# Measuring the Energy and Carbon Emission Efficiency of Regional Transportation Systems in China: Chance-Constrained DEA Models

Authors: Jianwei Ren; Bin Gao; Jiewei Zhang; Chunhua Chen
Journal: Mathematical Problems in Engineering
 (2020)

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## Abstract

In China, the transportation sector contributes about 18% of the total carbon emissions. This research contributes to measuring the energy and carbon emission efficiency (ECEE) of regional transportation systems (RTS) in China considering uncertain carbon emissions. A radial chance-constrained data envelopment analysis (DEA) model is developed to estimate the overall efficiency, and a nonradial chance-constrained DEA model is presented to evaluate the pure energy efficiency (PEE) and the pure carbon emission efficiency (PCEE). We prove that the proposed chance-constrained DEA models can effectively address the uncertain carbon emissions when measuring efficiency. We find that most of China’s RTS have low ECEE and the inefficiencies are mainly due to the lower gasoline utilization efficiency and the lower kerosene utilization efficiency. In addition, east China performs better than central China, and central China performs better than west China. In China, the unbalanced regional development of the ECEE in transportation corresponds with the unbalanced regional economic development. We provide some valuable suggestions based on the evaluation of the potential cuts in each kind of energy and the potential decreases in carbon emissions.


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## Body

## 1. Introduction

Since China started economic reforms in 1978, the country has been experiencing rapid economic development [1, 2]. According to the International Monetary Fund (IMF), China had a nominal Gross Domestic Product (GDP) of about 13.37 trillion U.S dollars in 2018. The nominal GDP value of China accounted for approximately 15.7 percent of the global economy [3]. IMF rated China as the largest economy by purchasing power parity (PPP) in the world [4].China’s rapid economic growth has significantly expanded its energy consumption [5]. Therefore, China should make every effort to shift to a green economy. Chinese government has been implementing many policies and measures to increase energy efficiency and reduce carbon emissions. By 2020, China intends to contract carbon dioxide (CO2) emissions per unit of GDP by 18% compared with the level in 2015 [6].The energy consumption and carbon emissions in the transportation sector are very high [7, 8]. The total energy consumption in the transportation sector of China was approximately 402 million tons of standard coal equivalent in 2017, an increase of 4.6% on the previous year. The transportation energy consumption in east China, central China, and west China (the detailed information of the three areas is shown in Section 3) occupied about 49% (197 million tons), 32% (127 million tons), and 19% (78 million tons) of the total energy consumption, respectively. In China, the transportation sector contributes about 18% of the total carbon emissions [9]. Hence, it is necessary to research the energy and carbon emission efficiency (ECEE) of the transportation sector in China.Several mathematical approaches can be used to evaluate the ECEE. However, data envelopment analysis (DEA) is most widely used (see the following paragraphs) [10]. DEA is a nonparametric mathematical method to measure the efficiency of decision-making units (DMUs) [11, 12]. DEA has been applied to evaluate the performance of hospitals, supply chains, universities, and other entities [13]. The CCR model (proposed by Charnes et al.) and the BCC model (proposed by Banker et al.) are two basic DEA models [14, 15]. The former assumes that technology exhibits constant returns to scale (CRS), and the latter is developed under the condition of variable returns to scale (VRS). In the past forty years, many DEA models, e.g., integer-valued DEA models [16], super-efficiency DEA models [17], generalized DEA models [18], slack-based DEA models [19], network DEA models [20], and stochastic DEA models [21], have been proposed based on the two models.Scholars have been studying the energy efficiency measurement for a long time. Ramanathan applied the CCR model and the BCC model to evaluate the energy efficiency of railways and roadways in India [22]. Hu and Wang used the DEA method to measure the total-factor energy efficiency of 29 regions in China [23]. Wu et al. proposed a DEA technique with nonhomogeneous variables to estimate the energy efficiency of industrial sectors in China [24]. Geng et al. proposed a DEA approach with the affinity propagation clustering algorithm (AP-DEA) to evaluate the energy efficiency of petrochemical industries [25]. However, undesirable outputs, e.g., carbon emissions, are not considered in the aforementioned DEA models. These energy efficiency evaluation models are not suitable in reality because the fossil fuel energy consumption will definitely generate carbon emissions [26]. Therefore, the efficiency scores obtained from these models may be distorted.Zhou et al. proposed slacks-based measures (SBM) to evaluate the CO2 emission efficiency of 30 OECD countries (the Organization for Economic Cooperation and Development) [27]. Zhou et al. applied DEA approaches to evaluate the carbon emission efficiency of eight world regions [28]. Wang et al. developed DEA approaches to compare the environmental efficiency of several provinces in China by taking CO2 emissions into account [29]. Wei et al. evaluated the CO2 emission efficiency of China’s 29 provinces by an extended SBM-DEA model [30]. Wang et al. applied a DEA window analysis approach to evaluate the regional environmental efficiency in China considering CO2 emissions [31]. Guo et al. developed a dynamic DEA model to measure the energy efficiency of OECD countries by taking CO2 emissions into consideration [32]. Cheng et al. used a time substitution DEA approach to estimate the carbon emission efficiency of China [33]. Chu et al. proposed an SBM-DEA approach to evaluate the environmental efficiency of China’s transportation system considering CO2 emissions [34]. Cui developed a network DEA approach to measure the greenhouse gas emission efficiency of 28 international airlines [35]. Djordjevic and Krmac applied a nonradial DEA and TOPSIS (the Technique for Order of Preference by Similarity to Ideal Solution) approach to measure the environmental efficiency of European transport systems by taking greenhouse gas emissions into account [36]. Zhou et al. proposed a DEA method according to an exponential transformation to evaluate the energy efficiency of China’s industry considering greenhouse gas emissions [37]. Omrani et al. developed a DEA-cooperative game method to estimate the energy efficiency of the transportation system in Iran by taking greenhouse gas emissions into account [38]. The disadvantage of the abovementioned literature is that they assume deterministic carbon emissions. However, it is impossible to get precise data related to carbon emissions, which could be caused by measurement errors, natural uncertainty of carbon emissions, and so on [39]. The results would be erroneous if decision-makers do not consider the uncertainty of carbon emissions when measuring the ECEE [39–43]. As a matter of fact, the deterministic DEA model is only a particular case of the uncertain DEA model [39].Wu et al. [40], Jin et al. [41], Zha et al. [39], Chen et al. [42], and Zhou et al. [43] used the chance-constrained DEA method to evaluate the environmental efficiency considering uncertain undesirable outputs. However, as far as we know, there is no literature on measuring the efficiency of regional transportation systems (RTS) by taking the uncertainty of carbon emissions into account, especially China’s RTS. It is necessary to research the RTS because of the unbalanced regional development in China [44]. The Chinese government should set up different policies for different RTS to improve their ECEE.The innovation of this paper is that, to the best of our knowledge, this is the first paper to measure the efficiency of RTS by taking uncertain carbon emissions into consideration. The contributions of this paper are that (1) a radial chance-constrained DEA model is presented to evaluate the overall efficiency; (2) a nonradial chance-constrained DEA model is developed to accurately estimate the pure energy efficiency (PEE) and the pure carbon emission efficiency (PCEE); (3) the proposed approaches are applied in the RTS in China and some valuable suggestions are provided.This paper is structured as follows. The chance-constrained DEA models are developed by taking uncertain carbon emissions into consideration in Section2. In Section 3, these models are applied to estimate the ECEE of thirty RTS in China, and some valuable suggestions are provided. Some conclusions are proposed in Section 4.


