Journal of Applied Mathematics
Volume 2015 (2015), Article ID 395360, 15 pages
http://dx.doi.org/10.1155/2015/395360

Research Article

An Empirical Study of Hybrid DEA and Grey System Theory on Analyzing Performance: A Case from Indian Mining Industry

Lai-Wang Wang,¹ Thanh-Tuyen Tran,1,2 and Nhu-Ty Nguyen²

¹Department of Industrial Engineering and Management, National Kaohsiung University of Applied Sciences, No. 415, JianGong Road, Sanmin District, Kaohsiung 807, Taiwan
²International Relations Office, Lac Hong University, No. 10 Huynh Van Nghe, Bien Hoa, Dong Nai 71000, Vietnam

Received 26 August 2014; Accepted 19 November 2014

Academic Editor: Sebastien Thomassey

Copyright © 2015 Lai-Wang Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract.

India, which has long been recognized as a well-endowed nation in natural mineral resources, is a major minerals producer. According to the report of Indian Ministry of Mines 2013, Indian mining and metals sector ranked the fourth among the mineral producer countries, behind China, United States, and Russia and had in fact led the economy into recovery from the global financial crisis. Since this industry has turned into a significant issue, this paper attempts to rank the performance of 23 Indian mining and metal companies and to evaluate and measure the productivity change of these sectors during different time periods (2010–2014). Besides, the authors would like to choose one advanced model of MPI to see the performance of these companies in the past-present period and the 4-year future period (2015–2018) by using forecasting results of Grey system theory. The results revealed that from the past to future period the National Mineral Development Corporation, Hindalco Industries Limited, and Coal India always keep their highest best rankings among 23 DMUs regarding performance scores. This study contributes better insights of Indian mining industry as it is the core of the economy.

1. Introduction

India is a growing economy, and its mineral and energy demands are likely to grow fast [1]. As one of the world’s leading mineral producers, India is endowed with a rich resource base of several metallic, nonmetallic, and fuel minerals that offer huge opportunities to both domestic and global players for investment. India’s mineral policy is also aimed at attracting foreign investment and encouraging foreign technology and foreign participation in exploration mining for high value. Report of Indian Ministry of Mines (2012-2013) revealed that the country’s mining and metals sector has contributed to lead the national economy into recovery out of the period time of global financial crisis of 2007–2009. The total value of mineral production during 2012-2013 has been estimated at rupees (Rs.), 2006 billion reflecting an increase of around 11.83%, while the sector’s share in the total gross domestic product (GDP) has remained flat at 2% over the last 15 years. In addition, financially, this sector has performed reasonable well in the last few years, as reflected in the volume and profit growth of some large mining companies, namely Coal India, National Mineral Development Corporation, and Manganese Ore India.

Since around the turn of the century, the country is a leading producer of certain key minerals such as iron ore and bauxite; thus, it is considered as a key segment of Indian economy [2]. In the year 2013, mining industry provides daily direct employment to about 1 million people and is largely fragmented into small scale operational mines. The number of small mines in India was 3,108 in 2012-2013 as against 3,236 in the previous year. However, during this period of time, the public sector or Government-owned Corporation continued to play a dominant role in mineral production accounting for 67.7%, while small mines, mostly from the private sector, continued to be operated manually either as proprietary or as partnership ventures.

Previous studies on measuring productivity of Indian coal mining activity have shown a steady increase and performance of the different companies also depends on the state of technology and economic efficiency of the regions Kulshreshtha and Parikh [3]. This study attempts to analyze performance of Indian mining activity in the various coal producing companies across the country from 2010 to 2014. The objective is to derive performance measures for the different mining companies into adopting a right approach to policy decisions to improve performance.

One way to propose productive efficiency is the ability to combine inputs and outputs in optimal proportions at their prevailing prices, under a behavioural assumption for the decision making units (DMUs), for example, cost minimisation, revenue maximisation, and so forth [4]. A nonparametric approach to frontier analysis, the DEA, is used in this paper in order to distinguish between well-performing companies of coal mining and the inefficient ones. With DEA methodology, the author evaluates the enterprises’ performance by classifying input and output data to propose productive efficiency. Moreover, Grey system theory is also used in this study for the purpose of forecasting companies’ productivity for the next four years (2015–2018) concisely.

Super SBM method is also applied in this study to rank companies’ performance and this method is followed by Malmquist nonradial and Malmquist radial models. DEA can be applied to measure the productivity of multiple input and output decision-making units, whereas the DEA-based Malmquist productivity index can be used as a tool for measuring the productivity change of coal mining sectors during different time periods (2010–2014). At the same research procedure, the author also aims to test significant differences between MPI models and Malmquist nonradial and radial models to choose which model is effective for evaluating companies’ performance in recent years and future time.

2. Literature Review

The study of Kulshreshtha and Parikh [5] was an attempt that has been made to do an in-depth analysis of the productivity growth in the Indian coal sector during the period 1980–1992. Total factor productivity was calculated from the output and input indices for Coal India Ltd. Results of the analysis indicated that the labor productivity increase of around 37.6% was achieved. Study of the individual subsidiaries indicated that companies with larger share of underground mines have shown slower growth in productivity. The underutilization of capital, surplus labor, power shortages in the underground mines, inability to adapt to modern technologies, and a pricing structure of coal were the reasons of poor performance of Coal India Ltd.

Kasap et al. [6] conducted a study which aimed to examine the effects of noncontrollable factors as well as input parameters on the efficiency performances of eight enterprises within Turkish Coal Enterprises (TCE) from 2005 to 2007. For each enterprise, the outputs included the production sold and the total income; the controllable inputs consisted of investment expenditure, overburden stripping, and number of staff and the noncontrollable inputs consisted of total reserve and low heat values. Considering the noncontrollable inputs as a result of the analyses conducted with three-stage DEA model, it was determined that the average efficiency value of Turkish Coal Enterprises increased from 87.5% to 92.3%.

In the study of Xue et al. [7], the authors used an input-oriented model to measure the energy consumption productivity change from 1999 to 2008 of fourteen industry sectors in China as decision-making units. The results showed that there are only four sectors that experienced effective energy consumption throughout the whole reference period. The other ten sectors experienced inefficiency in some two-year time periods and the productivity changes were not steady. The data envelopment analysis-based Malmquist productivity index provided a good way to measure the energy consumption and can give China’s policy makers the information to promote their strategy of sustainable development.

Fang et al. [4] attempted to compare the technical efficiency performance of listed coal mining companies in China and the US using CCR and BCC models in the advanced DEA linear programming. The results showed that the level of relative efficiency in Chinese coal mining enterprises, regardless of total technical efficiency or decomposed pure technical and scale efficiency, is much lower than that in American coal firms.

