A non paramatic approach for performance assessment of generation utilities in india by ISERP ISERP

Shafali Jain et al. / (IJAEST) INTERNATIONAL JOURNAL OF ADVANCED ENGINEERING SCIENCES AND TECHNOLOGIES Vol No. 1, Issue No. 1, 023 - 029

A Non-Parametric Approach for Performance Assessment of Generation Utilities in India Tripta Thakur, Associate Professor, Electrical Department, MANIT-Bhopal, India-462003 tripta_thakur@yahoo.co.in,

Abstract— The technical efficiency of 30 Indian state owned

through the introduction of competition and improvement of efficiency, but did not proceed as it planned. At this stage it is essential to have documentation of the effects of such reforms. Such documentation has been done in developed countries, however from a few case studies: the experience of developing countries remains much less researched. This documentation can be made by performance evaluation for the structural change in electric power industry. We will be able to find out the direction of the structural change in electric power industry in India by analyzing the efficiency level of power generation companies in India. Such a review of performance of existing utilities is a need for the success of any reform program. Based on efficiency analysis, benchmarks can be set, and targets for improvement may be identified. The efficiency evaluation is also necessary for generating competition and for sector regulation.

Generation Utilities were investigated using Data Envelopment Analysis for the time period 2007-08. The above study provides the efficiency scores of electric utility so that they can rank themselves, identify their shortcomings, set targets, and try to achieve these targets. Input variables are: installed capacity, coal consumption, oil consumption, auxiliary consumption and energy losses and outputs are energy generated and Energy sold. In addition, slack evaluation and target evaluation for input variable has been carried out. The average overall efficiency is 84.83 % and nearly one third of the utilities lie below this average level. The above studies provides the scope for the improvement of internal efficiency of the state owned Generation Utilities which is always win to win situation for the utilities and consumers and especially relevant to the India as it needs addition in electricity generation to meet the growing demand.

Arun Shandilya, Professor, Electrical Department, MANIT-Bhopal India-462003 arunshandilya@yahoo.com

Shafali Jain, Research scholar, Electrical Department, MANIT-Bhopal, India-462003 shafalijain9@yahoo.co.in,

Index Terms—Data Envelopment Analysis (DEA), Stateowned Generation Utilities, Efficiency score, Slack analysis.

I. INTRODUCTION

ince the early 1980’s, many countries have implemented

electricity sector reforms. The main objective is to improve the efficiency of the sector even though the organization of the power sectors and the approaches to reform vary across the countries. The electric power industry which had been maintained as a vertically integrated system in the past, the restructuring of electric power industry in many countries in the world has been performed in the way so as to raise efficiency by introducing competition [3]. The restructuring of electric power industry in India kept pace with the worldwide trend and started with the purpose of decreasing the electricity price and to bridge the demand-supply gap

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This efficiency evaluation can be through by a number of approaches. Among many possible efficiency measurement methods, DEA is one method that has been used especially for the complicated systems with lots of inputs and outputs for benchmarking since its introduction by Charnes, Cooper and Rhodes in 1978 based on previous work by Farrell on production efficiency. This paper presents a case study which provides efficiency scores of generation utilities for the year 2007-08, so that they can rank themselves, identify their shortcomings, set targets and tries to achieve those targets. In addition, slack evaluation and target evaluation for input variable has been carried out. II. METHODOLOGY DEA has been applied to calculate efficiency of different types of DMUs including schools, hospitals and power plants etc. A DMU is an entity, which we measure the efficiency levels, to be compared with other entities in the population. DEA calculates an ―effici ent frontier‖ uses mathematical programming [15]. A benchmark, against which the comparative performance of all other firms or organizations that does not lie on the frontier can be judged, is created

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TABLE I Input

Output

Units generated Energy sold

Installed capacity coal consumption oil consumption auxiliary consumption energy losses

In this methodology, efficiency can be evaluated either on an input-oriented or output-oriented basis. For this paper, an input-oriented or input-minimizing approach was chosen since the purpose of the analysis was to suggest benchmarks for efficiency and reduction of inputs chosen in order to produce a given output. There can be two DEA models: CCR and BCC model and both of these models are applied in this analysis. The CCR model was suggested by Charnes et al. (1978), and hence is named as CCR model and assumes constant returns to scale (CRS) assumption. If assuming data on K inputs and M outputs for each of N firms, then for the i-th firm these are represented by the column vectors xi and yi respectively. The K×N input matrix, X, and the M×N output matrix, Y, represent the data for all N firms. A measure of the ratio of all outputs over all inputs would be obtained for each firm, such as uˈyi /vˈxi, where u is an M×1 vector of output weights and v is a K×1 vector of input weights [15]. The optimal weights are obtained by solving the mathematical programming problem: maxu,v (uˈyi /vˈxi), st uˈyj /vˈxj ≤ 1, j =1,2,….N, u,v ≥ 0. (1) It is required to calculate values of u and v, such that the efficiency measure for the i-th firm is maximized, subject to ISSN: 2230-7818