## 2. Methodology

A regional transportation system can be regarded as a DMU. Suppose thatDMUii∈1,2,…,q has p nonenergy inputs xjij=1,2,…,p, r energy inputs etit=1,2,…,r, m desirable outputs ylil=1,2,…,m, and an undesirable output ci (carbon emissions).To measure the environmental efficiency, Färe et al. handled undesirable outputs under the assumption of the weak disposability of undesirable outputs [45]. Nowadays, this method has been widely used. For given levels of inputs, it is impossible to simultaneously reduce carbon emissions and expand desirable outputs, e.g., passenger turnover, freight turnover, and transportation value-added. Therefore, to estimate the overall efficiency of RTS, we propose a radial DEA model (model 1) under the assumption of the weak disposability of the undesirable output (the amount of carbon emissions) [45, 46]. Model (1) is a radial DEA model as this model aims to proportionally reduce inputs and the undesirable output of DMUk [22, 45].(1)ΨkD=minθk−ε∑l=1msly++∑j=1psjx−+∑t=1rste−,s.t.∑i=1qλiyli−sly+=ylk,l=1,2,…,m,∑i=1qλici=θkck,∑i=1qλixji+sjx−=θkxjk,j=1,2,…,p,∑i=1qλieti+ste−=θketk,t=1,2,…,r,δ∑i=1qλi=δ,λi≥0,i=1,2,…,q,sly+≥0,l=1,2,…,m,sjx−≥0,j=1,2,…,p,ste−≥0,t=1,2,…,r,where λi is the weight of DMUi; ε is a non-Archimedean infinitesimal; and sjx−, ste−, and sly+ are the slack variables for the jth nonenergy input, the tth energy input, and the lth desirable output, respectively; δ=0 and δ=1 respectively represent the assumption of CRS and VRS.The optimal valueΨkD∗ is the technical efficiency score (or pure technical efficiency score) of DMUka when δ=0 (or δ=1). According to the definition of DEA efficiency, we have the following propositions: (i) DMUk is efficient when ΨkD∗=1(θk∗=1 and sjx−∗=sly+∗=ste−∗=0); (ii) DMUk is inefficient when ΨkD∗<1.Model (1) is called the radial deterministic DEA model because it can only be used when all the needed data are precise. However, as discussed above, the value of carbon emissions is uncertain. Therefore, we have to develop a stochastic DEA model. To do so, we first propose model (2) that is the dual of model (1). All slack variables are deleted in the following transformation processes for the sake of clarity.(2)ΨkD=max∑l=1mμlylk−δμ0,s.t.∑l=1mμlyli−δμ0−∑j=1pvjxji−∑t=1rfteti−wci≤0,i=1,2,…,q,∑j=1pvjxjk+∑t=1rftetk+wck=1,μl≥0,l=1,2,…,m,vj≥0,j=1,2,…,p,ft≥0,t=1,2,…,r,wandμ0are free,where μl, vj, ft, and w are the weights for the lth desirable output, the jth nonenergy input, the t th energy input, and the undesirable out, respectively.As stated in Section1, the stochastic chance-constrained DEA is an effective method to evaluate the environmental efficiency considering uncertain undesirable outputs. Thus, we also propose a radial stochastic chance-constrained DEA model (model 3) based on model (2) to measure the overall efficiency of RTS by taking uncertain carbon emissions into consideration.(3)ΨkS=max∑l=1mμlylk−δμ0,s.t.P∑l=1mμlyli−δμ0−∑j=1pvjxji−∑t=1rfteti−wci∧≤0≥1−αi,i=1,2,…,q,∑j=1pvjxjk+∑t=1rftetk+wEck∧=1,μl≥0,l=1,2,…,m,vj≥0,j=1,2,…,p,ft≥0,t=1,2,…,r,wandμ0are free,where ci∧ indicates stochastic carbon emissions; Eck∧ represents the expected value of ck∧; P is the “probability” measurement of the corresponding constraint; and 1−αi is the probability of satisfying the inequality ∑l=1mμlyli−δμ0−∑j=1pvjxji−∑t=1rfteti−wci∧≤0. In other words, 1−αi indicates a confidence level while αi represents a risk criterion [47, 48].As model (3) is a nonlinear model, we should transform it into a linear model. Obviously, inequality (4) is only a transformation of the stochastic chance constraint in model (3).(4)P∑l=1mμlyli−δμ0−∑j=1pvjxji−∑t=1rfteti≤wci∧≥1−αi.Let us define thatci¯ denotes the expected value of ci∧ and Gi indicates the variance of wci∧. The inequality (4) then can be transformed into the following inequality:(5)P∑l=1mμlyli−δμ0−∑j=1pvjxji−∑t=1rfteti−wci¯Gi≤wci∧−wci¯Gi≥1−αi.Assume thatwci∧−wci¯/Gi obeys N0,1 (standard normal distribution) and Φ denotes its cumulative distribution function. The inequality (5) then can be transformed into the following inequality:(6)∑l=1mμlyli−δμ0−∑j=1pvjxji−∑t=1rfteti−wci¯Gi≤Φ−1αi,where Φ−1 represents the inverse function of Φ. We assume ci∧=ci¯+φiκi and Eci∧=ci¯, where ci¯ represents ci∧’s expected value and φi denotes the standard deviation. Assume that κi=wci∧−wci¯/Gi follows N0,1. Then, we have Gi=wφi2, and model (3) can be transformed into the following model:(7)ΨkS=max∑l=1mμlylk−δμ0,s.t.∑l=1mμlyli−δμ0−∑j=1pvjxji−∑t=1rfteti−wci¯+Φ−1αiφi≤0,i=1,2,…,q,∑j=1pvjxjk+∑t=1rftetk+wck¯=1,μl≥0,l=1,2,…,m,vj≥0,j=1,2,…,p,ft≥0,t=1,2,…,r,wandμ0are free.The dual of model (7) can be denoted by model (8) that aims to proportionally reduce inputs and uncertain carbon emissions of DMUk. It is worth noting that slack variables are added into model (8). We have transformed nonlinear model (3) into linear model (8) that is called the radial chance-constrained DEA model. The optimal objective function value ΨkS∗ of model (8) is the technical efficiency score (or pure technical efficiency score) of DMUk when δ=0 (or δ=1).(8)ΨkS=minθk−ε∑l=1msly++∑j=1psjx−+∑t=1rste−,s.t.∑i=1qλiyli−sly+=ylk,l=1,2,…,m,∑i=1qλici¯+Φ−1αiφi=θkck¯,∑i=1qλixji+sjx−=θkxjk,j=1,2,…,p,∑i=1qλieti+ste−=θketk,t=1,2,...,r,δ∑i=1qλi=δ,λi≥0,i=1,2,…,q,sly+≥0,l=1,2,…,m,sjx−≥0,j=1,2,…,p,ste−≥0,t=1,2,…,r.According to the definition of DEA efficiency, we have the following propositions: (i)DMUk is superefficient when ΨkS∗>1; (ii) DMUk is efficient when ΨkS∗=1(θk∗=1 and sjx−∗=sly+∗=ste−∗=0); (iii) DMUk is inefficient when ΨkS∗<1.The advantages of the radial chance-constrained DEA model are that (1) it can be used to deal with undesirable outputs that cannot be disposed of; (2) it can be used to handle stochastic variables. However, model (8) cannot be used to evaluate the PEE or PCEE. Therefore, we have to extend it to a nonradial chance-constrained DEA model (model 9). Model (9) optimizes the carbon emissions and energy consumption without changing the desirable outputs and nonenergy inputs. We evaluate the ECEE by assigning weights to the PEE and PCEE [29, 39].(9)ΨkES=minϖe∑t=1rρtθte+ϖcθc−ε∑l=1msly++∑j=1psjx−+∑t=1rste−,s.t.∑i=1qλiyli−sly+=ylk,l=1,2,…,m,∑i=1qλici¯+φiΦ−αi=θcck¯,∑i=1qλixji+sjx−=xjk,j=1,2,…,p,∑i=1qλieti+ste−=θteetk,t=1,2,...,r,δ∑i=1qλi=δ,λi≥0,i=1,2,…,q,sly+≥0,l=1,2,…,m,sjx−≥0,j=1,2,…,p,ste−≥0,t=1,2,…,r,where θte indicates the tth PEE (pure efficiency of energy t); θc is the PCEE; ϖe and ϖc respectively represent the weights of the PEE and PCEE; and ρt is the weight of the t th energy input. There must be ϖe+ϖc=1 and ∑t=1rρt=1. The PEE indicates the utilization performance of transportation fuels, and the PCEE reflects the performance of carbon emission cuts.For an inefficient regional transportation system, its potential energy savings and carbon emission cuts can be calculated using the following equations, respectively:(10)Δetk=1−θte∗etk+ste−∗,(11)Δck¯=1−θc∗ck¯.


## 3. Empirical Study

The proposed models are used to estimate the ECEE of China’s RTS in 2017.


### 3.1. Data

Mainland China includes 31 provinces, and the regional disparity is wide. These provinces can be classified into three areas, i.e., the eastern area, the central area, and the western area. The eastern area, which is the most developed and densely populated area, comprises of eleven provinces; The central area includes ten provinces; The western area, which is the least developed and sparsely populated area, is composed of ten provinces [44]. The data about transportation energy consumption in Tibet are not available so that we have to exclude Tibet. Therefore, thirty provinces are involved in this research.We select employed persons (labor), fixed-asset investment (capital), and civil motor vehicles as three nonenergy input variables. Gasoline consumption, kerosene consumption, and diesel consumption are regarded as three energy input variables. Passenger turnover, freight turnover, and transportation value-added are selected as three desirable output variables. The amount of carbon emissions from transportation is defined as a single undesirable output.The chosen nonenergy input, desirable outputs, and undesirable outputs in this paper are vital indicators for transport systems and have been used widely in previous research [36, 38]. Gasoline, kerosene, and diesel are selected as three energy inputs because they are the dominant transportation fuels in China. As shown in Figure 1, diesel makes up more than 40% of the total transportation energy consumption, gasoline occupies more than 20%, and kerosene accounts for more than 10% [49]. We cannot select all transportation fuels as energy inputs according to the rule of thumb [50].Figure 1
China’s transportation energy consumption.The data related to employed persons (unit: 10 thousand persons), civil motor vehicles (unit: 10 thousand vehicles), fixed-asset investment (unit: 1 billion CNY), passenger turnover (unit: 1 billion passenger/km), freight turnover (unit: 1 billion ton/km), and transportation value-added (unit: 1 billion CNY) are obtained from [51]. The data related to energy consumption (unit: 10 thousand tons of standard coal equivalent) are calculated using the following equation:(12)eti=zti×Ft,t=1,2,3,where eti (unit: 10 thousand tons of standard coal equivalent) represents the consumption of energy t by DMUi; zti (unit: 10 thousand tons) also indicates the consumption of energy t by DMUi; and Ft denotes the standard coal coefficient of the tth energy (gasoline, 1.4714; kerosene, 1.4714; diesel, 1.4571) [52]. The values of ztit=1,2,3 are obtained from [49].The amount of carbon emissions from transportation (units: 10 thousand tons) can be calculated using the following equation:(13)ci=∑t=16eti×Dt,where ci represents the carbon emissions of DMUi; eti indicates the consumption of the tth energy by DMUi; and Dt denotes the carbon emission coefficient for the tth energy (gasoline, 0.5538; kerosene, 0.5714; diesel, 0.5921; coal, 0.7559; fuel oil, 0.6185; natural gas, 0.4483) [53]. Although we only select three transportation fuels as energy inputs, we want to calculate carbon emissions generated from all transportation fuels. Note that the electric power, which can be generated by wind power and hydropower, is not included in our research because the carbon emission coefficients of both wind power and hydropower are zero.We suppose that the expected carbon emissions from transportation are equal to the estimated carbon emissions. Therefore, we haveEci∧=ci¯=ci∧i=1,2,…,q. The standard deviation of carbon emissions from transportation is calculated using the dataset of the estimated carbon emissions from 2013 to 2017. The descriptive statistics of all selected variables of RTS in mainland China are shown in Table 1. Table 2 shows the detailed data related to carbon emissions from transportation.Table 1
Descriptive statistics of all selected variables.
Variable
Max
Min
Mean
Std. dev.
Employed persons
52.05
3.23
22.11
12.00
Fixed-asset investment
449.26
33.01
188.70
114.44
Civil motor vehicles
1922.38
98.73
688.92
494.96
Gasoline
853.54
12.09
264.67
216.21
Kerosene
958.79
0.00
170.73
233.92
Diesel
1618.71
61.74
520.02
351.02
Passenger turnover
201.23
9.92
77.52
50.59
Freight turnover
2791.98
51.95
632.24
651.67
Added-value
358.09
10.37
133.48
89.72
Carbon emissions
1848.20
101.50
659.15
386.65Table 2
Carbon emissions.
Area
Province
Mean
Std. dev.
East
Beijing
622.92
38.24
Tianjin
233.78
5.39
Hebei
487.88
31.90
Liaoning
1008.50
61.30
Shanghai
1241.82
142.31
Jiangsu
1077.54
72.99
Zhejiang
793.02
33.80
Fujian
560.66
48.75
Shandong
1082.88
76.60
Guangdong
1668.08
140.85
Hainan
162.14
4.35
Central
Shanxi
517.54
27.50
Nei Mongol
632.02
111.62
Jilin
464.58
40.56
Heilongjiang
614.18
23.60
Anhui
555.98
31.15
Jiangxi
378.08
22.92
Henan
696.00
32.46
Hubei
865.16
108.76
Hunan
739.22
80.20
Guangxi
486.14
58.30
West
Chongqing
491.32
51.57
Sichuan
594.00
159.15
Guizhou
393.00
29.62
Yunnan
566.96
34.73
Shaanxi
394.06
27.25
Gansu
276.88
8.04
Qinghai
89.10
13.91
Ningxia
100.90
3.31
Xinjiang
501.36
64.89


