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

Authors: Lai-Wang Wang; Thanh-Tuyen Tran; Nhu-Ty Nguyen
Journal: Journal of Applied Mathematics
 (2015)

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## 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.


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## Body

## 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: RMMILZhu [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
2.96In 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.GM(1,1) 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, GM(1,1) 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 (x01,y01) and (x02,y02), respectively. We employ the following notation for the efficiency score of DMU x0,y0t1 measured by the frontier technology t2. δt2(x0,y0t1) (t1=1,2 and t2=1,2).Then, the catch-up effect is measured by the following formula:(1)C=δ2x0,y02δ1x0,y01.The frontier-shift effect is described as(2)F=δ1x0,y01δ2x0,y01×δ1x0,y02δ2x0,y021/2.Malmquist index (MI) is the product ofC andF; that is,Malmquist index = (catch-up)×(frontier-shift) or MI = C*F or (3)MI=δ1x0,y02δ1x0,y01×δ2x0,y02δ2x0,y011/2.(C); (F); (MI) > 1 indicates progress in relative efficiency from period 1 to period 2, while (C); (F); (MI) = 1 and (C); (F); (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 theoutput-oriented MI as well by means of theoutput-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):(4)δsx0,y0s=min⁡θ,λ⁡θsubjecttox0s≥Xsλ1θy0s≤YsλL≤eλ≤Uλ≥0.Intertemporal score in output-orientation (O-V):(5)δsx0,y0t=min⁡θ,λ⁡θsubjecttox0t≥Xsλ1θy0t≤YsλL≤eλ≤Uλ≥0.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 thenonradial 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 theoutput-oriented case, we solve the following LPs.SBM-O
(6)
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### 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 theGM(1,1) model to try to forecast the variance of primitive series.First, create the primitive series:X(0) = (13,045.20; 11,465.20; 14,875.50; 13,231.40; 14,888.80).Second, perform the accumulated generating operation (AGO):X(1) = (13,045.20; 25,401.40; 40,276.90; 53,508.30; 68,397.10)X(1) = x(0)(1) = 13,045.20x(1)(2)=x(0)(1)+x(0)(2) = 25,401.40x(1)(3)=x(0)(1)+x(0)(2)+x(0)(3) = 40,276.90x(1)(4)=x(0)(1)+x(0)(2)+x(0)(3)+x(0)(4) = 53,508.30x15=x01+x02+x03+x04+x05=68,397.10.Third, create the different equations ofGM(1,1).To findZ series, the following steps can be caculated to obtain the results:z12=1/213,045.20+25,401.40 = 38446.6z13=1/225,401.40+40,276.90 = 65,678.3z14=1/240,276.90+53,508.30 = 93,785.2z15=1/253,508.30+68,397.10 = 121,905.4.Fourth, solve equations.To finda and b, the primitive series values are substituted into the Grey differential equation to obtain (8)11,465.20+a×38446.6=b14,875.50+a×65,678.3=b13,231.40+a×93,785.2=b14,888.80+a×121,905.4=b.Convert the linear equations into the form of a matrix.Let(9)B=-38446.6-65,678.3-93,785.2-121,905.4,θ^=ab,yN=11,465.2014,875.5013,231.4014,888.80.And then use the least square method to find a and b:(10)ab=θ^=BTB-1BTyN=-0.061711194.99.Use the two coefficients a and b to generate the whitening equation of the differential equation:(11)dx(1)dt-0.0617×x1=11194.99.Find the prediction model from (12)X1k+1=X01-bae-ak+bax1k+1=13045.2-11194.99-0.0617e0.0617k+11194.99-0.0617k+1=194487.5e0.0696k-181442.3.Substitute different values of k into the equation: k=0  X11=13045.20k=1X12 = 25423.89k=2X13 = 38591.00k=3X14 = 52596.73k=4X15 = 67494.50k=5X16 = 83341.12k=6X(1)(7) = 100197.02k=7X(1)(8) = 118126.49k=8X(1)(9) = 137197.91.Derive the predicted value of the original series according to the accumulated generating operation and obtain x^01=x11 = 13045.2—for the year 2010x^02=x12-x11= 12,378.69—forecasted for 2011x^03=x13-x12= 13,167.11—forecasted for 2012x^04=x14-x13= 14,005.73—forecasted for 2013x^05=x15-x14= 17,897.77—forecasted for 2014x^06=x16-x15= 15,846.62—forecasted for 2015x^07=x17-x16= 16,855.90—forecasted for 2016x^08=x18-x17= 17,929.47—forecasted for 2017x^09=x19-x18= 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:(13)MAPE=1n∑Actual-ForecastActual×100;nisforecastingnumberofsteps.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.”