In the study of Tsolas [8], the author presented DEA model combined with bootstrapping to assess performance in mining operations. Since DEA-type indicators based on nonparametric production analysis are simply point estimates without any standard error, the author provides a methodology to assess the performance of strip mining operations by means of a DEA bootstrapping approach. Although omitting undesirable output resulted in biased performance estimates, these findings were based on sample specific results and indicate that this bias is not statistically significant.

3. Methodology

3.1. Research Process

In this study, the author attempts to measure productive efficiency of 23 listed companies in India covering the period time from 2010 to 2014. The data are collected from the websites of Bombay Stock Exchange and Money Control that contain the financial data of individual Indian mining companies and these pages are currently considered as one of the India’s number one financial portal [9–11]. In our study consideration, we skip some mining companies for which financial data have not been found on the websites. The selected companies chosen for this research are listed in Table 1. These mining sectors are named Decision Making Unit from DMU1 to DMU23, respectively.

Table 1: List of mining companies of India.

Category
Name of Companies
Type
Sector
Financial index symbols

Section  1: Companies listed on the website of Bombay Stock Exchange

DMU1
Hindustan Copper Limited
Government owned
Mining and smelting
BSE: 513599; NSE: HINDCOPPER

DMU2
J & K Mineral Development
State-owned enterprise
Minerals and metals
BSE: 526371; NSE: NMDC

DMU3
National Aluminium Company
Government owned
Aluminium metal
BSE: 532234; NSE: NATIONALUM

DMU4
Manganese Ore India
State-owned enterprise
Manganese ore
BSE: 533286; NSE: MOIL

DMU5
Oil and Natural Gas Corporation
Public sector rise
Mining and oil
BSE: 500312; NSE: ONGC

DMU6
National Mineral Development
State-owned enterprise
Minerals and meta
BSE: 526371; NSE: NMDC

DMU7
Sterlite Industries
Public company
Metal and mining
BSE: 500900; NYSE: SLT

DMU8
Hindalco Industries
Public company
Mining and metals
BSE: 500440; NSE: HINDALCO

DMU9
Hindustan Zinc Limited
Public company
Mining and smelting
BSE: 500188; NSE: HINDZINC

DMU10
Sesa Sterlite Limited
Public limited
Mining
BSE: 500295; NSE: SESAGOA

Section  2: Companies listed on the website of Money Control

DMU11
Gujarat Mineral Development
State-owned enterprise
Mining and smelting
BSE: 532181; NSE: GMDCLTD

DMU12
Rohit Ferro Tech
Public company
Mining and minerals
BSE: 532731; NSE: ROHITFERRO

DMU13
Indian Metals & Ferro Alloys
Public company
Mining and minerals
BSE: 533047; NSE: IMFA

DMU14
Maithan Alloys
Public company
Mining and minerals
BSE: 590078; NSE: MAITHANALL

DMU15
Impex Ferro Tech
Public company
Mining and minerals
BSE: 532614; NSE: IMPEXFERRO

DMU16
Ferro Alloys Corporation
Public company
Mining and minerals
BSE: 500141; NSE: FERROALLOY

DMU17
Coal India
State-owned enterprise
Mining and minerals
BSE: 533278; NSE: COALINDIA

DMU18
20 Microns
Public company
Mining and minerals
BSE: 533022; NSE: 20 MICRONS

DMU19
Facor Alloys
Public company
Mining and minerals
BSE: 532656; NSE: FACORALLOY

DMU20
Associated Stone Industries
Public company
Mining and minerals
BSE: 502015; NSE: ASOCSTONE

DMU21
Sandur Manganese and Iron Ores
Public company
Mining and minerals
BSE: 504918; NSE: SANDUR

DMU22
Nagpur Power Industries
Public company
Mining and minerals
BSE: 532362; NSE: NAGPUR

DMU23
Resurgere Mines and Minerals
State-owned enterprise
Mining and minerals
BSE: 533017; NSE: RMMIL

Zhu [12] emphasized that levels of employees, assets, and equity may actually increase revenue and profit levels. Moreover, according to the study of T.-Y. Chen and L.-H. Chen [13], the elements of profitability; relative market position; change in profitability and cash flow; and growth in sales and market share, total expenditure, equity capital, net income, net profit, and EPS (earnings per share) are considered as key factors that contribute directly to the performance of companies. Table 2 presents in detail real stock market data collected from the websites of Bombay Stock Exchange and Money Control. Collected data are derived as two classes: inputs and outputs. Data inputs consist of the capital expenditure and equity capital indices; and the outputs consist of the indices of net sale or income from operations, net profit, and basic EPS after extraordinary items.

Table 2: Financial results of Indian mining companies in 2014 (Rs. million; except EPS).

DMUs
Expenditure (I)
Equity capital (I)
Net sales (O)
Net profit (O)
EPS (O)

DMU1
(11,509.50)
4,626.10
14,888.80
2,864.20
3.10

DMU2
(44,371.50)
3,964.70
120,582.00
64,200.80
16.19

DMU3
(63,713.80)
12,886.20
67,808.50
6,423.50
2.49

DMU4
(45,283.10)
16,777.10
59,672.30
15,018.80
8.95

DMU5
(44,371.50)
3,964.70
120,582.00
64,200.80
16.19

DMU6
(581,698.70)
42,777.60
838,889.30
220,948.10
25.83

DMU7
(183,682.30)
3,361.20
189,210.30
15,772.70
4.69

DMU8
(261,823.40)
2,064.80
278,509.30
14,133.30
7.09

DMU9
(74,591.10)
8,450.60
136,360.40
69,046.20
16.34

DMU10
(277,294.00)
2,965.00
285,365.30
10,760.90
3.67

DMU11
7,974.50
636.00
12,896.70
4,391.30
13.81

DMU12
25,934.50
1,137.80
25,503.00
(2,284.90)
20.08

DMU13
11,682.10
259.80
12,433.40
391.20
15.06

DMU14
7,840.30
145.60
9,551.10
113.10
7.83

DMU15
7,341.60
816.00
6,875.00
548.60
7.47

DMU16
5,947.70
185.30
6,326.30
313.60
1.69

DMU17
7,250.90
63,163.60
3,142.50
150,085.40
23.76

DMU18
2,773.80
169.10
2,902.30
1.30
0.04

DMU19
2,734.80
195.50
2,401.10
282.60
1.42

DMU20
1,121.40
66.30
1,307.40
100.70
7.60

DMU21
2,575.40
87.50
2,959.10
383.70
43.85

DMU22
38.20
131.00
15.40
8.40
0.64

DMU23
370.70
1,988.70
0.70
588.40
2.96

In last sections, we have mentioned information about introduction, motivation, selection of companies, and selection attributes of these firms. After the setting stages, we go to the analysis stage at which research models are applied. In performing evaluation by ranking, super SBM is employed. is used for forecasting the parameters that can then be used for future estimated ranking among mining companies. On the other side, Malmquist nonradial and radial models are applied to demonstrate performance evaluation. However, we need to see whether significant differences exist between these models and then Wilcoxon can handle this task. Again, in the previous section is utilized to see future trends. Finally, we could easily analyze the efficiency change based MPI.