### 3.2. Results

#### 3.2.1. Overall Efficiency

The overall efficiency of the thirty RTS in mainland China is calculated using the proposed radial chance-constrained DEA model (model 8). We also compare the efficiency scores resulting from model (8) with those resulting from the radial deterministic DEA model (model 1).Tables3 and 4 respectively show the efficiency scores under the assumption of CRS δ=0 and VRS δ=1. We use four groups of values (αi=0.5, αi=0.1, αi=0.05, and αi=0.01) to study the effects of αi on the results of efficiency evaluation, and we select αi=0.05 as the risk criterion in this study as it is set 0.05 in the related literature [39–43].Table 3
Overall technical efficiency (assuming CRS).
Area
Province
Model 1
Model 8
α
i
=
0.5
α
i
=
0.1
α
i
=
0.05
α
i
=
0.01
East
Beijing
1.000
1.000
0.977
0.971
0.961
Tianjin
1.000
1.000
1.029
1.037
1.053
Hebei
1.000
1.000
1.085
1.109
1.154
Liaoning
1.000
1.000
1.056
1.072
1.101
Shanghai
1.000
1.000
1.120
1.154
1.216
Jiangsu
1.000
1.000
0.919
0.905
0.886
Zhejiang
1.000
1.000
1.002
1.003
1.004
Fujian
0.992
0.992
0.906
0.892
0.875
Shandong
1.000
1.000
1.033
1.042
1.058
Guangdong
1.000
1.000
0.948
0.937
0.918
Hainan
1.000
1.000
0.995
0.994
0.991
Central
Shanxi
1.000
1.000
1.011
1.013
1.018
Nei Mongol
1.000
1.000
0.974
0.969
0.963
Jilin
1.000
1.000
0.975
0.969
0.959
Heilongjiang
1.000
1.000
1.021
1.027
1.038
Anhui
1.000
1.000
1.047
1.060
1.085
Jiangxi
1.000
1.000
1.071
1.092
1.130
Henan
1.000
1.000
1.051
1.066
1.097
Hubei
1.000
1.000
0.965
0.958
0.947
Hunan
1.000
1.000
1.060
1.075
1.101
Guangxi
0.857
0.857
0.843
0.846
0.857
West
Chongqing
1.000
1.000
0.927
0.912
0.890
Sichuan
0.808
0.808
0.819
0.822
0.827
Guizhou
1.000
1.000
1.043
1.054
1.073
Yunnan
0.435
0.435
0.421
0.426
0.436
Shaanxi
1.000
1.000
1.020
1.024
1.031
Gansu
1.000
1.000
1.031
1.041
1.061
Qinghai
1.000
1.000
1.155
1.198
1.278
Ningxia
1.000
1.000
1.042
1.054
1.076
Xinjiang
1.000
1.000
0.948
0.937
0.919
Average
0.970
0.970
0.983
0.989
1.000Table 4
Overall pure technical efficiency (assuming VRS).
Area
Province
Model 1
Model 8
α
i
=
0.5
α
i
=
0.1
α
i
=
0.05
α
i
=
0.01
East
Beijing
1.000
1.000
0.977
0.972
0.962
Tianjin
1.000
1.000
1.029
1.037
1.053
Hebei
1.000
1.000
1.085
1.109
1.154
Liaoning
1.000
1.000
1.057
1.073
1.102
Shanghai
1.000
1.000
1.129
1.165
1.234
Jiangsu
1.000
1.000
1.080
1.102
1.144
Zhejiang
1.000
1.000
1.006
1.007
1.010
Fujian
0.996
0.996
0.910
0.897
0.876
Shandong
1.000
1.000
1.080
1.103
1.145
Guangdong
1.000
1.000
1.097
1.125
1.176
Hainan
1.000
1.000
1.027
1.035
1.049
Central
Shanxi
1.000
1.000
1.019
1.025
1.034
Nei Mongol
1.000
1.000
1.040
1.047
1.058
Jilin
1.000
1.000
0.975
0.969
0.960
Heilongjiang
1.000
1.000
1.024
1.031
1.043
Anhui
1.000
1.000
1.048
1.061
1.086
Jiangxi
1.000
1.000
1.072
1.092
1.130
Henan
1.000
1.000
1.058
1.074
1.105
Hubei
1.000
1.000
0.969
0.963
0.960
Hunan
1.000
1.000
1.076
1.095
1.128
Guangxi
0.895
0.895
0.877
0.881
0.887
West
Chongqing
1.000
1.000
0.929
0.915
0.894
Sichuan
0.853
0.853
0.834
0.834
0.833
Guizhou
1.000
1.000
1.051
1.064
1.085
Yunnan
0.622
0.622
0.495
0.497
0.503
Shaanxi
1.000
1.000
1.023
1.027
1.035
Gansu
1.000
1.000
1.038
1.049
1.069
Qinghai
1.000
1.000
1.159
1.201
1.280
Ningxia
1.000
1.000
1.042
1.054
1.076
Xinjiang
1.000
1.000
0.983
0.979
0.972
Average
0.979
0.979
1.006
1.016
1.035As shown in Table3, the efficiency scores resulting from model (1) are the same as those resulting from model (8) with αi=0.5, which implies that the radial deterministic DEA model (model 1) is only a particular case of the radial chance-constrained DEA model (model 8). Furthermore, only four RTS are regarded as inefficient DMUs based on their overall technical efficiency scores resulting from model (1). However, based on their overall technical efficiency scores resulting from model (8), we have thirteen inefficient RTS when αi=0.1, αi=0.05, or αi=0.01. The results prove that decision-makers should take the uncertainty of carbon emissions into account when they measure the efficiency of RTS. Otherwise, the results may be doubtful. As shown in Table 4, we can get the same results under the assumption of VRS δ=1.The proposed radial chance-constrained DEA model (model 8) is more effective than the radial deterministic DEA model (model 1) because (i) it has higher discriminatory ability than model (1) as stated above; (ii) we cannot rank efficient RTS because all of their efficiency scores obtained from model (1) are equal to one (for example, as shown in Table 3, Beijing, Tianjin, Hebei, Liaoning, Shanghai, Jiangsu, Zhejiang, Shandong, Guangdong, Hainan, Shanxi, Nei Mongol, Jilin, Heilongjiang, Anhui, Jiangxi, Henan, Hubei, Hunan, Chongqing, Guizhou, Shaanxi, Gansu, Qinghai, Ningxia, and Xinjiang.), but their efficiency scores resulting from the radial chance-constrained DEA model can be greater than one, which makes it possible to differentiate the efficient RTS.As shown in Tables3 and 4, the efficiency scores (technical efficiency score and pure technical efficiency score) of Qinghai are the highest, while Yunnan has the lowest scores. Therefore, Yunnan should make every effort to improve the performance of its transportation system.As shown in Table5, based on the overall efficiency scores of the three areas under both CRS and VRS, the performance of east China is the best while west China is the worst. It indicates that the unbalanced regional development of overall efficiency in transportation corresponds with the unbalanced regional economic development.Table 5
Overall efficiency of east, central, and west China.
Area
Technology
Model 1
Model 8
α
i
=
0.5
α
i
=
0.1
α
i
=
0.05
α
i
=
0.01
East
CRS
0.999
0.999
1.006
1.011
1.020
Central
CRS
0.986
0.986
1.002
1.008
1.019
West
CRS
0.916
0.916
0.934
0.941
0.955
East
VRS
1.000
1.000
1.043
1.057
1.082
Central
VRS
0.989
0.989
1.016
1.024
1.039
West
VRS
0.942
0.942
0.950
0.958
0.972


