\ &\quad \lambda\_{\bar{\beta}} = 1, s\_{\bar{\beta}}^+, s\_{\bar{\alpha}}^+, s\_{\bar{\alpha}}^+, s\_{\bar{\rho}}^+, s\_{\bar{\rho}}^+, s\_{\bar{\alpha}}^- \ge 0, \ j = 1, 2, \dots, n. \end{aligned}$$

In Model (1), *θi* represents the operational performance score; *s*−*l* , *s*−*d* , *<sup>s</sup>*<sup>−</sup>*t* , *<sup>s</sup>*<sup>−</sup>*e* , *s*+*p* , *s*+*r* , and *<sup>s</sup>*<sup>−</sup>*c* are slacks of line mileage, station, train, energy, passenger transport volume, revenue passenger kilometers, and CO2 emission, respectively, representing either the excess of the input or the shortfall of the output. *λj* expresses the participation degree of each DMU in constructing the production frontier. Note that Model (1) is non-linear. To simplify the calculation, a linear form is transformed following the proposed method by Tone [40] as follows:

*θi* = min(*t* − 14 ( *<sup>S</sup>*<sup>−</sup>*l XLi* + *<sup>S</sup>*<sup>−</sup>*d XDi* + *<sup>S</sup>*<sup>−</sup>*t XTi* + *S*<sup>−</sup>*e XEi*)) s.t. *t* + 13 ( *S*+*p YPi* + *<sup>S</sup>*+*r YRi* + *S*<sup>−</sup>*c YCi*) = 1 *n* ∑ *j*=1 *<sup>η</sup>jXLj* + *<sup>S</sup>*<sup>−</sup>*l* = *tXLi*, *n* ∑ *j*=1 *<sup>η</sup>jXDj* + *<sup>S</sup>*<sup>−</sup>*d* = *tXDi*, *n* ∑ *j*=1 *<sup>η</sup>jXTj* + *S*<sup>−</sup>*t* = *tXTi*, *n* ∑ *j*=1 *<sup>η</sup>jXEj* + *S*<sup>−</sup>*e* = *tXEi*, *n* ∑ *j*=1 *<sup>η</sup>jYPj* − *S*+*p* = *tYPi*, *n* ∑ *j*=1 *<sup>η</sup>jYRj* − *S*+*r* = *tYRi*, *n* ∑ *j*=1 *<sup>η</sup>jYCj* + *S* − *c* = *tYCi*, *n* ∑ *j*=1 *ηj* = *t*, *ηj*, *<sup>S</sup>*<sup>−</sup>*l* , *<sup>S</sup>*<sup>−</sup>*d* , *S*<sup>−</sup>*t* , *S*<sup>−</sup>*e* , *S*+*p* , *<sup>S</sup>*+*r* , *S*<sup>−</sup>*c* ≥ 0, *j* = 1, 2, . . . , *n*. (2)

The variables in Model (1) undergo the following transformations in Model (2): *λt* = *η*, *ts*<sup>−</sup>*l* = *<sup>S</sup>*<sup>−</sup>*l* , *ts*<sup>−</sup>*d* = *<sup>S</sup>*<sup>−</sup>*d* , *ts*<sup>−</sup>*t* = *S*<sup>−</sup>*t* , *ts*<sup>−</sup>*e* = *S*<sup>−</sup>*e* , *ts*+*p* = *S*+*p* , *ts*+*r* = *<sup>S</sup>*+*r* , *ts*<sup>−</sup>*c* = *S*<sup>−</sup>*c* . The optimal *η*∗*j* , *S*−∗ *l* , *S*−∗ *d* , *S*−∗ *t* , *S*−∗ *e* , *S*+∗ *p* , *S*+∗ *r* , *S*−∗ *c* , and *t*∗ are measured for operational performance, *θ*∗*i* . If *θ*∗*i* = 1 and all optimal slacks are equivalent to 0, the performance is efficient; otherwise, it is inefficient. Moreover, if a larger performance score of a DMU is obtained, it indicates that this DMU operates better than other DMUs.

In DEA theory, the projected point on the production frontier is the optimal target for each inefficient DMU to pursue. Hence, the DEA method can be used to set the optimization targets of inputs and outputs to improve performance. The target energy expresses a minimum level of energy input to achieve optimal operational performance. Naturally, the target energy input can be obtained with the following equation:

$$TE\_i = \sum\_{j=1}^{n} \lambda\_j X E\_j \tag{3}$$

Hence, energy efficiency, *ρi*, is defined as the ratio of target energy to its actual consumed energy in this study. It is can be expressed as follows:

$$
\rho\_i = \frac{TE\_i}{XE\_i} \tag{4}
$$

For ease of reading, the formulas for calculating the improvement potentials of variables are provided in Appendix A.

