**1. Introduction**

Over the past two decades, urban rail transit (URT) has rapidly developed to mitigate traffic congestion in China's megacities [1]. According to statistics, by the end of 2021, 50 cities on the Chinese mainland operated 283 URT lines with a total length of 9206.8 km [2]. Compared with other means of public transportation, URT is faster, more frequent, and punctual, which is an important part of urban public transportation. Due to the rapid increase in modernization and the advance of rail transit planning in urban agglomerations, URT has a larger potential development space in China. Improving the operational efficiency of URT makes a grea<sup>t</sup> impact on economic and social activities. Operational efficiency evaluation can identify sources of inefficiency and improve URT's operation, which has become one of the most important investigation topics [3,4].

In the literature, URT is usually considered a complex system with multiple inputs (e.g., train, line, station, and energy) to provide transit services and thereby produce multiple outputs (e.g., passenger kilometers, passenger volume, and train kilometers). The efficiency evaluation of public transport is always investigated by comparing multiple inputs and outputs comprehensively [5–8]. In this study, the operational efficiency of URT can be defined as the conversion efficiency between the input system and the output system. Multi-criteria decision analysis (MCDA) methods can be used to comprehensively evaluate alternatives [9–11]. However, different MCDA methods often produce contradictory results when comparing, and decisionmakers may obtain different decisions even using the same

**Citation:** Zhang, H.; Wang, X.; Chen, L.; Luo, Y.; Peng, S. Evaluation of the Operational Efficiency and Energy Efficiency of Rail Transit in China's Megacities Using a DEA Model. *Energies* **2022**, *15*, 7758. https:// doi.org/10.3390/en15207758

Academic Editors: Xi Gu, Tangbin Xia, Ershun Pan, Rongxi Wang and Yupeng Li

Received: 27 August 2022 Accepted: 7 October 2022 Published: 20 October 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

criteria weights and criterial evaluations of variants [11]. As one of the non-parametric approaches, data envelopment analysis (DEA) has the advantage of having no pre-determined weights, which is applicable in estimating the relative efficiency of decision-making units (DMUs) with multiple inputs and outputs. Since first proposed by Charnes et al. [12], DEA has been successfully and widely applied to measure efficiency in the public transport sector, such as railways (e.g., [13–15]), highway bus transit (e.g., [16–18]), shipping and ports (e.g., [19–21]), and airlines and airports (e.g., [22–24]).

In terms of the efficiency of URT, it can be measured at different levels, such as the city level and the company level. In this sense, Karlaftis [19] used the DEA model to measure the efficiency and effectiveness of 256 US URT systems, and the results showed that efficiency is positively correlated with effectiveness. Jain et al. [25] applied DEA to explore the relationship between technical efficiency and ownership structure for 15 global URT systems and found that privatization directly and positively impacts efficiency. Qin et al. [26] adopted a slacks-based multi-stage network DEA to assess the efficiency of 17 URT systems in China in 2012 and found that lower average overall efficiency is more related to inefficiencies in the earning stage and construction stage. Tsai et al. [27] used DEA to measure the efficiency of 20 international URT systems from 2009 to 2011 and suggested that the number of stations and population density impact efficiency significantly. Costa et al. [28] utilized DEA to compute the efficiency of four URT systems in Portugal from 2009 to 2018 and explored the impact of the ownership model on efficiency. The findings indicated that privately managed firms were more efficient than public firms. Although the above studies made grea<sup>t</sup> progress, estimation at the city or company level cannot identify the efficiency of specific lines or provide deeper insight into the improvement of efficiency at the line level.

To the best of our knowledge, studies on the efficiency of URT at the line level are scarce. Kang et al. [29] developed a mixed network DEA model and a hybrid two-stage network DEA model to explore the efficiency of two metro systems, including six lines in Taipei, and found that the efficiency results between the two models differed significantly. Le et al. [30] used the DEA model to measure the operational efficiency, cost efficiency, and revenue efficiency of 18 URT lines in the Tokyo Metropolitan Area in 2017. The results indicated that the in-vehicle congestion rate can be a reflection of the service quality in the operational efficiency measurement. Unfortunately, these two studies did not consider carbon emissions in the efficiency evaluation process. Due to growing environmental concerns, carbon emissions are considered an undesirable output in efficiency estimations in the transportation sector [31–33]. An efficiency measurement without considering carbon emissions may lead to imprecise operational efficiency results, which leaves a research gap.

In addition, with the increase in URT mileage, the corresponding energy consumption is also rising. The measurement of URT's energy efficiency can help operators save electricity and reduce operating costs and carbon emissions. However, while there are many studies on energy efficiency in the transportation sector [7,33–35], few works focus on the URT field. To the best of our knowledge, two studies are closely related to this topic. Xiao et al. [36] applied the DEA model to evaluate the energy efficiency of URT in Beijing Metro Lines 5 and 15 and the Batong Line without considering carbon emissions in the evaluation. To et al. [37] used the dimensional indicator to discuss the energy efficiency of Hong Kong's mass transit railway over the period from 2008–2017 and found that the energy efficiency was between 0.076 and 0.093 kWh per passenger–km and CO2 emissions were between 0.055–0.071 kg per passenger–km. Notably, the energy efficiency in this study was similar to the energy intensity. The efficiency evaluation did not consider other inputs and outputs and may not provide significant implications. Hence, there exists another gap related to energy efficiency in URT lines, which needs to be explored.

To fill the gaps, this study aims to estimate operational efficiency and energy efficiency considering CO2 emissions for URT at the line level, which is the novelty of this paper. To achieve this, an evaluation model based on the slacks-based measure (SBM) is developed to assess operational efficiency and energy efficiency synchronously. Furthermore, a method

of detecting the improvement potentials of inputs and outputs is proposed. Then, this study applies the proposed model to the URT lines in China's four megacities (Beijing, Shanghai, Guangzhou, and Shenzhen).

In summary, the contributions of this study are listed as follows. First, this study measures the operational efficiency and energy efficiency of the URT in consideration of CO2 emissions at the line level, which is a step further than previous studies have taken on undesirable outputs. Second, the proposed model can evaluate operational efficiency and energy efficiency simultaneously and provide more precise results. Third, an empirical study of China's 61 URT lines in four major cities verifies the effectiveness of the proposed model. This micro-level research may enrich the theoretical literature and provide new managemen<sup>t</sup> enlightenment for efficiency improvement in URT operation.

The remainder of this paper is structured as follows. The methodology is presented in Section 2. Section 3 presents the results, and Section 4 provides discussions. Finally, Section 5 illustrates the conclusions and limitations.
