## 2 Literature Review  
### DEA Introduction  
Based on [PERSON] [11], in which an efficiency concept was introduced with one single information and one yield, DEA was introduced by [PERSON] et al. (1978) [12]. It is a linear programming method that can be used to assess the relative efficiency of DMUs. Through identifying a subset of efficient \"best practice\" DMUs, the DMU can construct a frontier and determine the relative efficiency for the remaining DMUs by measuring their distance from this frontier. The DEA model proposed by [PERSON] et al. [12] is termed the CCR model in homage to those authors. The DEA model was advanced to include numerous sources of information and various yields for a DMU under the prerequisite of constant returns to scale (CRS). In a later study [13], this prerequisite was relaxed, and the DEA advanced to incorporate variable returns to scale (VRS). This DEA model is termed the BCC model. DEA is a kind of non-parametric methodology, which calculates frontier directly from the observations of DMUs. DEA has likewise been utilized to provide new comprehension of exercises (substances) that do not have comparative units in information sources and yields [14]. For applications, DEA has been used in various areas such as banking, agriculture, medicinal services, transportation, assembling, and administration [15]. The conventional DEA assumes an isotonocity property for variables. The isotonocity property means that the increase of input may reduce the efficiency, while the increase of output may increase efficiency [16]. However, this assumption is not suitable for some cases. For example, the increase of undesired outputs such as pollutants will decrease efficiency. Therefore, DEA has been advanced to handle undesired output. Reference [17] included a concise review and gave a detailed structure of DEA efficiency measurement with undesired output. Based on [PERSON] and [PERSON] [18], Figure 1 gives a structure of approaches available for DEA efficiency measurement with undesired output. For more details, please refer to reference [17]. DEA efficiency measurements with undesired output can be classified into the two main kinds: indirect and direct approaches [18]. The indirect approaches transform the data of the undesired output to become the desired output [17]. As the indirect approaches manipulate the undesired output value, they can be included in the standard DEA model with the desired output. Methods including \"additive inverse,\" \"undesirable output as input,\" and \"translation invariance\" are belonging to the indirect approaches. They are introduced as follows. The \"additive inverse method\" transforms the undesired output by multiplying its value by -1 [19]. The \"undesirable output as input method\" considers undesired outputs as inputs. The undesired outputs variables are moved from the output side to the input side of the DEA model [20]. However, such treatment does not conform to physical laws and standard production theory as it incurs conceptual confusion and does not reflect the true production process in the DEA result [21]. The \"translation invariance method\" adds a large scalar to each of the undesired output values to make the resulting output positive [22]. However, one drawback of this approach is that the scalar selected can change the efficient frontier and shift the position of zero. The authors of reference [18] suggested the incorporation of undesired outputs with desired outputs by giving a negative sign to an undesired output. However, the efficiency scores and ranking obtained for the variables from this kind of \"non-separating\" outputs approach are different from those obtained from those with separation on the outputs. This approach is applicable in cases were there is only one negative output (or undesired output). The direct approach uses undesired output data directly to treat undesired outputs appropriately [17]. They include the Hyperbolic Efficiency (HE) model, the Slack-Based Measure (SBM)model, and the Directional Distance Function (DDF) model.