3.2. Models of Data Envelopment Analysis (DEA)

The DEA pioneered by Charnes et al. [14] and developed by Banker et al. [15] and Fare et al. [16] is a mathematical programming approach which characterises the relationship among multiple inputs and multiple outputs by envelopment of the observed data to determine the best practice frontier for production. DEA involves the use of linear programming methods to construct a nonparametric piecewise surface or frontier over the data. Efficiency measures are then calculated relative to this surface which can be perceived as the production possibility frontier.

The Malmquist index evaluates the efficiency change of a DMU between two time periods. It is defined as the product of “catch-up” and “frontier-shift” terms. The catch-up term is related to the degree of efforts that the DMU attained for improving its efficiency, while the frontier-shift term reflects the change in the efficient frontiers surrounding the DMU between the two time periods 1 and 2. We denote DMU₀ at the time periods 1 and 2 by and , respectively. We employ the following notation for the efficiency score of DMU measured by the frontier technology . ( and ).

Then, the catch-up effect is measured by the following formula:

The frontier-shift effect is described as

Malmquist index (MI) is the product of C and F; that is, Malmquist index = (catch-up) (frontier-shift) or MI = or

; ; (MI) > 1 indicates progress in relative efficiency from period 1 to period 2, while ; (F); (MI) = 1 and ; ; (MI) < 1 indicate the status quo and regress in efficiency, respectively.

(Note that DEA efficiency is considered a distance measure in the literature as it reflects the efficiency of converting inputs to outputs [16]).

We can develop the output-oriented MI as well by means of the output-oriented radial DEA models. The output-oriented models take all output slacks into account but no input slacks. This is explained below—within score in output-orientation (O-V):

Intertemporal score in output-orientation (O-V):

The radial approaches suffer from one general problem, that is, the neglect of slacks. In an effort to overcome this problem, Tone [17, 18] has developed the nonradial measures of efficiency and super-efficiency slack-based measure (SBM) and super SBM. Using these measures, we develop here the nonradial and slacks-based MI. In the output-oriented case, we solve the following LPs.

SBM-O

where the vector denotes the output-slacks.

Super SBM-O

3.3. Grey Forecasting Model

The researchers use GM(1, 1) model to predict the realistic input/output factors for the next 4 years (2015 to 2018). In this section, the study takes company DMU1 as an example to understand how to compute in GM(1, 1) model in the period 2010–2014. We also take the net sales of DMU1 as an example to explain calculation procedure, and other variables are calculated in the same way. The procedure is carried out step by step as follows.

First, the researchers use the model to try to forecast the variance of primitive series.

 First, create the primitive series:  = (13,045.20; 11,465.20; 14,875.50; 13,231.40; 14,888.80). Second, perform the accumulated generating operation (AGO):  = (13,045.20; 25,401.40; 40,276.90; 53,508.30; 68,397.10)  = = 13,045.20  = 25,401.40  = 40,276.90  = 53,508.30  . Third, create the different equations of . To find series, the following steps can be caculated to obtain the results:  = 38446.6  = 65,678.3  = 93,785.2  = 121,905.4. Fourth, solve equations. To find and , the primitive series values are substituted into the Grey differential equation to obtain

Convert the linear equations into the form of a matrix.

Let

And then use the least square method to find and :

Use the two coefficients and to generate the whitening equation of the differential equation:

Find the prediction model from

Substitute different values of into the equation:

     = 25423.89  = 38591.00  = 52596.73  = 67494.50  = 83341.12  = 100197.02  = 118126.49  = 137197.91.

Derive the predicted value of the original series according to the accumulated generating operation and obtain

  = 13045.2—for the year 2010  12,378.69—forecasted for 2011  13,167.11—forecasted for 2012  14,005.73—forecasted for 2013  17,897.77—forecasted for 2014  15,846.62—forecasted for 2015  16,855.90—forecasted for 2016  17,929.47—forecasted for 2017  19,071.42—forecasted for 2018.

Similarly to the above computation process, the study could get the forecasting results of all DMUs from 2015 and 2018; the detailed numbers are shown in Tables 3 and 4, respectively.

Table 3: Forecasted values of outputs of all DMUs from 2015 to 2018.

DMUs
Outputs (Rs. millions, except EPS)