#### 3.2.2. PEE and PCEE

The proposed nonradial chance-constrained DEA model (model 9) is used to evaluate the PEE and PCEE of China’s RTS. We setϖe=ϖc=0.5 because carbon emissions are generated by combusting energy fuels. Moreover, the weights for the three energy inputs can be calculated using the following equation [39]:(14)ρt=Dt∑t=13Dt,where Dt is the carbon emission coefficient of energy t (as shown in Section 3.1). We finally obtain ρkerosene=0.332732, ρkerosene=0.332732, and ρdiesel=0.344785.Tables6 and 7 show the efficiency scores of these RTS resulting from the nonradial chance-constrained DEA model (model 9) under the assumption of CRS δ=0 and VRS δ=1, respectively. It can be observed that the transportation system of Ningxia does not have feasible solutions for its kerosene utilization efficiency. The reason is that the consumption of kerosene in Ningxia’s transportation system is zero.Table 6
PEE and PCEE (assuming CRS).
Area
Province
Ψ
k
ES
Ψ
k
Gas
Ψ
k
Ker
Ψ
k
Die
Ψ
k
c
East
Beijing
0.455
0.448
0.180
0.835
0.418
Tianjin
1.019
1.000
1.000
1.000
1.037
Hebei
1.055
1.000
1.000
1.000
1.109
Liaoning
1.047
1.000
1.000
1.000
1.095
Shanghai
1.083
1.000
1.000
1.000
1.165
Jiangsu
0.520
0.170
0.400
0.877
0.551
Zhejiang
0.510
0.155
0.160
1.086
0.543
Fujian
0.621
0.326
0.626
0.780
0.661
Shandong
1.052
1.000
1.000
1.000
1.103
Guangdong
0.728
0.497
0.878
0.629
0.788
Hainan
0.437
0.460
0.060
1.017
0.355
Central
Shanxi
0.709
0.676
1.179
0.510
0.634
Nei Mongol
0.560
0.170
0.837
0.890
0.480
Jilin
0.611
0.886
0.969
0.640
0.394
Heilongjiang
0.469
0.130
0.101
1.573
0.320
Anhui
1.043
1.000
1.000
1.000
1.086
Jiangxi
1.046
1.000
1.000
1.000
1.092
Henan
0.970
1.351
0.313
0.945
1.075
Hubei
0.537
0.383
0.235
0.842
0.583
Hunan
1.079
1.000
1.000
1.000
1.157
Guangxi
0.511
0.385
0.155
0.673
0.615
West
Chongqing
0.447
0.808
0.257
0.372
0.420
Sichuan
0.429
0.197
0.062
0.906
0.464
Guizhou
1.062
1.000
1.000
1.000
1.124
Yunnan
0.254
0.206
0.087
0.303
0.309
Shaanxi
0.771
0.527
0.245
1.053
0.928
Gansu
1.024
1.000
1.000
1.000
1.049
Qinghai
1.104
1.000
1.000
1.000
1.208
Ningxia
0.860
1.000
—
1.000
1.054
Xinjiang
0.332
0.412
0.170
0.375
0.346
Average
0.745
0.673
0.618
0.877
0.772Table 7
PEE and PCEE (assuming VRS).
Area
Province
Ψ
k
ES
Ψ
k
Gas
Ψ
k
Ker
Ψ
k
Die
Ψ
k
c
East
Beijing
0.560
0.472
0.180
1.164
0.508
Tianjin
1.019
1.000
1.000
1.000
1.037
Hebei
1.055
1.000
1.000
1.000
1.109
Liaoning
1.047
1.000
1.000
1.000
1.095
Shanghai
1.083
1.000
1.000
1.000
1.165
Jiangsu
1.051
1.000
1.000
1.000
1.102
Zhejiang
0.517
0.162
0.151
1.101
0.553
Fujian
0.631
0.329
0.630
0.797
0.671
Shandong
1.052
1.000
1.000
1.000
1.103
Guangdong
1.063
1.000
1.000
1.000
1.125
Hainan
1.021
1.000
1.000
1.000
1.043
Central
Shanxi
1.041
1.000
1.000
1.000
1.082
Nei Mongol
0.679
0.343
0.547
1.313
0.613
Jilin
0.653
0.921
0.681
0.851
0.489
Heilongjiang
0.583
0.123
0.133
1.997
0.393
Anhui
1.043
1.000
1.000
1.000
1.086
Jiangxi
1.046
1.000
1.000
1.000
1.092
Henan
1.037
1.000
1.000
1.000
1.075
Hubei
0.720
0.448
0.703
0.801
0.785
Hunan
1.079
1.000
1.000
1.000
1.157
Guangxi
0.542
0.398
0.160
0.723
0.653
West
Chongqing
0.492
0.714
0.370
0.409
0.490
Sichuan
0.454
0.206
0.058
0.970
0.490
Guizhou
1.062
1.000
1.000
1.000
1.124
Yunnan
0.305
0.277
0.052
0.372
0.376
Shaanxi
0.778
0.523
0.255
1.063
0.937
Gansu
1.024
1.000
1.000
1.000
1.049
Qinghai
1.104
1.000
1.000
1.000
1.208
Ningxia
0.860
1.000
—
1.000
1.054
Xinjiang
0.380
0.327
0.307
0.421
0.408
Average
0.833
0.741
0.697
0.966
0.869Table6 shows that the technical efficiency score ΨkES of energy utilization and carbon emissions in Qinghai is the highest while Yunnan has the lowest score. The results are consistent with those obtained from model (8) under the CRS condition. The technical efficiency score ΨkGas of gasoline utilization in Henan is the highest while Heilongjiang has the lowest score. The technical efficiency score ΨkKer of kerosene utilization in Shanxi is the highest while Hainan has the lowest score. The technical efficiency score ΨkDie of diesel utilization in Heilongjiang is the highest while Yunnan has the lowest score. The technical efficiency score Ψkc of carbon emissions in Qinghai is the highest while Yunnan has the lowest score.The averageΨkES, ΨkGas, ΨkKer, ΨkDie, and Ψkc under CRS are 0.745, 0.673, 0.618, 0.877, and 0.772, respectively, which implies that the technical inefficiencies of energy utilization and carbon emissions ΨkES in transportation are mainly due to the lower technical efficiency of gasoline utilization ΨkGas and the lower technical efficiency of kerosene utilization ΨkKer.Table7 shows that the pure technical efficiency score ΨkES of energy utilization and carbon emissions in Qinghai is the highest while Yunnan has the lowest score. The results are consistent with those obtained from model (8) under the assumption of VRS. There is no pure technical superefficient province of gasoline utilization or kerosene utilization. The pure technical efficiency score ΨkGas of gasoline utilization in Heilongjiang is the lowest, and the pure technical efficiency score ΨkKer of kerosene utilization in Yunnan is the lowest. The pure technical efficiency score ΨkDie of diesel utilization in Heilongjiang is the highest while Yunnan has the lowest score. The pure technical efficiency score Ψkc of carbon emissions in Qinghai is the highest while Yunnan has the lowest score.The averageΨkES, ΨkGas, ΨkKer, ΨkDie, and Ψkc under VRS are 0.833, 0.741, 0.697, 0.966, 0.869, respectively, which implies that the pure technical inefficiencies of energy utilization and carbon emissions ΨkGas in transportation are mainly due to the lower pure technical efficiency of gasoline utilization ΨkGas and the lower pure technical efficiency of kerosene utilization ΨkKer.As shown in Table8, under both CRS and VRS, the ECEE ΨkES of the eastern area is the best while the western area is the worst. The results are consistent with those obtained from model (8). The PCEE Ψkc of the eastern area is also the best under both CRS and VRS. However, the rankings of the central area and the western area are different under different assumptions of production technology. The PEE (ΨkGas, ΨkKer, or ΨkDie) of the eastern area is not always the highest in mainland China. For instance, the eastern area has the lowest technical efficiency score of gasoline utilization.Table 8
PEE and PCEE of east, central, and west China.
Area
Technology
Ψ
k
ES
Ψ
k
Gas
Ψ
k
Ker
Ψ
k
Die
Ψ
k
c
East
CRS
0.775
0.641
0.664
0.929
0.802
Central
CRS
0.754
0.698
0.679
0.907
0.743
West
CRS
0.698
0.683
0.478
0.779
0.767
East
VRS
0.918
0.815
0.815
1.006
0.956
Central
VRS
0.842
0.723
0.722
1.069
0.843
West
VRS
0.718
0.672
0.505
0.804
0.793


### 3.3. Discussion and Suggestion

The uncertainty of carbon emissions can significantly affect the results of efficiency evaluation. Therefore, decision-makers should take uncertain carbon emissions into account when they measure the performance of RTS [54, 55]. The risk criterion also has effects on the results of efficiency evaluation. Hence, a scientific risk criterion is required when decision-makers measure the performance of DMUs using the proposed chance-constrained DEA models.The performance of Yunnan’s transportation system is the worst in mainland China. It has the lowest overall efficiency scores (the technical efficiency score and the pure technical efficiency score), the lowest pure technical efficiency score of kerosene utilization, the lowest efficiency scores (the technical efficiency score and the pure technical efficiency score) of diesel utilization, and the lowest efficiency scores (the technical efficiency score and the pure technical efficiency score) of carbon emissions. Therefore, Yunnan should put forth the greatest possible effort to increase the efficiency of its transportation system. The transportation system of Heilongjiang should make every effort to increase its efficiency of gasoline utilization. The transportation system of Hainan should put forth its best effort to increase its technical efficiency of kerosene utilization.In China, the unbalanced regional development of the ECEE in transportation corresponds with the unbalanced regional economic development. East China performs better than central China, and central China performs better than west China. Hence, China should try its best to improve the performance of RTS in the western area.Figure2 shows the potential cuts in each kind of energy and the potential decreases in carbon emissions of each inefficient regional transportation system under the assumption of CRS. It is noteworthy that there are twelve efficient DMUs, i.e., Tianjin, Hebei, Liaoning, Shanghai, Shandong, Anhui, Jiangxi, Hunan, Guizhou, Gansu, Qinghai, and Ningxia (as shown in Table 6). It can be observed that the eastern area (especially, Jiangsu, Zhejiang, and Guangdong) can save many energy fuels and reduce lots of carbon emissions as the eastern area is the largest transportation fuel consumer and the largest carbon emitter in the three areas. Hence, China should also improve the efficiency of RTS in the eastern area.Figure 2
The potential energy savings and the potential carbon emission cuts.


