Tugas metode penelitian ringkasan jurnal Considering undesirable variables in PCA-DEA method: a case of road safety evaluation in Iran

Considering undesirable variables in PCA-DEA method: a case of road safety evaluation in Iran

Data envelopment analysis (DEA) is a linear programming based technique for measuring the relative performance of organisational units where the presence of multiple inputs and outputs makes comparisons difficult. This tutorial paper introduces the technique and uses an example to show how relative efficiencies can be determined and targets for inefficient units set. The paper also considers a number of practical issues of concern in applying the technique. 

Standard DEA models rely on some restrictive assumptions, e.g. variables need to be strictly positive and as independent as possible, increasing inputs and decreasing outputs are not allowed (treating undesirable variables), excessive number of variables toward DMUs often arising discrimination problems (considering efficient DMUs as inefficient and vice versa) and so on. A unique feature of this paper is proposing a new method considering aforementioned restrictions simultaneously. Several approaches have been proposed to improve discrimination and full ranking; deriving common weights (e.g. Hermans et al., 2009), setting a range of weights corresponding experts' opinions to restrict input and output’s weight (e.g. (Hermans et al., 2009)), and reducing data.

Data reduction is a way to improve discrimination power of DEA performing by the use of multivariate statistical analysis methods such as Variable Reduction (Jenkins and Anderson, 2003) and PCA. Originally, PCA is a data reduction method. PCA was used to evaluate comparable DMUs prior to DEA (Jenkins and Anderson, 2003). The idea of working with the ratio of every output to inputs proposed by Zhu (1998) and slightly modified by Permchandra (2001). Shanmugam and Johnson (2007) mentioned a new method to evaluate DMUs by PCA. PCA is used to improve discrimination power of DEA and making variables as independent as possible to avoid overlapping of decision making units (DMU’s) information. There are some difficulties in performance evaluation of DMUs in DEA method: (1)Overlapping of DMU’s information because of variables dependency (2)Necessity of full ranking achievement and (3)Existing undesirable variables.

To improve discrimination and variables dependency, PCA was applied to deal with the data before implementation of DEA model. PCA transforms a set of correlated variables into an uncorrelated (and smaller number of) new variables, called principle component (PCs), which are linear combination of original variables with minimum loss of information. The first principle, accounts for the maximum variance in the sample data, the second new variable, accounts for the maximum variance which is not considered by first component and so on. To implement PCA Cauchy distributed and highly correlated variables are necessary. For comprehensive domain envelopment one may choose as many indices as possible, but in a DEA model, the selected indices must be as In ependent as possible and multiple inputs and outputs lead to multiple correlations making the information of DMUs overlap. Also an excessive number of input and output variables toward number of DMUs result in a large number of efficient units. Thus it is preferable to keep this ratio low. PCA can be used for these purposes with minimum loss of information whilst ensuring similar results to those achieved by the original DEA model. DEA is usually performed to compare similar decision making units’ efficiency, in this case the road safety of Iran’s state, through the use of weighted averages and to improve the efficiency of those units that are not efficient. When assessing the performance of roads, DEA combines performance in terms of several desirable and undesirable attributes into a single measure, the efficiency score.

Pointed out that before applying PCA, multivariate Gaussian distribution assumption of data variables (whether input or output) should be tested. Undesirable input variable; trespass percent and undesirable output variables; crash number and casualty number are considered by reversing (multiplying by minus). To avoid finding the ratio of input to the output data; PCA is performed on input data: fleet age percent, way light percent, highway percent, removed black spot number, police station number, road red arc number, reversed trespass percent, public instruction percent and driver instruction number and on reversed output data; crash number and crash fatality separately. Because of un-positivity possibility of input and output principle components, the researchers consider a DEA model possessing general translation invariance property (normalized additive DEA model). The advantages of the proposed method are: (i)Avoidance of finding the ratio of input to output and falling into Cauchy distribution trap. (ii)Considering undesirable input and output variables simultaneously in composite PCA-DEA method.

Sumber :

http://journals.azad.ac.ir/jiei/public/Paper.aspx?id=937
link ppt :
https://drive.google.com/open?id=1DMOinC33eLyhslblNoIcRXcKkJbX7rZT