## 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: RMMILZhu [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
2.96In 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.GM(1,1) 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, GM(1,1) 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 (x01,y01) and (x02,y02), respectively. We employ the following notation for the efficiency score of DMU x0,y0t1 measured by the frontier technology t2. δt2(x0,y0t1) (t1=1,2 and t2=1,2).Then, the catch-up effect is measured by the following formula:(1)C=δ2x0,y02δ1x0,y01.The frontier-shift effect is described as(2)F=δ1x0,y01δ2x0,y01×δ1x0,y02δ2x0,y021/2.Malmquist index (MI) is the product ofC andF; that is,Malmquist index = (catch-up)×(frontier-shift) or MI = C*F or (3)MI=δ1x0,y02δ1x0,y01×δ2x0,y02δ2x0,y011/2.(C); (F); (MI) > 1 indicates progress in relative efficiency from period 1 to period 2, while (C); (F); (MI) = 1 and (C); (F); (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 theoutput-oriented MI as well by means of theoutput-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):(4)δsx0,y0s=min⁡θ,λ⁡θsubjecttox0s≥Xsλ1θy0s≤YsλL≤eλ≤Uλ≥0.Intertemporal score in output-orientation (O-V):(5)δsx0,y0t=min⁡θ,λ⁡θsubjecttox0t≥Xsλ1θy0t≤YsλL≤eλ≤Uλ≥0.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 thenonradial 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 theoutput-oriented case, we solve the following LPs.SBM-O
(6)
δ
t
x
0
,
y
0
s
=
min
⁡
λ
,
s
+
1
1
+
1
/
q
∑
i
=
1
q
s
i
+
/
y
i
0
s
subject
to
x
0
s
≥
X
t
λ
y
0
s
=
Y
t
λ
-
s
+
L
≤
e
λ
≤
U
λ
≥
0
,
s
+
≥
0
,where the vector s+∈Rq denotes the output-slacks.Super SBM-O
(7)
δ
t
x
0
,
y
0
s
=
min
⁡
λ
,
s
+
1
1
-
1
/
q
∑
i
=
1
q
s
i
+
/
y
i
0
t
subject
to
x
0
s
≥
X
t
λ
y
0
s
≤
Y
t
λ
+
s
+
L
≤
e
λ
≤
U
λ
≥
0
,
s
+
≥
0
.