## 3.1. Data

Mainland China includes 31 provinces, and the regional disparity is wide. These provinces can be classified into three areas, i.e., the eastern area, the central area, and the western area. The eastern area, which is the most developed and densely populated area, comprises of eleven provinces; The central area includes ten provinces; The western area, which is the least developed and sparsely populated area, is composed of ten provinces [44]. The data about transportation energy consumption in Tibet are not available so that we have to exclude Tibet. Therefore, thirty provinces are involved in this research.We select employed persons (labor), fixed-asset investment (capital), and civil motor vehicles as three nonenergy input variables. Gasoline consumption, kerosene consumption, and diesel consumption are regarded as three energy input variables. Passenger turnover, freight turnover, and transportation value-added are selected as three desirable output variables. The amount of carbon emissions from transportation is defined as a single undesirable output.The chosen nonenergy input, desirable outputs, and undesirable outputs in this paper are vital indicators for transport systems and have been used widely in previous research [36, 38]. Gasoline, kerosene, and diesel are selected as three energy inputs because they are the dominant transportation fuels in China. As shown in Figure 1, diesel makes up more than 40% of the total transportation energy consumption, gasoline occupies more than 20%, and kerosene accounts for more than 10% [49]. We cannot select all transportation fuels as energy inputs according to the rule of thumb [50].Figure 1
China’s transportation energy consumption.The data related to employed persons (unit: 10 thousand persons), civil motor vehicles (unit: 10 thousand vehicles), fixed-asset investment (unit: 1 billion CNY), passenger turnover (unit: 1 billion passenger/km), freight turnover (unit: 1 billion ton/km), and transportation value-added (unit: 1 billion CNY) are obtained from [51]. The data related to energy consumption (unit: 10 thousand tons of standard coal equivalent) are calculated using the following equation:(12)eti=zti×Ft,t=1,2,3,where eti (unit: 10 thousand tons of standard coal equivalent) represents the consumption of energy t by DMUi; zti (unit: 10 thousand tons) also indicates the consumption of energy t by DMUi; and Ft denotes the standard coal coefficient of the tth energy (gasoline, 1.4714; kerosene, 1.4714; diesel, 1.4571) [52]. The values of ztit=1,2,3 are obtained from [49].The amount of carbon emissions from transportation (units: 10 thousand tons) can be calculated using the following equation:(13)ci=∑t=16eti×Dt,where ci represents the carbon emissions of DMUi; eti indicates the consumption of the tth energy by DMUi; and Dt denotes the carbon emission coefficient for the tth energy (gasoline, 0.5538; kerosene, 0.5714; diesel, 0.5921; coal, 0.7559; fuel oil, 0.6185; natural gas, 0.4483) [53]. Although we only select three transportation fuels as energy inputs, we want to calculate carbon emissions generated from all transportation fuels. Note that the electric power, which can be generated by wind power and hydropower, is not included in our research because the carbon emission coefficients of both wind power and hydropower are zero.We suppose that the expected carbon emissions from transportation are equal to the estimated carbon emissions. Therefore, we haveEci∧=ci¯=ci∧i=1,2,…,q. The standard deviation of carbon emissions from transportation is calculated using the dataset of the estimated carbon emissions from 2013 to 2017. The descriptive statistics of all selected variables of RTS in mainland China are shown in Table 1. Table 2 shows the detailed data related to carbon emissions from transportation.Table 1
Descriptive statistics of all selected variables.
Variable
Max
Min
Mean
Std. dev.
Employed persons
52.05
3.23
22.11
12.00
Fixed-asset investment
449.26
33.01
188.70
114.44
Civil motor vehicles
1922.38
98.73
688.92
494.96
Gasoline
853.54
12.09
264.67
216.21
Kerosene
958.79
0.00
170.73
233.92
Diesel
1618.71
61.74
520.02
351.02
Passenger turnover
201.23
9.92
77.52
50.59
Freight turnover
2791.98
51.95
632.24
651.67
Added-value
358.09
10.37
133.48
89.72
Carbon emissions
1848.20
101.50
659.15
386.65Table 2
Carbon emissions.
Area
Province
Mean
Std. dev.
East
Beijing
622.92
38.24
Tianjin
233.78
5.39
Hebei
487.88
31.90
Liaoning
1008.50
61.30
Shanghai
1241.82
142.31
Jiangsu
1077.54
72.99
Zhejiang
793.02
33.80
Fujian
560.66
48.75
Shandong
1082.88
76.60
Guangdong
1668.08
140.85
Hainan
162.14
4.35
Central
Shanxi
517.54
27.50
Nei Mongol
632.02
111.62
Jilin
464.58
40.56
Heilongjiang
614.18
23.60
Anhui
555.98
31.15
Jiangxi
378.08
22.92
Henan
696.00
32.46
Hubei
865.16
108.76
Hunan
739.22
80.20
Guangxi
486.14
58.30
West
Chongqing
491.32
51.57
Sichuan
594.00
159.15
Guizhou
393.00
29.62
Yunnan
566.96
34.73
Shaanxi
394.06
27.25
Gansu
276.88
8.04
Qinghai
89.10
13.91
Ningxia
100.90
3.31
Xinjiang
501.36
64.89


## 3.2. Results

### 3.2.1. Overall Efficiency

The overall efficiency of the thirty RTS in mainland China is calculated using the proposed radial chance-constrained DEA model (model 8). We also compare the efficiency scores resulting from model (8) with those resulting from the radial deterministic DEA model (model 1).Tables3 and 4 respectively show the efficiency scores under the assumption of CRS δ=0 and VRS δ=1. We use four groups of values (αi=0.5, αi=0.1, αi=0.05, and αi=0.01) to study the effects of αi on the results of efficiency evaluation, and we select αi=0.05 as the risk criterion in this study as it is set 0.05 in the related literature [39–43].Table 3
Overall technical efficiency (assuming CRS).
Area
Province
Model 1
Model 8
α
i
=
0.5
α
i
=
0.1
α
i
=
0.05
α
i
=
0.01
East
Beijing
1.000
1.000
0.977
0.971
0.961
Tianjin
1.000
1.000
1.029
1.037
1.053
Hebei
1.000
1.000
1.085
1.109
1.154
Liaoning
1.000
1.000
1.056
1.072
1.101
Shanghai
1.000
1.000
1.120
1.154
1.216
Jiangsu
1.000
1.000
0.919
0.905
0.886
Zhejiang
1.000
1.000
1.002
1.003
1.004
Fujian
0.992
0.992
0.906
0.892
0.875
Shandong
1.000
1.000
1.033
1.042
1.058
Guangdong
1.000
1.000
0.948
0.937
0.918
Hainan
1.000
1.000
0.995
0.994
0.991
Central
Shanxi
1.000
1.000
1.011
1.013
1.018
Nei Mongol
1.000
1.000
0.974
0.969
0.963
Jilin
1.000
1.000
0.975
0.969
0.959
Heilongjiang
1.000
1.000
1.021
1.027
1.038
Anhui
1.000
1.000
1.047
1.060
1.085
Jiangxi
1.000
1.000
1.071
1.092
1.130
Henan
1.000
1.000
1.051
1.066
1.097
Hubei
1.000
1.000
0.965
0.958
0.947
Hunan
1.000
1.000
1.060
1.075
1.101
Guangxi
0.857
0.857
0.843
0.846
0.857
West
Chongqing
1.000
1.000
0.927
0.912
0.890
Sichuan
0.808
0.808
0.819
0.822
0.827
Guizhou
1.000
1.000
1.043
1.054
1.073
Yunnan
0.435
0.435
0.421
0.426
0.436
Shaanxi
1.000
1.000
1.020
1.024
1.031
Gansu
1.000
1.000
1.031
1.041
1.061
Qinghai
1.000
1.000
1.155
1.198
1.278
Ningxia
1.000
1.000
1.042
1.054
1.076
Xinjiang
1.000
1.000
0.948
0.937
0.919
Average
0.970
0.970
0.983
0.989
1.000Table 4
Overall pure technical efficiency (assuming VRS).
Area
Province
Model 1
Model 8
α
i
=
0.5
α
i
=
0.1
α
i
=
0.05
α
i
=
0.01
East
Beijing
1.000
1.000
0.977
0.972
0.962
Tianjin
1.000
1.000
1.029
1.037
1.053
Hebei
1.000
1.000
1.085
1.109
1.154
Liaoning
1.000
1.000
1.057
1.073
1.102
Shanghai
1.000
1.000
1.129
1.165
1.234
Jiangsu
1.000
1.000
1.080
1.102
1.144
Zhejiang
1.000
1.000
1.006
1.007
1.010
Fujian
0.996
0.996
0.910
0.897
0.876
Shandong
1.000
1.000
1.080
1.103
1.145
Guangdong
1.000
1.000
1.097
1.125
1.176
Hainan
1.000
1.000
1.027
1.035
1.049
Central
Shanxi
1.000
1.000
1.019
1.025
1.034
Nei Mongol
1.000
1.000
1.040
1.047
1.058
Jilin
1.000
1.000
0.975
0.969
0.960
Heilongjiang
1.000
1.000
1.024
1.031
1.043
Anhui
1.000
1.000
1.048
1.061
1.086
Jiangxi
1.000
1.000
1.072
1.092
1.130
Henan
1.000
1.000
1.058
1.074
1.105
Hubei
1.000
1.000
0.969
0.963
0.960
Hunan
1.000
1.000
1.076
1.095
1.128
Guangxi
0.895
0.895
0.877
0.881
0.887
West
Chongqing
1.000
1.000
0.929
0.915
0.894
Sichuan
0.853
0.853
0.834
0.834
0.833
Guizhou
1.000
1.000
1.051
1.064
1.085
Yunnan
0.622
0.622
0.495
0.497
0.503
Shaanxi
1.000
1.000
1.023
1.027
1.035
Gansu
1.000
1.000
1.038
1.049
1.069
Qinghai
1.000
1.000
1.159
1.201
1.280
Ningxia
1.000
1.000
1.042
1.054
1.076
Xinjiang
1.000
1.000
0.983
0.979
0.972
Average
0.979
0.979
1.006
1.016
1.035As shown in Table3, the efficiency scores resulting from model (1) are the same as those resulting from model (8) with αi=0.5, which implies that the radial deterministic DEA model (model 1) is only a particular case of the radial chance-constrained DEA model (model 8). Furthermore, only four RTS are regarded as inefficient DMUs based on their overall technical efficiency scores resulting from model (1). However, based on their overall technical efficiency scores resulting from model (8), we have thirteen inefficient RTS when αi=0.1, αi=0.05, or αi=0.01. The results prove that decision-makers should take the uncertainty of carbon emissions into account when they measure the efficiency of RTS. Otherwise, the results may be doubtful. As shown in Table 4, we can get the same results under the assumption of VRS δ=1.The proposed radial chance-constrained DEA model (model 8) is more effective than the radial deterministic DEA model (model 1) because (i) it has higher discriminatory ability than model (1) as stated above; (ii) we cannot rank efficient RTS because all of their efficiency scores obtained from model (1) are equal to one (for example, as shown in Table 3, Beijing, Tianjin, Hebei, Liaoning, Shanghai, Jiangsu, Zhejiang, Shandong, Guangdong, Hainan, Shanxi, Nei Mongol, Jilin, Heilongjiang, Anhui, Jiangxi, Henan, Hubei, Hunan, Chongqing, Guizhou, Shaanxi, Gansu, Qinghai, Ningxia, and Xinjiang.), but their efficiency scores resulting from the radial chance-constrained DEA model can be greater than one, which makes it possible to differentiate the efficient RTS.As shown in Tables3 and 4, the efficiency scores (technical efficiency score and pure technical efficiency score) of Qinghai are the highest, while Yunnan has the lowest scores. Therefore, Yunnan should make every effort to improve the performance of its transportation system.As shown in Table5, based on the overall efficiency scores of the three areas under both CRS and VRS, the performance of east China is the best while west China is the worst. It indicates that the unbalanced regional development of overall efficiency in transportation corresponds with the unbalanced regional economic development.Table 5
Overall efficiency of east, central, and west China.
Area
Technology
Model 1
Model 8
α
i
=
0.5
α
i
=
0.1
α
i
=
0.05
α
i
=
0.01
East
CRS
0.999
0.999
1.006
1.011
1.020
Central
CRS
0.986
0.986
1.002
1.008
1.019
West
CRS
0.916
0.916
0.934
0.941
0.955
East
VRS
1.000
1.000
1.043
1.057
1.082
Central
VRS
0.989
0.989
1.016
1.024
1.039
West
VRS
0.942
0.942
0.950
0.958
0.972