(O) Net sale
(O) Net profit
(O) EPS

‘15
‘16
‘17
‘18
‘15
‘16
‘17
‘18
‘15
‘16
‘17
‘18

DMU1
15,846.62
16,855.90
17,929.47
19,071.42
3498.10
3736.30
3990.72
4262.47
3.78
4.04
4.32
4.62

DMU2
117,408.21
119,022.55
120,659.08
122,318.12
63524.04
62444.81
61383.92
60341.05
16.02
15.75
15.48
15.22

DMU3
72,203.19
74,912.73
77,723.95
80,640.67
4512.24
3659.75
2968.31
2407.51
1.77
1.44
1.17
0.95

DMU4
69,654.52
79,310.72
90,305.56
102,824.62
15882.79
16630.55
17413.51
18233.34
9.46
9.91
10.37
10.86

DMU5
117,408.21
119,022.55
120,659.08
122,318.12
63524.04
62444.81
61383.92
60341.05
16.02
15.75
15.48
15.22

DMU6
913,629.42
973,669.79
1,037,655.7
1,105,846.71
230656.89
236100.11
241671.79
247374.95
26.97
27.60
28.26
28.93

DMU7
219,108.91
247,255.18
279,017.07
314,859.02
20323.30
23922.28
28158.58
33145.07
2.46
1.77
1.27
0.92

DMU8
290,498.75
303,415.46
316,906.49
330,997.39
13089.95
11400.75
9929.53
8648.16
6.63
5.72
4.94
4.26

DMU9
152,381.10
168,446.89
186,206.52
205,838.57
80780.25
90989.33
102488.64
115441.24
19.12
21.53
24.25
27.31

DMU10
75104.60
65134.50
21879.20
285365.30
1917.26
942.61
463.43
227.84
1.09
0.45
0.18
0.08

DMU11
14,284.14
13,997.80
13,717.21
13,442.23
5480.60
5805.70
6150.09
6514.90
17.23
18.25
19.33
20.48

DMU12
33,547.14
42,602.86
54,103.08
68,707.68
324.70
440.30
395.90
291.70
−0.05
−0.05
6.82
3.21

DMU13
13,138.04
13,776.97
14,446.98
15,149.56
151.86
85.20
47.80
26.81
5.95
3.37
1.90
1.08

DMU14
11,696.07
13,749.55
16,163.56
19,001.40
140.57
93.42
62.08
41.26
9.86
6.58
4.39
2.93

DMU15
7,098.15
7,554.20
8,039.54
8,556.07
57.10
68.00
35.90
39.70
1.22
1.36
0.69
0.59

DMU16
6,603.83
7,228.25
7,911.72
8,659.81
269.88
289.35
310.22
332.60
1.46
1.58
1.70
1.82

DMU17
2,952.48
2,695.00
2,459.98
2,245.45
207114.37
295181.64
420696.07
599580.59
32.84
46.74
66.52
94.67

DMU18
3,121.05
3,327.60
3,547.81
3,782.60
20.85
15.01
10.81
7.78
1.10
0.74
0.50
0.34

DMU19
1,780.98
1,451.45
1,182.90
964.03
140.30
328.50
71.20
8.00
−1.42
0.52
1.69
0.36

DMU20
1,356.48
1,266.35
1,182.21
1,103.66
107.47
106.31
105.15
104.01
8.11
8.02
7.93
7.84

DMU21
1,931.12
1,758.03
1,600.44
1,456.99
102.21
62.37
38.06
23.22
11.63
7.09
4.32
2.63

DMU22
16.10
15.40
110.10
18.30
3.95
2.26
1.29
0.74
0.30
0.17
4.11
3.35

DMU23
6.23
1.14
0.21
0.04
−588.40
−770.00
43.90
−588.40
−7.79
−13.57
7.65
−0.03

Source: calculated by researchers.

Table 4: Average MAPE of DMUs.

DMUs
Average MAPE

DMU1
10.27%

DMU2
5.42%

DMU3
6.06%

DMU4
1.87%

DMU5
5.42%

DMU6
5.61%

DMU7
10.50%

DMU8
4.42%

DMU9
3.14%

DMU10
15.55%

DMU11
11.40%

DMU12
7.33%

DMU13
12.54%

DMU14
14.65%

DMU15
8.64%

DMU16
5.89%

DMU17
5.56%

DMU18
20.18%

DMU19
10.54%

DMU20
9.15%

DMU21
13.40%

DMU22
8.06%

DMU23
32.48%

Average of all MAPEs: 9.92%

3.4. Forecasting Accuracy

The mean absolute percentage error (MAPE) is a measure of accuracy of a method for constructing fitted time series values in statistics, specifically in trend estimation [19–21]. The MAPE measures the size of the error in percentage terms. Many previous studies focus primarily on the MAPE when assessing forecast accuracy. It is calculated as the average of the unsigned percentage error as follows:

The parameters of MAPE stating out the forecasting ability are as follows:

 MAPE < 10% “Excellent” 10% < MAPE < 20% “Good” 20% < MAPE < 50% “Reasonable” MAPE > 50% “Poor.”

4. Data Analysis and Results

4.1. Forecasting Results

Forecasting results from 2015 to 2018 of 23 Indian mining companies were shown in Table 3.

The authors employed MAPE to test the forecasting accuracy of 23 Indian mining companies and MAPE is a very important tool to solve the mathematical concerns about the forecasting method. As shown in Table 4, average MAPE of each DMU is ranked from 3% to 10%. In particular, the average MAPE of total 23 DMUs is 9.92% which is below 10%; thus, it can conclude that the model provides highly accurate prediction for the case of this research.

4.2. Pearson Correlation

To apply DEA model, the authors have to make sure that the relationship between input and output factors is correlated, which means if the input quantity increases, the output quantity could not decrease under the same condition [22]. Firstly, a simple correlation test, Pearson correlation, to measures the degree of association between two variables is conducted. Higher correlation coefficient means closer relation between two variables, while lower correlation coefficient means that they are less correlated.

The interpretation of the correlation coefficient is explained in more detail as follows. The correlation coefficient is always between −1 and +1. The closer the correlation is to ±1, the closer it is to a perfect linear relationship. Its general meaning was shown in Table 5.

Table 5: Pearson correlation coefficient.

Correlation coefficient
Degree of correlation

>0.8
Very high

0.6–0.8
High

0.4–0.6
Medium

0.2–0.4
Low

<0.2
Very low

In the empirical study, the results in Table 6 indicate that the correlation complies well with the prerequisite condition of the DEA model because their correlation coefficient shows strong positive associations. Therefore, these positive correlations also demonstrate very clearly the fact that the researcher’s choice of input and output variables at the beginning is appropriate. Obviously, none of variables removal is necessary. From these results, we can justify the reason for why we use these indicators for DEA methodologies. The correlation is also very significant which will affect the performance.

Table 6: Correlation coefficient (2014).

Staff cost
Energy purchase
Other expenses
Equity capital
Net income
Net profit
Basic EPS

Staff cost
1
0.380873213
0.98075502
0.627931207
0.221718204
1
0.380873213

Energy purchase
0.380873213
1
0.418084532
0.844263775
0.39597191
0.380873213
1

Other expenses
0.98075502
0.418084532
1
0.718349623
0.284462435
0.98075502
0.418084532

Equity capital
0.627931207
0.844263775
0.718349623
1
0.501068342
0.627931207
0.844263775

Net income
0.221718204
0.39597191
0.284462435
0.501068342
1
0.221718204
0.39597191

Net profit
1
0.380873213
0.98075502
0.627931207
0.221718204
1
0.380873213

Basic EPS
0.380873213
1
0.418084532
0.844263775
0.39597191
0.380873213
1

4.3. Performance Rankings of Super SBM

Table 7 shows summary of super SBM results for data of the year 2014. Data are set at value Returns to Scale = Variable (Sum of Lambda = 1). The total number of DMUs is 23 with none of inappropriate data. The number of efficient DMUs is 13, while the result reveals 10 DUMs that work inefficiently. The results demonstrated that SBM has the ability to distinguish all DMUs with significant differences on their scoring. The results also revealed that a large number of inefficient mining companies still exist.

Table 7: Summary of super SBM results for 2014.

Number of DMUs in data: 23

Number of DMUs with inappropriate data: 0

Number of evaluated DMUs: 23

Average of scores: 0.6230249

Number of efficient DMUs: 13

Number of inefficient DMUs: 10

Number of over iteration DMUs: 0

Table 8 shows the five-year data with efficiency scores and ranking of DMUs based on DEA-super SBM. This indicates that the ranking of the Indian mining industries is tending to change in a very slight manner on yearly basis. However, the majority of these companies are maintaining their “efficient” levels even after yearly changes on their financial nature.

Table 8: Past-present period scores and rankings of Indian mining companies.