the constraints that all efficiency measures must be less than or equal to one. The difficulty in this ratio formulation is that it has an infinite number of solutions. This can be avoided by imposing the constraint vˈxi = 1, which provides: maxµ,v (µˈyi ), st vˈxi = 1, µˈyj - vˈxj ≤ 0, j =1,2,….N, µ,v ≥ 0, (2) where the notation is changed from u and v to µ and v, to stress that this is a different linear programming problem. Equation (2) is known as the multiplier form of the DEA linear programming problem. By the duality in linear programming, equivalent envelopment form of this problem can be derived as: minθ,λ θ , st -yi + Yλ ≥ 0, θ xi – Xλ ≥ 0, λ ≥ 0, (3) where θ is a scalar and λ is a N×1 vector of constants. The efficiency score for the i-th firm will be the value of θ According to the Farell (1957) definition, it will satisfy: θ ≤ 1, with a value of 1 indicating a point on the frontier and hence the firm is technically efficient firm.

through this frontier. The efficient frontier is formed from the observed performances of the participating firms in the sample, determined by the relationships between the inputs and outputs of the firms in the sample. The technique was suggested by Charnes, Cooper and Rhodes and is built on the idea of Farrell [16]. There can be a number of input/output variables for evaluating the efficiency of electric utilities. The most important job in this efficiency analysis is the right selection of inputs and outputs. No universally applicable rational template is available for selection of variables [1]. In the context of efficiency measurement, the inputs must reflect the resources used and the outputs chosen must represent the activity levels of the utilities. . A study of standard literature reveals significant insights into the choice of variables. The most widely used variables based on international experience have been outlined in the literature. . Input variables chosen for DEA model are: installed capacity (MW), coal consumption (Million tonnes), oil consumption (Kilo litres), auxiliary consumption (GWh) ,energy losses (GWh) and the outputs are units generated (GWh) and energy sold (GWh) as shown in Table I.

If the utilities do not perform at optimal scales, this CCR model can be modified to take into account variable returns to scale (VRS) conditions by adding a convexity constraint. BCC model was suggested by Banker, Charnes and Cooper (1984) investigates whether the performance of each DMU was conducted in region of increasing, constant or decreasing returns to scale in multiple outputs and multiple inputs situations. The CCR efficiency can be decomposed into the Pure technical and scale efficiency components by this BCC model, thus investigating the scale effects. According to this model an inefficient firm is only ―ben chmarked‖ against firms of a similar size. The CRS linear programming problem can be easily modified to account for VRS by adding the convexity constraint: N1ˈλ=1 to (3) to provide: minθ,λ θ , st -yi + Yλ ≥ 0, θ xi – Xλ ≥ 0, N1ˈλ=1 λ ≥ 0, (4) where N1 is an N×1 vector of ones. This approach forms a convex hull of interesting planes which envelope the data points more tightly than the CRS conical hull and thus provides technical efficiency scores which are greater than or equal to those obtained using the CRS model. The VRS specification has been the most commonly used specification in the 1990s. III. DATA COLLECTION AND COMPILATION DEA was used to derive the benchmarks based on the comparison of the 30 SOEUs in which 8 entities were the SEBs, 7 entities comprised various electricity departments (EDs), and 15 entities comprised the unbundled SOEUs. The

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physical data for various states were obtained for the different years from ―G eneral Review‖ published by CEA [11]. Descriptive statistics of the data for year 2007-08 is presented in Table II in the form of mean, median, standard deviation, minimum and maximum values. To increase the validity of the proposed model, the assumption of the ―i sotonicity‖ relationship, i.e. an increase in an input must not correspond with a decrease in an output, was examined amongst the input and output variables using correlations [1]. TABLE II