### 3.2.2. PEE and PCEE

The proposed nonradial chance-constrained DEA model (model 9) is used to evaluate the PEE and PCEE of China’s RTS. We setϖe=ϖc=0.5 because carbon emissions are generated by combusting energy fuels. Moreover, the weights for the three energy inputs can be calculated using the following equation [39]:(14)ρt=Dt∑t=13Dt,where Dt is the carbon emission coefficient of energy t (as shown in Section 3.1). We finally obtain ρkerosene=0.332732, ρkerosene=0.332732, and ρdiesel=0.344785.Tables6 and 7 show the efficiency scores of these RTS resulting from the nonradial chance-constrained DEA model (model 9) under the assumption of CRS δ=0 and VRS δ=1, respectively. It can be observed that the transportation system of Ningxia does not have feasible solutions for its kerosene utilization efficiency. The reason is that the consumption of kerosene in Ningxia’s transportation system is zero.Table 6
PEE and PCEE (assuming CRS).
Area
Province
Ψ
k
ES
Ψ
k
Gas
Ψ
k
Ker
Ψ
k
Die
Ψ
k
c
East
Beijing
0.455
0.448
0.180
0.835
0.418
Tianjin
1.019
1.000
1.000
1.000
1.037
Hebei
1.055
1.000
1.000
1.000
1.109
Liaoning
1.047
1.000
1.000
1.000
1.095
Shanghai
1.083
1.000
1.000
1.000
1.165
Jiangsu
0.520
0.170
0.400
0.877
0.551
Zhejiang
0.510
0.155
0.160
1.086
0.543
Fujian
0.621
0.326
0.626
0.780
0.661
Shandong
1.052
1.000
1.000
1.000
1.103
Guangdong
0.728
0.497
0.878
0.629
0.788
Hainan
0.437
0.460
0.060
1.017
0.355
Central
Shanxi
0.709
0.676
1.179
0.510
0.634
Nei Mongol
0.560
0.170
0.837
0.890
0.480
Jilin
0.611
0.886
0.969
0.640
0.394
Heilongjiang
0.469
0.130
0.101
1.573
0.320
Anhui
1.043
1.000
1.000
1.000
1.086
Jiangxi
1.046
1.000
1.000
1.000
1.092
Henan
0.970
1.351
0.313
0.945
1.075
Hubei
0.537
0.383
0.235
0.842
0.583
Hunan
1.079
1.000
1.000
1.000
1.157
Guangxi
0.511
0.385
0.155
0.673
0.615
West
Chongqing
0.447
0.808
0.257
0.372
0.420
Sichuan
0.429
0.197
0.062
0.906
0.464
Guizhou
1.062
1.000
1.000
1.000
1.124
Yunnan
0.254
0.206
0.087
0.303
0.309
Shaanxi
0.771
0.527
0.245
1.053
0.928
Gansu
1.024
1.000
1.000
1.000
1.049
Qinghai
1.104
1.000
1.000
1.000
1.208
Ningxia
0.860
1.000
—
1.000
1.054
Xinjiang
0.332
0.412
0.170
0.375
0.346
Average
0.745
0.673
0.618
0.877
0.772Table 7
PEE and PCEE (assuming VRS).
Area
Province
Ψ
k
ES
Ψ
k
Gas
Ψ
k
Ker
Ψ
k
Die
Ψ
k
c
East
Beijing
0.560
0.472
0.180
1.164
0.508
Tianjin
1.019
1.000
1.000
1.000
1.037
Hebei
1.055
1.000
1.000
1.000
1.109
Liaoning
1.047
1.000
1.000
1.000
1.095
Shanghai
1.083
1.000
1.000
1.000
1.165
Jiangsu
1.051
1.000
1.000
1.000
1.102
Zhejiang
0.517
0.162
0.151
1.101
0.553
Fujian
0.631
0.329
0.630
0.797
0.671
Shandong
1.052
1.000
1.000
1.000
1.103
Guangdong
1.063
1.000
1.000
1.000
1.125
Hainan
1.021
1.000
1.000
1.000
1.043
Central
Shanxi
1.041
1.000
1.000
1.000
1.082
Nei Mongol
0.679
0.343
0.547
1.313
0.613
Jilin
0.653
0.921
0.681
0.851
0.489
Heilongjiang
0.583
0.123
0.133
1.997
0.393
Anhui
1.043
1.000
1.000
1.000
1.086
Jiangxi
1.046
1.000
1.000
1.000
1.092
Henan
1.037
1.000
1.000
1.000
1.075
Hubei
0.720
0.448
0.703
0.801
0.785
Hunan
1.079
1.000
1.000
1.000
1.157
Guangxi
0.542
0.398
0.160
0.723
0.653
West
Chongqing
0.492
0.714
0.370
0.409
0.490
Sichuan
0.454
0.206
0.058
0.970
0.490
Guizhou
1.062
1.000
1.000
1.000
1.124
Yunnan
0.305
0.277
0.052
0.372
0.376
Shaanxi
0.778
0.523
0.255
1.063
0.937
Gansu
1.024
1.000
1.000
1.000
1.049
Qinghai
1.104
1.000
1.000
1.000
1.208
Ningxia
0.860
1.000
—
1.000
1.054
Xinjiang
0.380
0.327
0.307
0.421
0.408
Average
0.833
0.741
0.697
0.966
0.869Table6 shows that the technical efficiency score ΨkES of energy utilization and carbon emissions in Qinghai is the highest while Yunnan has the lowest score. The results are consistent with those obtained from model (8) under the CRS condition. The technical efficiency score ΨkGas of gasoline utilization in Henan is the highest while Heilongjiang has the lowest score. The technical efficiency score ΨkKer of kerosene utilization in Shanxi is the highest while Hainan has the lowest score. The technical efficiency score ΨkDie of diesel utilization in Heilongjiang is the highest while Yunnan has the lowest score. The technical efficiency score Ψkc of carbon emissions in Qinghai is the highest while Yunnan has the lowest score.The averageΨkES, ΨkGas, ΨkKer, ΨkDie, and Ψkc under CRS are 0.745, 0.673, 0.618, 0.877, and 0.772, respectively, which implies that the technical inefficiencies of energy utilization and carbon emissions ΨkES in transportation are mainly due to the lower technical efficiency of gasoline utilization ΨkGas and the lower technical efficiency of kerosene utilization ΨkKer.Table7 shows that the pure technical efficiency score ΨkES of energy utilization and carbon emissions in Qinghai is the highest while Yunnan has the lowest score. The results are consistent with those obtained from model (8) under the assumption of VRS. There is no pure technical superefficient province of gasoline utilization or kerosene utilization. The pure technical efficiency score ΨkGas of gasoline utilization in Heilongjiang is the lowest, and the pure technical efficiency score ΨkKer of kerosene utilization in Yunnan is the lowest. The pure technical efficiency score ΨkDie of diesel utilization in Heilongjiang is the highest while Yunnan has the lowest score. The pure technical efficiency score Ψkc of carbon emissions in Qinghai is the highest while Yunnan has the lowest score.The averageΨkES, ΨkGas, ΨkKer, ΨkDie, and Ψkc under VRS are 0.833, 0.741, 0.697, 0.966, 0.869, respectively, which implies that the pure technical inefficiencies of energy utilization and carbon emissions ΨkGas in transportation are mainly due to the lower pure technical efficiency of gasoline utilization ΨkGas and the lower pure technical efficiency of kerosene utilization ΨkKer.As shown in Table8, under both CRS and VRS, the ECEE ΨkES of the eastern area is the best while the western area is the worst. The results are consistent with those obtained from model (8). The PCEE Ψkc of the eastern area is also the best under both CRS and VRS. However, the rankings of the central area and the western area are different under different assumptions of production technology. The PEE (ΨkGas, ΨkKer, or ΨkDie) of the eastern area is not always the highest in mainland China. For instance, the eastern area has the lowest technical efficiency score of gasoline utilization.Table 8
PEE and PCEE of east, central, and west China.
Area
Technology
Ψ
k
ES
Ψ
k
Gas
Ψ
k
Ker
Ψ
k
Die
Ψ
k
c
East
CRS
0.775
0.641
0.664
0.929
0.802
Central
CRS
0.754
0.698
0.679
0.907
0.743
West
CRS
0.698
0.683
0.478
0.779
0.767
East
VRS
0.918
0.815
0.815
1.006
0.956
Central
VRS
0.842
0.723
0.722
1.069
0.843
West
VRS
0.718
0.672
0.505
0.804
0.793