## 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 theGM(1,1) model to try to forecast the variance of primitive series.First, create the primitive series:X(0) = (13,045.20; 11,465.20; 14,875.50; 13,231.40; 14,888.80).Second, perform the accumulated generating operation (AGO):X(1) = (13,045.20; 25,401.40; 40,276.90; 53,508.30; 68,397.10)X(1) = x(0)(1) = 13,045.20x(1)(2)=x(0)(1)+x(0)(2) = 25,401.40x(1)(3)=x(0)(1)+x(0)(2)+x(0)(3) = 40,276.90x(1)(4)=x(0)(1)+x(0)(2)+x(0)(3)+x(0)(4) = 53,508.30x15=x01+x02+x03+x04+x05=68,397.10.Third, create the different equations ofGM(1,1).To findZ series, the following steps can be caculated to obtain the results:z12=1/213,045.20+25,401.40 = 38446.6z13=1/225,401.40+40,276.90 = 65,678.3z14=1/240,276.90+53,508.30 = 93,785.2z15=1/253,508.30+68,397.10 = 121,905.4.Fourth, solve equations.To finda and b, the primitive series values are substituted into the Grey differential equation to obtain (8)11,465.20+a×38446.6=b14,875.50+a×65,678.3=b13,231.40+a×93,785.2=b14,888.80+a×121,905.4=b.Convert the linear equations into the form of a matrix.Let(9)B=-38446.6-65,678.3-93,785.2-121,905.4,θ^=ab,yN=11,465.2014,875.5013,231.4014,888.80.And then use the least square method to find a and b:(10)ab=θ^=BTB-1BTyN=-0.061711194.99.Use the two coefficients a and b to generate the whitening equation of the differential equation:(11)dx(1)dt-0.0617×x1=11194.99.Find the prediction model from (12)X1k+1=X01-bae-ak+bax1k+1=13045.2-11194.99-0.0617e0.0617k+11194.99-0.0617k+1=194487.5e0.0696k-181442.3.Substitute different values of k into the equation: k=0  X11=13045.20k=1X12 = 25423.89k=2X13 = 38591.00k=3X14 = 52596.73k=4X15 = 67494.50k=5X16 = 83341.12k=6X(1)(7) = 100197.02k=7X(1)(8) = 118126.49k=8X(1)(9) = 137197.91.Derive the predicted value of the original series according to the accumulated generating operation and obtain x^01=x11 = 13045.2—for the year 2010x^02=x12-x11= 12,378.69—forecasted for 2011x^03=x13-x12= 13,167.11—forecasted for 2012x^04=x14-x13= 14,005.73—forecasted for 2013x^05=x15-x14= 17,897.77—forecasted for 2014x^06=x16-x15= 15,846.62—forecasted for 2015x^07=x17-x16= 16,855.90—forecasted for 2016x^08=x18-x17= 17,929.47—forecasted for 2017x^09=x19-x18= 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:(13)MAPE=1n∑Actual-ForecastActual×100;nisforecastingnumberofsteps.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 Table3.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 Table4, 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 GM(1,1) 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 Table5.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 lowIn the empirical study, the results in Table6 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

Table7 shows summary of super SBM results for data of the year 2014. Data are set at valueReturns 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: 0Table8 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
21Table9 shows forecasting results for companies’ future ranking by applying GM(1,1). 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 andMalmquist 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
6.083926361In Table11, 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.
N
Correlation
Sig.
Nonradial and radial
23
−0.264
0.223The results (shown in Table11) indicate that the correlations between two pared samples at (n=23, correlation = −0.264, P=0.223, P<0.05), which means that there is significant difference between correlations of the two models mentioned.Next, the results of Wilcoxon test (Table12) show that M=-2.39, SD=5.59, 95% CI = −4.81; 2.42, t=-2.05, df=22, P=0.052, in which 95% confidence interval of the difference goes through 0 and Pvalue > 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
t
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
2.42223412Because 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
5.821886Figure 1
Efficiency change of the India mining industry.Figure1 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 Table14 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
0.184302772Figure 2
Frontier change over the period 2010 to 2014.Figure2 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 Table15 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
5.533163948Figure 3
Productivity index (MPI) change over the period 2010 to 2014.Figure3 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.GM
(
1,1
) 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
4.823734506Figure 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.


## 4.1. Forecasting Results

Forecasting results from 2015 to 2018 of 23 Indian mining companies were shown in Table3.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 Table4, 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 GM(1,1) 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 Table5.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 lowIn the empirical study, the results in Table6 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

Table7 shows summary of super SBM results for data of the year 2014. Data are set at valueReturns 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: 0Table8 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
21Table9 shows forecasting results for companies’ future ranking by applying GM(1,1). 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 andMalmquist 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
6.083926361In Table11, 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.
N
Correlation
Sig.
Nonradial and radial
23
−0.264
0.223The results (shown in Table11) indicate that the correlations between two pared samples at (n=23, correlation = −0.264, P=0.223, P<0.05), which means that there is significant difference between correlations of the two models mentioned.Next, the results of Wilcoxon test (Table12) show that M=-2.39, SD=5.59, 95% CI = −4.81; 2.42, t=-2.05, df=22, P=0.052, in which 95% confidence interval of the difference goes through 0 and Pvalue > 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
t
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
2.42223412Because 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
5.821886Figure 1
Efficiency change of the India mining industry.Figure1 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 Table14 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
0.184302772Figure 2
Frontier change over the period 2010 to 2014.Figure2 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 Table15 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
5.533163948Figure 3
Productivity index (MPI) change over the period 2010 to 2014.Figure3 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.GM
(
1,1
) 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
4.823734506Figure 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 withGM(1,1)), 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 (Table12) 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.



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*Source: 395360-2015-01-27.xml*