Year
2010
2011
2012
2013
2014

DMUs
Score
Rank
Score
Rank
Score
Rank
Score
Rank
Score
Rank

DMU1
0.08222255
20
0.0656456541
18
0.170071799
17
0.17558929
15
0.138931313
16

DMU2
1
8
1
6
1
7
1
6
1
6

DMU3
0.2055158
15
0.113620718
16
0.162615278
18
0.134712868
16
0.125793692
17

DMU4
0.19229379
16
0.198593163
15
0.291067259
15
0.34429635
14
0.318260742
14

DMU5
1
8
1
6
1
7
1
6
1
6

DMU6
2.16770264
1
2.033090027
1
2.80326237
1
2.31536708
1
1.95872746
1

DMU7
0.77740861
12
0.366271981
13
0.331701432
14
0.451008567
12
0.410027591
13

DMU8
1.15413633
6
1.199295331
5
1.272546625
3
1.289155822
4
1.161877176
4

DMU9
1.42647404
3
0.455163255
10
0.672443382
11
0.917292682
10
0.882773643
10

DMU10
1.46305544
2
1.461774497
3
1.147627203
5
0.084511232
18
0.599494462
11

DMU11
0.45409773
13
0.243722044
14
0.568035889
12
0.673623254
11
0.475303705
12

DMU12
0.12372762
19
0.077112542
17
0.0752215685
19
0.042416986
19
0.000171154
23

DMU13
0.23899823
14
0.418336879
11
0.407331963
13
0.381797764
13
0.270659073
15

DMU14
1.09447397
7
0.369363507
12
1.238128139
4
1.022411301
5
1.018807964
5

DMU15
0.02661588
22
0.0154215465
22
0.009125436
23
0.010363164
21
0.000335555
22

DMU16
0.01421234
23
0.0492145623
20
0.0262563212
21
0.087653698
17
0.091590783
18

DMU17
1.34986652
4
1.323199209
4
1.402620489
2
1.409316421
2
1.457257143
2

DMU18
0.169931707
17
0.0656414141
19
0.176270834
16
0.036263254
20
0.001525555
19

DMU19
0.05345621
21
0.042986456
21
0.039523654
20
0.002632693
22
0.001275366
20

DMU20
1
8
0.99985281
9
1
7
1
6
1
6

DMU21
1.173117286
5
1.503902073
2
1.053500985
6
1.335737125
3
1.417097825
3

DMU22
1
8
1
6
1
7
1
6
0.999033846
9

DMU23
0.159980331
18
0.0090814569
23
0.016914788
22
0.0019455655
23
0.000641568
21

Table 9 shows forecasting results for companies’ future ranking by applying . In the future, obviously, these mining companies are keeping their performance and they just show slight changes between the efficiency scores. However, we can still see some of the companies are under “1” of efficiency, that is, inefficiency.

Table 9: Future scores and rankings of Indian mining companies.

Year
2015
2016
2017
2018

DMUs
Score
Rank
Score
Rank
Score
Rank
Score
Rank

DMU1
0.229972135
15
0.213906606
17
0.194115582
16
0.16885867
15

DMU2
1
10
1
8
1
7
1
8

DMU3
0.091149209
18
0.065455222
20
0.04547795
20
0.058719106
18

DMU4
0.310139476
14
0.283446393
15
0.24829818
14
0.207261952
14

DMU5
1
10
1
8
1
7
1
8

DMU6
1.706458481
2
1.5043684
2
1.405519183
2
1.376640904
2

DMU7
1.11595166
5
0.366177711
13
0.308945554
12
1.036782468
7

DMU8
1.15220434
3
1.223512939
3
1.205320998
5
1.164404419
5

DMU9
1.04140483
8
1.114485601
5
1.206617814
4
1.288194472
4

DMU10
1.133620135
4
1.076409889
6
0.02375703
21
0.012712324
21

DMU11
1.107899893
6
1.20380724
4
1.263214488
3
1.293168383
3

DMU12
0.047504052
20
0.025649868
22
0.072401558
18
0.058719106
17

DMU13
0.131526256
17
0.085196414
19
0.050240732
19
0.030354919
19

DMU14
1.02542509
9
1.037274478
7
1.062498136
6
1.092104258
6

DMU15
0.02226702
22
0.02306484
23
0.01248637
23
0.011367331
23

DMU16
0.199700493
16
0.239275087
16
0.263227147
13
0.293008055
13

DMU17
1.934646173
1
2.120759681
1
2.286584498
1
2.429443651
1

DMU18
0.040603593
21
0.029652426
21
0.01865052
22
0.012372634
22

DMU19
0.059686158
19
0.12894573
18
0.118590775
17
0.014157442
20

DMU20
1
10
1
8
1
7
1
8

DMU21
1.098633465
7
0.320449656
14
0.206757982
15
0.131634947
16

DMU22
1
10
0.999085759
11
1
7
1
8

DMU23
0.01187598
23
0.997461493
12
1
7
0.997033889
12

4.4. Performance Efficiency Evaluation: Malmquist Radial Model versus Malmquist Nonradial Model

Seiford and Zhu [23] stated that the performance efficiency evaluation is very essential to test the progress of development of an industry. The authors in this case used the two models: Malmquist Radial and Malmquist nonradial. Then, the results of Malmquist are shown in Table 10. Malmquist radial model has the average score of 0.992449 compared with 3.186667092 of Malmquist nonradial model.

Table 10: The average indices of Malmquist radial and Malmquist nonradial models.

DMUs
Average of Malmquist radial model
Average Malmquist nonradial model

DMU1
1.133494181
1.787272636

DMU2
1.151012585
1.078393423

DMU3
0.952467408
0.392025795

DMU4
1.076600714
1.090141392

DMU5
1.151012585
1.078393423

DMU6
0.803070747
0.802696168

DMU7
0.922470548
0.446041138

DMU8
1.173203288
1.048869372

DMU9
0.713581338
0.714687685

DMU10
0.868461435
0.58990751

DMU11
1.074534927
1.245075457

DMU12
0.907476297
6.041737971

DMU13
1.165347005
0.918020595

DMU14
1.014276704
0.969117286

DMU15
0.842045652
25.50093872

DMU16
1.197349339
8.304036297

DMU17
2.506109416
2.060379686

DMU18
0.948798068
0.011004036

DMU19
0.832072153
16.49060082

DMU20
0.904174513
0.969111616

DMU21
1.269170129
1.359494943

DMU22
0.209590622
0.382229953

DMU23
0.01
0.013167199

Mean
0.992449
3.186667092

Max
2.506109
25.50093872

Min
0.01
0.011004036

SD
0.443929
6.083926361

In Table 11, the authors used Wilcoxon to test the differences. The authors, firstly, decide to formulate the null hypothesis as “There is no difference of performance efficiency evaluation between Malmquist radial and Malmquist nonradial models.”

Table 11: Paired samples correlations.

Correlation
Sig.

Nonradial and radial
23
−0.264
0.223

The results (shown in Table 11) indicate that the correlations between two pared samples at (, correlation = −0.264, , ), which means that there is significant difference between correlations of the two models mentioned.

Next, the results of Wilcoxon test (Table 12) show that , , 95% CI = −4.81; 2.42, , , , in which 95% confidence interval of the difference goes through 0 and value > 0.05. Thus, the authors can conclude that there is no significant difference between the two models: Malmquist radial and Malmquist nonradial.

Table 12: Paired samples test.