## 3.2.1. Overall Efficiency

The overall efficiency of the thirty RTS in mainland China is calculated using the proposed radial chance-constrained DEA model (model 8). We also compare the efficiency scores resulting from model (8) with those resulting from the radial deterministic DEA model (model 1).Tables3 and 4 respectively show the efficiency scores under the assumption of CRS δ=0 and VRS δ=1. We use four groups of values (αi=0.5, αi=0.1, αi=0.05, and αi=0.01) to study the effects of αi on the results of efficiency evaluation, and we select αi=0.05 as the risk criterion in this study as it is set 0.05 in the related literature [39–43].Table 3
Overall technical efficiency (assuming CRS).
Area
Province
Model 1
Model 8
α
i
=
0.5
α
i
=
0.1
α
i
=
0.05
α
i
=
0.01
East
Beijing
1.000
1.000
0.977
0.971
0.961
Tianjin
1.000
1.000
1.029
1.037
1.053
Hebei
1.000
1.000
1.085
1.109
1.154
Liaoning
1.000
1.000
1.056
1.072
1.101
Shanghai
1.000
1.000
1.120
1.154
1.216
Jiangsu
1.000
1.000
0.919
0.905
0.886
Zhejiang
1.000
1.000
1.002
1.003
1.004
Fujian
0.992
0.992
0.906
0.892
0.875
Shandong
1.000
1.000
1.033
1.042
1.058
Guangdong
1.000
1.000
0.948
0.937
0.918
Hainan
1.000
1.000
0.995
0.994
0.991
Central
Shanxi
1.000
1.000
1.011
1.013
1.018
Nei Mongol
1.000
1.000
0.974
0.969
0.963
Jilin
1.000
1.000
0.975
0.969
0.959
Heilongjiang
1.000
1.000
1.021
1.027
1.038
Anhui
1.000
1.000
1.047
1.060
1.085
Jiangxi
1.000
1.000
1.071
1.092
1.130
Henan
1.000
1.000
1.051
1.066
1.097
Hubei
1.000
1.000
0.965
0.958
0.947
Hunan
1.000
1.000
1.060
1.075
1.101
Guangxi
0.857
0.857
0.843
0.846
0.857
West
Chongqing
1.000
1.000
0.927
0.912
0.890
Sichuan
0.808
0.808
0.819
0.822
0.827
Guizhou
1.000
1.000
1.043
1.054
1.073
Yunnan
0.435
0.435
0.421
0.426
0.436
Shaanxi
1.000
1.000
1.020
1.024
1.031
Gansu
1.000
1.000
1.031
1.041
1.061
Qinghai
1.000
1.000
1.155
1.198
1.278
Ningxia
1.000
1.000
1.042
1.054
1.076
Xinjiang
1.000
1.000
0.948
0.937
0.919
Average
0.970
0.970
0.983
0.989
1.000Table 4
Overall pure technical efficiency (assuming VRS).
Area
Province
Model 1
Model 8
α
i
=
0.5
α
i
=
0.1
α
i
=
0.05
α
i
=
0.01
East
Beijing
1.000
1.000
0.977
0.972
0.962
Tianjin
1.000
1.000
1.029
1.037
1.053
Hebei
1.000
1.000
1.085
1.109
1.154
Liaoning
1.000
1.000
1.057
1.073
1.102
Shanghai
1.000
1.000
1.129
1.165
1.234
Jiangsu
1.000
1.000
1.080
1.102
1.144
Zhejiang
1.000
1.000
1.006
1.007
1.010
Fujian
0.996
0.996
0.910
0.897
0.876
Shandong
1.000
1.000
1.080
1.103
1.145
Guangdong
1.000
1.000
1.097
1.125
1.176
Hainan
1.000
1.000
1.027
1.035
1.049
Central
Shanxi
1.000
1.000
1.019
1.025
1.034
Nei Mongol
1.000
1.000
1.040
1.047
1.058
Jilin
1.000
1.000
0.975
0.969
0.960
Heilongjiang
1.000
1.000
1.024
1.031
1.043
Anhui
1.000
1.000
1.048
1.061
1.086
Jiangxi
1.000
1.000
1.072
1.092
1.130
Henan
1.000
1.000
1.058
1.074
1.105
Hubei
1.000
1.000
0.969
0.963
0.960
Hunan
1.000
1.000
1.076
1.095
1.128
Guangxi
0.895
0.895
0.877
0.881
0.887
West
Chongqing
1.000
1.000
0.929
0.915
0.894
Sichuan
0.853
0.853
0.834
0.834
0.833
Guizhou
1.000
1.000
1.051
1.064
1.085
Yunnan
0.622
0.622
0.495
0.497
0.503
Shaanxi
1.000
1.000
1.023
1.027
1.035
Gansu
1.000
1.000
1.038
1.049
1.069
Qinghai
1.000
1.000
1.159
1.201
1.280
Ningxia
1.000
1.000
1.042
1.054
1.076
Xinjiang
1.000
1.000
0.983
0.979
0.972
Average
0.979
0.979
1.006
1.016
1.035As shown in Table3, the efficiency scores resulting from model (1) are the same as those resulting from model (8) with αi=0.5, which implies that the radial deterministic DEA model (model 1) is only a particular case of the radial chance-constrained DEA model (model 8). Furthermore, only four RTS are regarded as inefficient DMUs based on their overall technical efficiency scores resulting from model (1). However, based on their overall technical efficiency scores resulting from model (8), we have thirteen inefficient RTS when αi=0.1, αi=0.05, or αi=0.01. The results prove that decision-makers should take the uncertainty of carbon emissions into account when they measure the efficiency of RTS. Otherwise, the results may be doubtful. As shown in Table 4, we can get the same results under the assumption of VRS δ=1.The proposed radial chance-constrained DEA model (model 8) is more effective than the radial deterministic DEA model (model 1) because (i) it has higher discriminatory ability than model (1) as stated above; (ii) we cannot rank efficient RTS because all of their efficiency scores obtained from model (1) are equal to one (for example, as shown in Table 3, Beijing, Tianjin, Hebei, Liaoning, Shanghai, Jiangsu, Zhejiang, Shandong, Guangdong, Hainan, Shanxi, Nei Mongol, Jilin, Heilongjiang, Anhui, Jiangxi, Henan, Hubei, Hunan, Chongqing, Guizhou, Shaanxi, Gansu, Qinghai, Ningxia, and Xinjiang.), but their efficiency scores resulting from the radial chance-constrained DEA model can be greater than one, which makes it possible to differentiate the efficient RTS.As shown in Tables3 and 4, the efficiency scores (technical efficiency score and pure technical efficiency score) of Qinghai are the highest, while Yunnan has the lowest scores. Therefore, Yunnan should make every effort to improve the performance of its transportation system.As shown in Table5, based on the overall efficiency scores of the three areas under both CRS and VRS, the performance of east China is the best while west China is the worst. It indicates that the unbalanced regional development of overall efficiency in transportation corresponds with the unbalanced regional economic development.Table 5
Overall efficiency of east, central, and west China.
Area
Technology
Model 1
Model 8
α
i
=
0.5
α
i
=
0.1
α
i
=
0.05
α
i
=
0.01
East
CRS
0.999
0.999
1.006
1.011
1.020
Central
CRS
0.986
0.986
1.002
1.008
1.019
West
CRS
0.916
0.916
0.934
0.941
0.955
East
VRS
1.000
1.000
1.043
1.057
1.082
Central
VRS
0.989
0.989
1.016
1.024
1.039
West
VRS
0.942
0.942
0.950
0.958
0.972


