## 3 Models and Methods  
Super-Efficiency Data Envelopment Analysis Model with Slack-Based Measure Considering Undesirable Outputs  
Data Envelopment Analysis (DEA) was first proposed by [PERSON] et al. in 1978 [48]. It is a non-parametric efficiency evaluation method that uses a mathematical planning model to calculate the distance between each Decision Making Unit (DMU) and the production frontier consisting of the best performing DMUs in practice, and further to calculate the efficiency score of each DMU. However, the traditional DEA model cannot deal with efficiency issues that include undesirable outputs. In 2001, a Slacks-Basic Measure (SBM) model based on relaxation measures was proposed by [PERSON] [49], which can solve the efficiency evaluation problem including undesired outputs. The SBM method, which is non-radial, can deal with input/output slacks directly and eliminate the radial and oriented deviation [50].  
In efficiency evaluation research field, there appear certain DMUs that simultaneously have the full efficient status (value = 1). To distinguish between the efficiency levels of these efficient DMUs, the Super-efficiency DEA was proposed by [PERSON]--a model that aims to make efficiency evaluation results more detailed and accurate [51]. In this study, we mainly considered the impact of the undesirable outputs of transport carbon emissions and traffic accident property losses, so the SBM model is very suitable and was chosen to calculate the integrated transport efficiency of 31 provinces in China. Besides, Super-efficiency DEA model can help to distinguish the efficiency levels among provinces. Accordingly, combining the SBM model and Super-efficiency DEA model, the Super-SBMDEA model was adopted. The Super-SBM DEA model based on undesirable outputs was constructed as Formula (1):  
\[\begin{split}\minITE_{k}&=\frac{1+\frac{1}{n}\sum\limits_ {i=1}^{\frac{n}{2}}\
icefrac{{\pi}}{{\pi_{i}}}}{1-\frac{1}{q_{1}+q_{2}}\left( \frac{q_{1}}{r-1}\
icefrac{{q_{1}}}{{q_{2}}}+\frac{q_{2}}{r-1}\
icefrac{{q_{2}} }{{q_{2}}}\right)}\\ s.t&\left\{\begin{array}{l}\sum\limits_{j=1,j\
eq k }^{n}x_{ij}\lambda_{j}-s_{i}^{-}\leq x_{ik}\\ \sum\limits_{j=1,j\
eq k}^{n}y_{rj}^{a}\lambda_{j}+s_{r}^{+}\geq y_{rk}^{a}\\ \sum\limits_{j=1,j\
eq k}^{n}y_{tk}^{b}\lambda_{j}-s_{t}^{-}\leq y_{tk}^{b}\\ 1-\frac{1}{q_{1}+q_{2}}\left(\sum\limits_{r=1}^{q_{1}}\
icefrac{{q_{1}}}{{q_{ r}}}+\sum\limits_{t=1}^{q_{2}}\
icefrac{{q_{1}}}{{q_{r}}}\right)>0\lambda,s^{-},s^{+} \geq 0;\\ k=1,2,3\cdots 31;\quad i=1,2,\cdots m;\\ r=1,2,3\cdots q_{1};\quad t=1,2,3\cdots q_{2};\end{array}\right.\end{split} \tag{1}\]  
where \(ITE_{k}\) is the value of the integrated transport efficiency of \(DMU_{k}\); \(m\), \(q_{1}\) and \(q_{2}\) represent the number of inputs, desirable outputs and undesirable outputs, respectively; \(x_{ik}\), \(y_{rk}\) and \(z_{tk}\) represent the \(i\)th input, \(r\)th desirable output, and \(t\)th undesirable output of \(DMU_{k}\), respectively; \(s_{i}^{-}\) is the redundant variable for the input; \(s_{r}^{+}\) is the slack variable for the desirable output; \(s_{t}^{-}\) is the redundant variable for the undesirable output; \(a\) and \(b\) are used to denote the variables of the desirable and undesirable outputs, respectively; \(y_{rk}^{a}\) represent the \(r\)th desirable output of \(DMU_{k}\); and \(y_{lk}^{b}\) represents the \(t\)th undesirable output of \(DMU_{k}\).