#### **3. Empirical Study**

#### *3.1. Data Source*

As for the empirical analysis, the datasets from the URT lines were collected from the yearbook of the China Urban Rail Transit Almanac 2021, which is an annual report released by the China Association of Urban Rail Transit. In total, 61 URT lines from Beijing, Shanghai, Guangzhou, and Shenzhen were considered for analysis. As shown in Figure 2, Beijing, Shanghai, Guangzhou, and Shenzhen are the top four cities in terms of economic strength on the Chinese mainland. Each city has a population of more than 10 million and an urban rail network of hundreds of kilometers. A large number of people take urban rail transit for their daily travel. Overall, data on line mileage, station, train, energy, passenger transport volume, and revenue passenger kilometers were collected from the aforementioned yearbook. While there are no official statistics on CO2 emissions, we calculated the carbon emission based on energy consumption and the regional grid carbon emission factor in 2019 following the approach of Yu et al. [44]. Descriptive statistics are shown in Table 1.


**Table 1.** Descriptive Statistics 1.

1 PT and PK are short for person-time and passenger kilometers, respectively.

**Figure 2.** Four megacities in mainland China.

#### *3.2. Efficiency Results*

Table 2 and Figure 3 show the efficiency results at the line level and the city level, respectively. As can be seen from Table 2, the average operational efficiency is 0.5634. Overall, the average room for URT lines to improve operational efficiencies is 43.66%. From a line angle, it can be seen that of the operational efficiencies of the 61 observed URT lines, 10 of which are evaluated as being an efficient level, another 15 lines are over the average level, and 36 lines are under the average level. There is a significant difference between URT lines in efficiency. From a city angle, Figure 3 suggests that the average operational efficiency of the URT lines in Guangzhou (0.6453) tops the list. The average operational efficiency of URT lines in Shanghai (0.5921) is higher than the average level, while those of the URT lines in Beijing (0.5054) and Shenzhen (0.5157) are slightly lower than the average level. That is to say, in terms of operational efficiency, there is a slight difference between URT lines at the city level. The reason might be that these megacities are similar in terms of their large population and high economic development level.

**Table 2.** The efficiency of the URT systems in case cities.



**Table 2.** *Cont.*

In particular, it can be seen that around five-sixths of the URT lines are inefficient. In Beijing, the operational efficiencies of 2 out of 20 observed URT lines are efficient, another 3 lines are over the overall average level, and 15 lines are under the overall average level. In Shanghai, the operational efficiencies of 3 out of 17 observed URT lines are efficient, another 4 lines are over the overall average level, and 10 lines are below the overall average level. In Guangzhou, the operational efficiencies of 4 out of 14 observed URT lines are efficient, another 4 lines are over the overall average level, and 6 lines are below the overall average level. In Shenzhen, the operational efficiencies of 1 out of 10 observed URT lines are efficient, another 4 lines are over the overall average level, and 5 lines are below the overall average level. Obviously, the operational efficiencies of most URT lines need to be improved further, as they are underperforming. For instance, the operational efficiency of Beijing Line 8 is 0.2583, suggesting that the operational efficiency can be improved by 30.51% and 76.17% to reach the overall average and optimal level, respectively. In a similar vein, in other case cities, the operational efficiencies of SH-Line 5 (0.3441), GZ-Line 14 (0.3138), and SZ-Line 2 (0.3099) can be improved by 65.59%, 68.62%, and 69.01%, respectively, to reach the optimal level. These lines with poor performance should make grea<sup>t</sup> efforts to improve operational efficiency to reach the overall average level first and then pursue a higher efficiency.

Similar results are also observed in energy efficiency. Overall, the average energy efficiency of the URT lines is 0.7641. That is to say, the URT lines are recommended to improve their energy efficiency by 23.59% on average to reach the optimal energy utilization level. From a line perspective, it can be found that of the energy efficiencies of the 61 observed URT lines, 14 of which are evaluated as an efficient level, another 17 lines are over the average level, and 30 lines are under the average level. There is a grea<sup>t</sup> disparity among URT lines in energy efficiency. From a city perspective, Figure 3 suggests that the average energy efficiency of the URT lines in Shanghai (0.7785) tops the list. The average operational efficiencies of URT lines in Guangzhou (0.7693) and Beijing (0.7684) are higher than the average level, while those of the URT lines in Shenzhen (0.7235) are lower than

the average performance level. That being said, there is no significant difference in energy efficiency between URT lines at the city level. It might be that these cities have developed URT in similar periods, with a mixture of new and old facilities and equipment in the lines.