Paired differences

df
Sig. (2-tailed)

Mean
Std. deviation
Std. error mean
95% confidence interval of the difference

Lower
Upper

Nonradial-radial
−2.39159063
5.58656757
1.16487986
−4.80740361
2.42223412

Because of no significant difference between the Malmquist radial and Malmquist nonradial models, the authors decided to use one type of Malmquist models which is nonradial O-V model, as it was mentioned above that the radial approaches suffer from one general problem, that is, the neglect of slacks. Avkiran [24] and Chen and Sherman [25] have developed the nonradial measures of efficiency and super-efficiency. Table 13 and Figure 1 show the efficiency change or what is named “catch-up” of the India mining industry over the year periods of time interval.

Table 13: Efficiency (catch-up) change over the period 2010 to 2014.

Catch-up
2010 => 2011
2011 => 2012
2012 => 2013
2013 => 2014
Average

DMU1
0.797164
2.59442
1.032442
0.791229
1.303814

DMU2
1
1
1
1
1

DMU3
0.552856
1.431211
0.828415
0.933791
0.936568

DMU4
1.032759
1.465646
1.182876
0.92438
1.151415

DMU5
1
1
1
1
1

DMU6
0.937901
1.378819
0.825954
0.845968
0.997161

DMU7
0.471145
0.905615
1.359682
0.909135
0.911394

DMU8
1.039128
1.061079
1.013052
0.90127
1.003632

DMU9
0.319083
1.477367
1.364119
0.962369
1.030734

DMU10
0.999124
0.785092
0.073613
7.096281
2.238527

DMU11
0.536717
2.330671
1.185882
0.705593
1.189716

DMU12
0.62322
0.975688
0.562964
18.58698
5.187213

DMU13
1.750376
0.973694
0.937314
0.708907
1.092573

DMU14
0.33748
3.352059
0.825772
0.996476
1.377947

DMU15
0.578274
0.584548
1.151855
59.18462
15.37482

DMU16
3.469142
16.39564
0.107797
1.053356
5.256485

DMU17
0.980244
1.060022
1.004774
1.033946
1.019747

DMU18
0.33236
3.121029
0.205235
0.042027
0.925162

DMU19
0.792118
0.940237
0.065941
100
25.44957

DMU20
1
1
1
1
1

DMU21
1.281971
0.699462
1.269806
1.060911
1.078037

DMU22
1
1
1
1
1

DMU23
0.05752
28.01865
0.010044
0.880411
7.241656

Average
0.908199
3.197868
0.826415
8.765985
3.424616

Max
3.469142
28.01865
1.364119
100
25.44957

Min
0.05752
0.584548
0.010044
0.042027
0.911394

SD
0.670389
6.293493
0.434709
23.49756
5.821886

Figure 1: Efficiency change of the India mining industry.

Figure 1 shows the efficiency change or what is named “catch-up” of the India mining industry. The efficiency changes are inconsistent because the activities of DMU financial management show its inconsistent nature over the years. Figure 1 also pointed out that wildly fluctuations of the changes exit among DMU19 (Facor Alloy), DMU15 (Impex Ferro), DMU12 (Rohit Ferro Tech), and DMU16 (Ferro Alloys Corporation), whereas the rest of Indian mining companies in this study have no big or very slight efficiency changes.

The technical or the frontier-shift changes of the companies over the period from 2010 to 2014 in the Indian mining industry are shown in Table 14 and Figure 2. Figure 2 shows that the tendency to change technical or innovative effect of most of the Indian mining companies is inconsistent. For example, DMU19 (Facor Alloy) and DMU16 (Ferro Alloys Corporation) have their up and down changes in efficiency, which again notably made some abrupt in technical changes over the beginning years and then go smoothly with the overall trend of the companies in the industry.

Table 14: Technical (Frontier) change over the period 2010 to 2014.

Frontier
2010 => 2011
2011 => 2012
2012 =>2013
2013 => 2014
Average

DMU1
1.939121602
0.504629603
0.996300267
1.06244232
1.125623448

DMU2
2.015905198
1.10571636
0.82675343
0.964586441
1.228240357

DMU3
0.886326283
0.558239264
0.854416817
1.163988937
0.865742825

DMU4
1.000476644
0.741267265
0.870616146
1.100278455
0.928159628

DMU5
2.015905198
1.10571636
0.82675343
0.964586441
1.228240357

DMU6
0.861710382
1.018301532
1.014340243
1.130278256
1.006157603

DMU7
1.430118052
0.647589191
0.913795938
1.088321211
1.019956098

DMU8
1.295194694
1.04381169
0.851005728
1.030519595
1.055132927

DMU9
1.674444152
0.750046037
0.847017068
1.035738188
1.076811361

DMU10
1.546932314
0.645062431
1.000197233
1.374187295
1.141594818

DMU11
2.100229237
0.534814478
1.001097942
1.07648664
1.178157074

DMU12
1.531741397
0.645525171
0.906630074
1.025145953
1.027260649

DMU13
2.152459816
0.373558899
0.909365366
1.066824671
1.125552188

DMU14
2.899201454
0.247983445
1.423331621
1.003169142
1.393421416

DMU15
1.937809329
0.783532361
0.866668618
0.875736904
1.115936803

DMU16
3.081717159
0.493051054
1.145757947
1.157888408
1.469603642

DMU17
1.252853816
1.467478027
1.019956535
1.439608261
1.29497416

DMU18
1.891744104
0.577088174
1.14044083
0.876535166
1.121452069

DMU19
3.388616607
0.23432004
1.99304714
0.947786186
1.640942493

DMU20
1.095824176
0.931013697
1.11412316
0.874974664
1.003983924

DMU21
1.959059779
0.389859532
1.749978617
0.969696801
1.267148682

DMU22
0.940015391
1
1
0.593251026
0.883316604

DMU23
1.503821085
1.195321455
0.709459198
0.888087167
1.074172226

Average
1.756575125
0.738866351
1.042654493
1.030874701
1.142242668

Max
3.388616607
1.467478027
1.99304714
1.439608261
1.640942493

Min
0.861710382
0.23432004
0.709459198
0.593251026
0.865742825

SD
0.681955633
0.321859374
0.302317354
0.171291998
0.184302772

Figure 2: Frontier change over the period 2010 to 2014.

Figure 2 shows frontier change over the period 2010 to 2014.

Finally, the most important element in the performance evaluation of the industry is Malmquist Productivity Index (MPI), which is clearly indicated in Table 15 and Figure 3. Overall, most of the companies have done well in their performance when the indices are larger than 1 (>1).

Table 15: Productivity index (Malmquist-MPI) change over the period 2010 to 2014.