## 3.2.2. PEE and PCEE

The proposed nonradial chance-constrained DEA model (model 9) is used to evaluate the PEE and PCEE of China’s RTS. We setϖe=ϖc=0.5 because carbon emissions are generated by combusting energy fuels. Moreover, the weights for the three energy inputs can be calculated using the following equation [39]:(14)ρt=Dt∑t=13Dt,where Dt is the carbon emission coefficient of energy t (as shown in Section 3.1). We finally obtain ρkerosene=0.332732, ρkerosene=0.332732, and ρdiesel=0.344785.Tables6 and 7 show the efficiency scores of these RTS resulting from the nonradial chance-constrained DEA model (model 9) under the assumption of CRS δ=0 and VRS δ=1, respectively. It can be observed that the transportation system of Ningxia does not have feasible solutions for its kerosene utilization efficiency. The reason is that the consumption of kerosene in Ningxia’s transportation system is zero.Table 6
PEE and PCEE (assuming CRS).
Area
Province
Ψ
k
ES
Ψ
k
Gas
Ψ
k
Ker
Ψ
k
Die
Ψ
k
c
East
Beijing
0.455
0.448
0.180
0.835
0.418
Tianjin
1.019
1.000
1.000
1.000
1.037
Hebei
1.055
1.000
1.000
1.000
1.109
Liaoning
1.047
1.000
1.000
1.000
1.095
Shanghai
1.083
1.000
1.000
1.000
1.165
Jiangsu
0.520
0.170
0.400
0.877
0.551
Zhejiang
0.510
0.155
0.160
1.086
0.543
Fujian
0.621
0.326
0.626
0.780
0.661
Shandong
1.052
1.000
1.000
1.000
1.103
Guangdong
0.728
0.497
0.878
0.629
0.788
Hainan
0.437
0.460
0.060
1.017
0.355
Central
Shanxi
0.709
0.676
1.179
0.510
0.634
Nei Mongol
0.560
0.170
0.837
0.890
0.480
Jilin
0.611
0.886
0.969
0.640
0.394
Heilongjiang
0.469
0.130
0.101
1.573
0.320
Anhui
1.043
1.000
1.000
1.000
1.086
Jiangxi
1.046
1.000
1.000
1.000
1.092
Henan
0.970
1.351
0.313
0.945
1.075
Hubei
0.537
0.383
0.235
0.842
0.583
Hunan
1.079
1.000
1.000
1.000
1.157
Guangxi
0.511
0.385
0.155
0.673
0.615
West
Chongqing
0.447
0.808
0.257
0.372
0.420
Sichuan
0.429
0.197
0.062
0.906
0.464
Guizhou
1.062
1.000
1.000
1.000
1.124
Yunnan
0.254
0.206
0.087
0.303
0.309
Shaanxi
0.771
0.527
0.245
1.053
0.928
Gansu
1.024
1.000
1.000
1.000
1.049
Qinghai
1.104
1.000
1.000
1.000
1.208
Ningxia
0.860
1.000
—
1.000
1.054
Xinjiang
0.332
0.412
0.170
0.375
0.346
Average
0.745
0.673
0.618
0.877
0.772Table 7
PEE and PCEE (assuming VRS).
Area
Province
Ψ
k
ES
Ψ
k
Gas
Ψ
k
Ker
Ψ
k
Die
Ψ
k
c
East
Beijing
0.560
0.472
0.180
1.164
0.508
Tianjin
1.019
1.000
1.000
1.000
1.037
Hebei
1.055
1.000
1.000
1.000
1.109
Liaoning
1.047
1.000
1.000
1.000
1.095
Shanghai
1.083
1.000
1.000
1.000
1.165
Jiangsu
1.051
1.000
1.000
1.000
1.102
Zhejiang
0.517
0.162
0.151
1.101
0.553
Fujian
0.631
0.329
0.630
0.797
0.671
Shandong
1.052
1.000
1.000
1.000
1.103
Guangdong
1.063
1.000
1.000
1.000
1.125
Hainan
1.021
1.000
1.000
1.000
1.043
Central
Shanxi
1.041
1.000
1.000
1.000
1.082
Nei Mongol
0.679
0.343
0.547
1.313
0.613
Jilin
0.653
0.921
0.681
0.851
0.489
Heilongjiang
0.583
0.123
0.133
1.997
0.393
Anhui
1.043
1.000
1.000
1.000
1.086
Jiangxi
1.046
1.000
1.000
1.000
1.092
Henan
1.037
1.000
1.000
1.000
1.075
Hubei
0.720
0.448
0.703
0.801
0.785
Hunan
1.079
1.000
1.000
1.000
1.157
Guangxi
0.542
0.398
0.160
0.723
0.653
West
Chongqing
0.492
0.714
0.370
0.409
0.490
Sichuan
0.454
0.206
0.058
0.970
0.490
Guizhou
1.062
1.000
1.000
1.000
1.124
Yunnan
0.305
0.277
0.052
0.372
0.376
Shaanxi
0.778
0.523
0.255
1.063
0.937
Gansu
1.024
1.000
1.000
1.000
1.049
Qinghai
1.104
1.000
1.000
1.000
1.208
Ningxia
0.860
1.000
—
1.000
1.054
Xinjiang
0.380
0.327
0.307
0.421
0.408
Average
0.833
0.741
0.697
0.966
0.869Table6 shows that the technical efficiency score ΨkES of energy utilization and carbon emissions in Qinghai is the highest while Yunnan has the lowest score. The results are consistent with those obtained from model (8) under the CRS condition. The technical efficiency score ΨkGas of gasoline utilization in Henan is the highest while Heilongjiang has the lowest score. The technical efficiency score ΨkKer of kerosene utilization in Shanxi is the highest while Hainan has the lowest score. The technical efficiency score ΨkDie of diesel utilization in Heilongjiang is the highest while Yunnan has the lowest score. The technical efficiency score Ψkc of carbon emissions in Qinghai is the highest while Yunnan has the lowest score.The averageΨkES, ΨkGas, ΨkKer, ΨkDie, and Ψkc under CRS are 0.745, 0.673, 0.618, 0.877, and 0.772, respectively, which implies that the technical inefficiencies of energy utilization and carbon emissions ΨkES in transportation are mainly due to the lower technical efficiency of gasoline utilization ΨkGas and the lower technical efficiency of kerosene utilization ΨkKer.Table7 shows that the pure technical efficiency score ΨkES of energy utilization and carbon emissions in Qinghai is the highest while Yunnan has the lowest score. The results are consistent with those obtained from model (8) under the assumption of VRS. There is no pure technical superefficient province of gasoline utilization or kerosene utilization. The pure technical efficiency score ΨkGas of gasoline utilization in Heilongjiang is the lowest, and the pure technical efficiency score ΨkKer of kerosene utilization in Yunnan is the lowest. The pure technical efficiency score ΨkDie of diesel utilization in Heilongjiang is the highest while Yunnan has the lowest score. The pure technical efficiency score Ψkc of carbon emissions in Qinghai is the highest while Yunnan has the lowest score.The averageΨkES, ΨkGas, ΨkKer, ΨkDie, and Ψkc under VRS are 0.833, 0.741, 0.697, 0.966, 0.869, respectively, which implies that the pure technical inefficiencies of energy utilization and carbon emissions ΨkGas in transportation are mainly due to the lower pure technical efficiency of gasoline utilization ΨkGas and the lower pure technical efficiency of kerosene utilization ΨkKer.As shown in Table8, under both CRS and VRS, the ECEE ΨkES of the eastern area is the best while the western area is the worst. The results are consistent with those obtained from model (8). The PCEE Ψkc of the eastern area is also the best under both CRS and VRS. However, the rankings of the central area and the western area are different under different assumptions of production technology. The PEE (ΨkGas, ΨkKer, or ΨkDie) of the eastern area is not always the highest in mainland China. For instance, the eastern area has the lowest technical efficiency score of gasoline utilization.Table 8
PEE and PCEE of east, central, and west China.
Area
Technology
Ψ
k
ES
Ψ
k
Gas
Ψ
k
Ker
Ψ
k
Die
Ψ
k
c
East
CRS
0.775
0.641
0.664
0.929
0.802
Central
CRS
0.754
0.698
0.679
0.907
0.743
West
CRS
0.698
0.683
0.478
0.779
0.767
East
VRS
0.918
0.815
0.815
1.006
0.956
Central
VRS
0.842
0.723
0.722
1.069
0.843
West
VRS
0.718
0.672
0.505
0.804
0.793


## 3.3. Discussion and Suggestion

The uncertainty of carbon emissions can significantly affect the results of efficiency evaluation. Therefore, decision-makers should take uncertain carbon emissions into account when they measure the performance of RTS [54, 55]. The risk criterion also has effects on the results of efficiency evaluation. Hence, a scientific risk criterion is required when decision-makers measure the performance of DMUs using the proposed chance-constrained DEA models.The performance of Yunnan’s transportation system is the worst in mainland China. It has the lowest overall efficiency scores (the technical efficiency score and the pure technical efficiency score), the lowest pure technical efficiency score of kerosene utilization, the lowest efficiency scores (the technical efficiency score and the pure technical efficiency score) of diesel utilization, and the lowest efficiency scores (the technical efficiency score and the pure technical efficiency score) of carbon emissions. Therefore, Yunnan should put forth the greatest possible effort to increase the efficiency of its transportation system. The transportation system of Heilongjiang should make every effort to increase its efficiency of gasoline utilization. The transportation system of Hainan should put forth its best effort to increase its technical efficiency of kerosene utilization.In China, the unbalanced regional development of the ECEE in transportation corresponds with the unbalanced regional economic development. East China performs better than central China, and central China performs better than west China. Hence, China should try its best to improve the performance of RTS in the western area.Figure2 shows the potential cuts in each kind of energy and the potential decreases in carbon emissions of each inefficient regional transportation system under the assumption of CRS. It is noteworthy that there are twelve efficient DMUs, i.e., Tianjin, Hebei, Liaoning, Shanghai, Shandong, Anhui, Jiangxi, Hunan, Guizhou, Gansu, Qinghai, and Ningxia (as shown in Table 6). It can be observed that the eastern area (especially, Jiangsu, Zhejiang, and Guangdong) can save many energy fuels and reduce lots of carbon emissions as the eastern area is the largest transportation fuel consumer and the largest carbon emitter in the three areas. Hence, China should also improve the efficiency of RTS in the eastern area.Figure 2
The potential energy savings and the potential carbon emission cuts.


## 4. Conclusion

This study proposes chance-constrained DEA models to estimate the energy and carbon emission efficiency (ECEE) of regional transportation systems (RTS) considering uncertain carbon emissions. The overall efficiency of thirty regional transportation systems in mainland China is calculated using the radial chance-constrained DEA model. We prove that the radial deterministic DEA model is only a particular case of the radial chance-constrained DEA model. The pure energy efficiency (PEE) and the pure carbon emission efficiency (PCEE) of the thirty regional transportation systems are estimated using the proposed nonradial chance-constrained DEA model. We prove that this model can provide more valuable information for decision-makers, i.e., how to save each transportation fuel and reduce carbon emissions. We find that most of China’s regional transportation systems have low energy and carbon emission efficiency and the inefficiencies are mainly due to the lower gasoline utilization efficiency and the lower kerosene utilization efficiency.We suggest that (1) China should try its best to improve the performance of the regional transportation systems in the western area because its efficiency is the lowest; (2) China should also improve the performance of the regional transportation systems in the eastern area because the eastern area can save many energy fuels and reduce lots of carbon emissions (especially, Jiangsu, Zhejiang, and Guangdong).Measuring the energy and carbon emission efficiency (ECEE) of regional transportation systems is an important and hot topic. The results of this study are helpful for the Chinese government to set up different policies for different RTS to improve their ECEE. In fact, the proposed approaches can be also applied to measure the RTS in other countries. In addition, we can measure the ECEE of RTS considering other uncertain inputs and outputs.



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*Source: 9740704-2020-04-21.xml*