Additionally, the results illustrate that the energy efficiency of most URT lines is inefficient. In Beijing, the operational efficiencies of 2 out of 20 observed URT lines are efficient, another 10 lines are over the overall average level, and 8 lines are below the overall average level. In Shanghai, the operational efficiencies of 3 out of 17 observed URT lines are efficient, another 6 lines are over the overall average level, and 8 lines are below the overall average level. In Guangzhou, the operational efficiencies of 4 out of 14 observed URT lines are efficient, another 2 lines are over the overall average level, and 6 lines are below the overall average level. In Shenzhen, the operational efficiencies of 2 out of 10 observed URT lines are efficient, another 2 lines are over the overall average level, and 6 lines are below the overall average level. Obviously, the energy efficiencies of most URT lines need to be improved further, as they are underperforming. For instance, the energy efficiency of some of the cases is much lower than the average level (e.g., the energy efficiency of BJ-Line 7 is 0.3621), suggesting that the operational efficiencies can be improved by 40.2% and 63.79% to reach the overall average and optimal level respectively. In a similar vein, in other case cities, the operational efficiencies of SH-Line 7 (0.3092), GZ-Line 21 (0.4218), and SZ-Line 9 (0.3974) can be improved by 69.08%, 57.82%, and 59.36%, respectively, to reach the optimal level. These lines with worse performance should make more efforts to improve operational efficiency to reach the overall average level first and then pursue a higher efficiency.

In other words, the efficiency of the energy consumption of these URT systems is optimized. Furthermore, of the 61 observed URT systems, 31 of them are above the average level; the energy efficiency of 14 observed URT systems is optimized. For those higher than the average level, the energy efficiency of 3 out of 20 URT systems in Beijing is optimized; the energy efficiency in 11 URT systems is above the average level). Likewise, 3 out of 17 URT systems in Shanghai are optimized in terms of energy efficiency; nine URT systems in Shanghai perform better than the average level in terms of energy efficiency. Meanwhile, in Guangzhou, 5 out of 14 URT systems reach the ideal level of energy consumption efficiency; the energy efficiency of nine URT systems in Guangzhou is higher than the average level. In Shenzhen, 2 out of 10 URT systems are fully optimized; the energy utilization level of four URT systems in Shenzhen is higher than the average level. In these cases, some of them are close to the optimal level. For example, the energy efficiency of BJ-Line 2 is 0.9338, which demonstrates a significant potential to reach the ideal energy consumption efficiency. In other cases, some of them are under the average level of energy consumption efficiency. For instance, the energy efficiency of the BJ-Fangshan Line is 0.736, which is close to the average value. In other words, there is a potential to further improve performance beyond the average level. Furthermore, the energy efficiency of some of the cases is much lower than the average level (e.g., the energy efficiency of SZ-Line 9 is 0.3948).

In addition to the efficiencies across cities, Table 3 reports a comparison of the efficiencies of URT lines operated by joint ventures and state-owned enterprises. The average operational efficiency of the state-owned lines (0.5684) is higher than that of the joint lines (0.4658). Specifically, there are three lines operated by joint ventures (i.e., BJ-Line 4, BJ-Yanfang Line, and SZ-Line 4). Only the operational efficiency of SZ-Line 4 (0.6102) is higher than the average level.

**Table 3.** The average efficiency of the URT systems in case cities.


Regarding energy efficiency, the average energy efficiency of URT lines operated by joint ventures is 0.8678, which is higher than the overall energy efficiency (0.7641), while the average energy efficiency of URT lines operated by state-owned enterprises (0.7587) is slightly lower than the overall value. The reason may be that the joint-owned lines were built in a more recent period, with more new energy-saving technologies. To sum up, state-owned enterprises are better at improving operational efficiency, while joint ventures are more concentrated on energy efficiency. This may be due to the difference between the two ownership models. In this sense, operators are encouraged to learn from each other's managemen<sup>t</sup> and technology advantages so as to maximize their efficiencies.

#### *3.3. Improvement Analysis*

As shown in Table 4 and Figure 4, the improvement potentials of inputs and outputs for the URT lines and case cities are presented. As mentioned in the previous methodology section, line mileage and station are not discussed in the adjustment analysis, as they cannot be easily changed after they are built.