Malmquist
2010 => 2011
2011 => 2012
2012 => 2013
2013 => 2014
Average

DMU1
1.545797114
1.309221254
1.028622365
0.840635021
1.181068938

DMU2
2.015905198
1.10571636
0.82675343
0.964586441
1.228240357

DMU3
0.490011136
0.798958453
0.70781135
1.08692264
0.770925894

DMU4
1.033251374
1.086435341
1.029830568
1.01707566
1.041648236

DMU5
2.015905198
1.10571636
0.82675343
0.964586441
1.228240357

DMU6
0.808198851
1.404053105
0.837798856
0.956179723
1.001557634

DMU7
0.673792601
0.586466544
1.242472165
0.989430703
0.873040503

DMU8
1.345873019
1.10756626
0.862113
0.928776162
1.06108211

DMU9
0.53428624
1.108093608
1.155431935
0.996761875
0.948643415

DMU10
1.545577938
0.506433239
0.073627354
9.751618997
2.969314382

DMU11
1.127229082
1.246476571
1.187183531
0.759561202
1.080112596

DMU12
0.954612304
0.629831235
0.510399744
19.05436823
5.287302877

DMU13
3.767615006
0.363731928
0.85236047
0.75627938
1.434996696

DMU14
0.978423652
0.831255052
1.175347113
0.999633621
0.99616486

DMU15
1.120585111
0.458012204
0.998276177
51.83015232
13.60175645

DMU16
10.69091327
8.083889578
0.123509827
1.219668695
5.029495342

DMU17
1.228103042
1.555559234
1.024825525
1.488477741
1.324241385

DMU18
0.628739377
1.801108782
0.234058131
0.036837705
0.675185999

DMU19
2.684183223
0.220316389
0.131423949
94.77861863
24.45363555

DMU20
1.095824176
0.931013697
1.11412316
0.874974664
1.003983924

DMU21
2.511457379
0.272691989
2.222132539
1.028761724
1.508760908

DMU22
0.940015391
1
1
0.593251026
0.883316604

DMU23
0.086500142
33.49129408
0.01
0.781881615
8.59241896

Average
1.731426079
2.652340925
0.833689331
8.37821914
3.398918869

Max
10.69091327
33.49129408
2.222132539
94.77861863
24.45363555

Min
0.086500142
0.220316389
0.01
0.036837705
0.675185999

SD
2.119828504
6.898136352
0.49641247
21.87797994
5.533163948

Figure 3: Productivity index (MPI) change over the period 2010 to 2014.

Figure 3 shows that DMU19, DMU15, DMU12, and DMU10 have slight changes over the beginning years; however, their MPI scores are going up sharply in the period of 2013–2014. DMU23 was shaking over the period 2010–2013, and finally in 2014 it goes to 0. The rest of the companies have also increased and decreased in their MPI scores but very slightly.

was used to forecast the future performance of the industry for the next four years (2015–2018) based on the results of Malmquist Productivity Index collected from 2010–2014. MPI change over the forecasted future period is done by Malmquist nonradial O-V model, which is illustrated in Table 16 and Figure 4. In the forecasting period (2014–2018), most of the MPIs of companies can reach the “efficiency” level or positive change year over year. Although some of companies still work inefficiently, we obviously see the stable changes of mining industry in the future period.

Table 16: MPI change over the forecasted period 2014 to 2018.

Malmquist
2014 => 2015
2015 => 2016
2016 => 2017
2017 => 2018
Average

DMU1
1.155377644
1.036943532
1.047454651
1.05440683
1.073545665

DMU2
0.941154142
0.941808396
0.946455953
0.962595312
0.948003451

DMU3
0.709387778
0.807083952
0.803241667
0.805875709
0.781397276

DMU4
1.050990953
1.032766941
1.026102588
1.029176837
1.03475933

DMU5
0.941154142
0.941808396
0.946455953
0.962595312
0.948003451

DMU6
0.953788767
0.950848108
0.979051059
1.00181251
0.971375111

DMU7
2.608808968
0.328959024
1.575407484
3.50365797
2.004208362

DMU8
1.014221762
1.030899367
0.995572443
0.970905349
1.00289973

DMU9
1.150544925
1.078417389
1.090671738
1.085395159
1.101257303

DMU10
1.940672028
0.340427772
0.02251981
0.560101027
0.715930159

DMU11
1.276180243
1.08751783
1.050084819
1.036211195
1.112498522

DMU12
0.169997844
0.875829328
0.611861239
0.784462215
0.610537657

DMU13
0.226873084
0.591108199
0.578352236
0.577229556
0.493390769

DMU14
1.869237094
0.973919273
1.024055164
1.039153116
1.226591162

DMU15
0.031602939
0.948432575
0.500567996
0.929526595
0.602532526

DMU16
0.873867965
1.0795813
1.083671912
1.086164776
1.030821488

DMU17
1.403725525
1.326313141
1.351549367
1.385723238
1.366827818

DMU18
20.67554712
0.718647781
0.618935022
0.652760872
5.666472699

DMU19
0.250804329
0.681482367
0.957742973
0.138790391
0.507205015

DMU20
1.028020624
0.985195792
0.985199371
0.985197534
0.99590333

DMU21
0.453076135
0.288464627
0.634050426
0.626207563
0.500449688

DMU22
1
0.915095672
1
0.818778182
0.933468464

DMU23
92.21332042
1
1
0.823358538
23.75916974

Average
5.823406714
0.867893511
0.905608864
0.992177643
2.147271683

Max
92.21332042
1.326313141
1.575407484
3.50365797
23.75916974

Min
0.031602939
0.288464627
0.02251981
0.138790391
0.493390769

SD
19.28212645
0.264628932
0.311183931
0.601826474
4.823734506

Figure 4: Productivity index (MPI) change over the period 2014–2018.

In the future, DMU23 and DMU18 will show a rocket-fuelled increase in their MPI up to the level of over 90 in the period of 2015-2016; however, in the next two periods, 2016-2017 and 2017-2018, they keep going down at around 1 of efficiency level.

Besides, we noticed that DMU7 will show its better performance in the future. Even though MPI scores of DMU7 will go down at around 1 of efficiency level in the period of 2015-2016, the scores will gradually keep going up in the next two periods, 2016-2017 and 2017-2018. The rest of the companies have also increased and decreased in their MPI scores but very slightly for the whole period.

5. Conclusion

In this study, the authors attempt to measure productive efficiency of 23 mining companies in India. The data covered the period from 2010 to 2014 and were collected from the websites of Bombay Stock Exchange and Money Control that contain the financial data of these companies. The results of rankings from super SBM model indicated that the ranking of the Indian mining industries is tending to change in a very slight manner on yearly basis. However, the majority of these companies are maintaining their “efficient” levels even after yearly changes on their financial nature.

The results also clearly stated out that during the period 2010–2014 the Coal India Ltd. (DMU17), National Mineral Development Corporation (DMU6), Hindalco Industry (DMU8), Maithan Alloys (DMU14), and Sandur Manganese Iron Ores (DMU21) always keep the ranking of the top five companies among 23 DMUs regarding the performance scores.

However, for the future period 2015–2018 (forecasting with ), although the Coal India Ltd. (DMU17), National Mineral Development Corporation (DMU6), and Hindalco Industry (DMU8) are still on top, Maithan Alloys (DMU14) and Sandur Manganese Iron Ores (DMU21) will be replaced by Hindustan Zinc Limited (DMU9) and Gujarat Mineral Development Corporation (DMU11) on the top performance scores.

Furthermore, Facor Alloys (DMU19), 20 Microns (DMU18), and Impex Ferro Tech (DMU15) were noticed as the inefficient companies which have the lowest score of performance over the past-present-future period. These DMUs need urgent action for improving the performance over partners in the research industry.

The results of Wilcoxon test (Table 12) show that there are no differences between the Malmquist radial and Malmquist nonradial models, so the authors used Malmquist nonradial model as a tool for measuring the productivity change of coal mining sectors during different time periods (2010–2014). The results have revealed that all companies in the mining industry have not shown sudden changes on their scores over the past-present-future period. This indicates that, although suffering from the financial crisis, the industry just only shows slight changes on the score performance, except some little changes between companies which are explained in the previous section.

After applying a hybrid DEA and Grey system theory on analyzing performance of 23 Indian mining companies, the authors have found many meaningful and noticeable results for this industry. Firstly, it minimizes the methodology limitation problems by deeply employing the best sides of an integration method. Secondly, it provides detailed insights of Indian mining industry as it is the core of the economy. Furthermore, according to forecasted MPI, companies with inefficient level (<1) need to be positive in changing or improving their management activities, business trends, size, or any other methods to make progress in the future time. By completing this research, the authors are aiming to suggest this case as a better model of performance analysis among the decision makers of variety of industries.

Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

References

K. Singh and K. Kalirajan, “A decade of economic reforms in India: the mining sector,” Resources Policy, vol. 29, no. 3-4, pp. 139–151, 2004.

A. Das, “Who extracts minerals more efficiently—public or private firms? A study of Indian mining industry,” Journal of Policy Modeling, vol. 34, no. 5, pp. 755–766, 2012.

M. Kulshreshtha and J. K. Parikh, “Study of efficiency and productivity growth in opencast and underground coal mining in India: a DEA analysis,” Energy Economics, vol. 24, no. 5, pp. 439–453, 2002.

H. Fang, J. Wu, and C. Zeng, “Comparative study on efficiency performance of listed coal mining companies in China and the US,” Energy Policy, vol. 37, no. 12, pp. 5140–5148, 2009.

M. Kulshreshtha and J. K. Parikh, “A study of productivity in the Indian coal sector,” Energy Policy, vol. 29, no. 9, pp. 701–713, 2001.

Y. Kasap, A. Konuk, R. N. Gasimov, and A. M. Kiliç, “The effects of non-controllable factors in efficiency evaluation of Turkish coal enterprises,” Energy Exploration and Exploitation, vol. 25, no. 6, pp. 429–450, 2007.

X. Xue, Q. Shen, Y. Wang, and J. Lu, “Measuring the productivity of the construction industry in China by using DEA-based malmquist productivity indices,” Journal of Construction Engineering and Management, vol. 134, no. 1, pp. 64–71, 2008.

I. E. Tsolas, “Performance assessment of mining operations using nonparametric production analysis: a bootstrapping approach in DEA,” Resources Policy, vol. 36, no. 2, pp. 159–167, 2011.

H. Berkman and V. R. Eleswarapu, “Short-term traders and liquidity :: a test using Bombay Stock Exchange. Paper presented at the WFA and the APFA/PACAP Conferences,” Journal of financial Economics, vol. 47, no. 3, pp. 339–355, 1998.

M. Jain, P. L. Meena, and T. N. Mathur, “Impact of foreign institutional investment on stock market with special reference to BSE, a study of last one decade,” Asian Journal of Research in Banking and Finance, vol. 2, no. 4, pp. 31–47, 2012.

C. N. Wang, N. T. Nguyen, and T. T. Tran, “Integrated DEA models and grey system theory to evaluate past-to-future performance: a case of Indian electricity industry,” The Scientific World Journal, vol. 2014, Article ID 638710, 23 pages, 2014.

J. Zhu, “Multi-factor performance measure model with an application to Fortune 500 companies,” European Journal of Operational Research, vol. 123, no. 1, pp. 105–124, 2000.

T.-Y. Chen and L.-H. Chen, “DEA performance evaluation based on BSC indicators incorporated: the case of semiconductor industry,” International Journal of Productivity and Performance Management, vol. 56, no. 4, pp. 335–357, 2007.

A. Charnes, W. W. Cooper, and E. Rhodes, “Measuring the efficiency of decision making units,” European Journal of Operational Research, vol. 2, no. 6, pp. 429–444, 1978.

R. Banker, A. Charnes, and W. W. Cooper, “Some models for estimating technical and scale inefficiency in data envelopment analysis,” Management Science, vol. 30, no. 9, pp. 1078–1092, 1984.

R. Fare, S. Grossfopf, and C. A. K. Lovell, Production Frontiers, Cambridge University Press, New York, NY, USA, 1994.

K. A. Tone, “Slacks-based measure of efficiency in data envelopment analysis,” European Journal of Operational Research, vol. 130, no. 3, pp. 498–509, 2001.

K. A. Tone, “A slacks-based measure of super-efficiency in data envelopment analysis,” European Journal of Operational Research, vol. 143, no. 1, pp. 32–41, 2002.

K. F. Lam, H. W. Mui, and H. K. Yuen, “A note of minimizing absolute percentage error in combined forecasts,” Computers and Operations Research, vol. 28, no. 11, pp. 1141–1147, 2001.

R. J. Hyndman and A. B. Koehler, “Another look at measures of forecast accuracy,” International Journal of Forecasting, vol. 22, no. 4, pp. 679–688, 2006.

W. Chia-Nan and N. N. Ty, “Forecasting the manpower requirement in Vietnamese tertiary institutions,” Asian Journal of Empirical Research, vol. 3, no. 5, pp. 563–575, 2013.

F.-Y. Lo, C.-F. Chien, and J. T. Lin, “A DEA study to evaluate the relative efficiency and investigate the district reorganization of the Taiwan Power Company,” IEEE Transactions on Power Systems, vol. 16, no. 1, pp. 170–178, 2001.

L. M. Seiford and J. Zhu, “Modeling undesirable factors in efficiency evaluation,” European Journal of Operational Research, vol. 142, no. 1, pp. 16–20, 2002.

N. K. Avkiran, “Association of DEA super-efficiency estimates with financial ratios: investigating the case for Chinese banks,” Omega, vol. 39, no. 3, pp. 323–334, 2011.

Y. Chen and H. D. Sherman, “The benefits of non-radial vs. radial super-efficiency DEA: an application to burden-sharing amongst NATO member nations,” Socio-Economic Planning Sciences, vol. 38, no. 4, pp. 307–320, 2004.