**Table 4.** The improvement values of the URT systems in case cities.

**Figure 4.** The average improvement values of the URT systems in case cities.

#### 3.3.1. Input Adjustment Plan

In terms of the number of allocated trains, the average improvement value of 51 inefficient lines is 46.07% (27.53). Only three URT lines (i.e., BJ-Line S1, GZ-Line 9, and GZ-Line 13) reach the optimal level. In total, 20 URT lines are under the average level, while 28 lines are above the average level. From the perspective of operation, there is a need to calculate the optimal number of trains and develop a dynamic scheduling mechanism. Different types of trains (e.g., short trains can be used during the off-peak period) should be used to optimize overall efficiency. For instance, for SZ-Line 10, 39.21% (10.20) of trains can be reduced based on optimal efficiency. Furthermore, some lines, such as BJ-Line 8 (80.87%) and SH-Line 6 (69.64%), show a high improvement potential to reach the maximized resource utilization level. In this sense, attention should be paid to such URT lines to optimize the number of allocated trains. At the city level, the average improvement values of the number of allocated trains for Beijing, Shanghai, Guangzhou, and Shenzhen are −48.79%, −53.04%, −28.82%, and −46.07%, respectively. Namely, Shanghai tops the list, while Guangzhou is closer to the ideal level compared with other case cities.

Regarding energy, the average improvement value of the lines is 28.22% (39.35 million kWh). Only four URT lines (i.e., BJ-Line 16, BJ-Yanfang Line, GZ-Line 8, and SZ-Line 10) reach the optimal level. In total, 24 lines are under the average level, while 23 lines are above the average level. That is to say, for most of the URT lines, there is a lot of room to improve overall efficiency by reducing energy. For instance, based on the benchmark, the

energy consumed by BJ-Line 6 can be reduced by around 43.31% (11.26 million kWh) to minimize energy wastage. Particularly, some lines (e.g., BJ-Line 7, BJ-Line 8, SH-Line 5, GZ-Line 14, GZ-Line 21, and SZ-Line 9) should take measures to improve the utilization of energy for their greater potential. At the city level, the average improvement values of the energy of Guangzhou ( −32.30%) and Shenzhen ( −30.72%) are larger than the average level, while those of Beijing ( −25.73%) and Shanghai ( −26.90%) are smaller than the average level. This indicates that the inefficient URT lines in Guangzhou and Shenzhen deserve more attention in terms of energy conservation.

#### 3.3.2. Output Adjustment Plan

In addition to the input plan, an improvement plan to maximize outputs is demonstrated. Firstly, in terms of passenger transport volume, the average improvement value of the passenger transport volume of observed lines is 53.50% (22.93 million person-times). In total, 21 URT lines (e.g., BJ-Line 1, SH-Line 6, GZ-Line 5, and SZ-Line 1) reach the optimal level. However, 16 lines are under the average level, while 14 lines are above the average level. Some lines (e.g., BJ-Yanfang Line, Daxing Airport Express, and SH-Line 16,) should improve passenger transport volume as much as possible for the lower output. At the city level, the average improvement value of the passenger transport volume of Shenzhen's URT lines is the closest to the optimal level among the case cities (i.e., 22.88%). By contrast, based on the results, the improvement values of Beijing (i.e., 89.96%) and Guangzhou (i.e., 52.28%) are lower than the average level. The lines with grea<sup>t</sup> improvement potential should be encouraged to expand passenger transport volume.

As for revenue passenger kilometers, the average improvement value of the URT lines is 34.54% (127.38 million passenger kilometers). In total, 29 URT lines (e.g., BJ-Line 1 and SZ-Line 1) are optimized, while 3 lines are above the average level and 19 lines are lower than the average value. It can be seen that most of the URT lines have produced sufficient passenger turnover output, while some lines have grea<sup>t</sup> improvement potential in passenger turnover, such as BJ-Line 16 (i.e., 259.66%) and BJ-Yanfang Line (i.e., 520.04%). From the city perspective, the average improvement value of URT lines in Shanghai is 7.15%, which is closer to the optimal level. At another extreme, the average improvement value of the URT lines in Beijing is 59.49%, which is much lower than the optimal level. The situations for Guangzhou and Shenzhen are between them.

Concerning CO2 emissions, the average improvement value of URT lines is 31.82% (36.5 kilotons). Only SZ-Line 10 reached the optimal level, while another 25 lines are above the average value and 26 are less than the average value. In particular, some lines are significantly lower than the optimal level, such as BJ-Line 7 (69.08%) and SZ-Line 9 (60.52%). There is a lot of room for these lines to decline CO2 emissions to maximize environmental sustainability. At the city level, compared with other cities, the average improvement value of CO2 emissions for the URT lines in Shanghai (25.82%) is closer to the ideal level. On the contrary, the largest gap between the actual CO2 emissions and the ideal emissions can be found in Beijing's URT lines (36.74%).