Installed Capacity Coal Consumptio n Oil Consumptio n Auxiliary Consumptio n

Mean

Median

Standard Deviation

Min

Max

3256.29

1754.05

3809.6

30.67

14580.46

6640.3

926

9444.78

39385

96543.91

8848

239836.16

1124510

910.78

195.94

1240.48

6201.84

4344.56

Units Generated

14477.57

5427.61

Energy Sold

16547.84

10956.17

4704.08

6661.42

129.7 4

28827.76

18407.74

21.08

72770.46

169.5 1

67930.96

Energy Losses

Variables

18604.46

1) Efficiency Scores CCR model measures the overall efficiency which is the efficiency measured against the CRS frontier. The results are presented in Table IV. It is evident from Table VI that Indian Electric Generation Utilities display significant variations in efficiency levels. The total efficiency had a mean score of 84.83 % for all the utilities and nearly one- third of utilities lie below this average value. Eleven utilities turned out to be the best practices. The remaining 19 utilities exhibited varying degree of inefficiencies. It is also observed that all the utilities, with the exception of the best practices and five utilities – Sikkim, Assam, Manipur, Arunachal Pradesh and Mizoram, exhibited decreasing returns to scale suggesting that the utilities exceeded their most productive scale size. This outcome supports the unbundling policy of the GoI, as envisaged in the Electricity Act. Five Utilities –Sikkim, Assam, Manipur, Arunachal Pradesh and Mizoram, exhibited increasing returns to scale, which indicates that these utilities are smaller than the most productive scale size. The management of the utilities, in general, does not have control over their scale of operation. Therefore, it is quite appropriate to assess efficiency relative to the VRS frontier. So, the technical efficiency of utilities is measured against the VRS frontier. To explore the scale effects, the BCC formulation that assumes a VRS by taking into consideration the sizes of utilities was employed. This formulation ensures that similar sized utilities are benchmarked and compared with each other. The results are presented in Table IV. The number of utilities that appear as efficient entities increased to 24, while remaining 6 utilities showed inefficiencies. The average technical efficiency is 97.9 %. The results indicate the possibility of restructuring of several utilities that display low scale efficiencies (Table IV). The low value of scale efficiencies and the fact that these utilities exhibit decreasing returns to scale indicate that these have considerable scope for improvements in their efficiencies by resizing (downsizing) their scales of operations to the optimal scale defined by more productive utilities in the sample.

DESCRIPTIVE STATISTICS

IV. ANALYSIS OF THE RESULTS

The results indicate that the variables do not isotonicity assumption. The values of correlation (Table III) indicate that the variables are correlated: neither too less of correlation nor correlation.

violate the coefficients reasonably too high a

TABLE III INPUT/OUTPUT CORRELATIONS

Variables

Installed Capacity

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Installed Capacity

Coal consumption

Oil consumption

Auxiliary Consumption

Energy Losses

Units Generated

Total Energy Sold

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Coal Consumption

0.939243

Oil Consumption

0.800981

0.790358

Auxiliary Consumption

0.946876

0.99216

0.753904

Energy Losses

0.898126

0.940558

0.746714

0.929716

Units Generated

0.988273

0.956928

0.813343

0.965917

0.92134

Energy Sold

0.977838

0.935366

0.765371

0.94689

0.92744

0.974358

TABLE IV RESULTS OF CCR AND BCC MODEL

Utility

Total efficiency

Technical efficiency

Scale efficiency

Returns to scale

Benchmarks

S.No.

Haryana

0.682

0.826

0.825

DRS

Himachal Pradesh

Jammu & Kashmir

Punjab

0.969

DRS

Rajasthan

0.846

DRS

Uttar Pradesh

0.644

DRS

Uttrakhand

Delhi

Gujarat

Madhya Pradesh

0.668

Chhattisgarh

0.774

Maharashtra

0.855

Goa

Andhra Pradesh

0.88

Karnataka

0.909

Kerala

Tamil Nadu

Puducherry

Bihar

Jharkhand

Orissa

West Bengal

Sikkim

Assam

Manipur

1 0.837 1

9 4 5 18 8

0.837

DRS

0.818

0.817

DRS

8 16 9 4 21

0.805

0.961

DRS

4 9 15 26

0.855

DRS

0.88

DRS

0.909

DRS

0.835

DRS

0.835

0.508

0.941

0.54

DRS

16 18 2 8 4

0.862

DRS

0.885

DRS

0.787

IRS

0.884

IRS

18 2

0.485

0.994

0.488

IRS

13 27 18

Meghalaya

Nagaland

Tripura

Arunachal Pradesh

0.751

0.985

0.763

IRS

2 13 27

Mizoram

0.388

IRS

2) Slack Analysis The piece-wise linear form of the nonparametric frontier in DEA can cause a few difficulties in efficiency measurement. The problem arises because of the sections of the piece-wise linear frontier that run parallel to the axes that do not occur in most parametric functions [15]. In such cases, even the efficient point is on frontier, one can reduce the amount of the input used and still produce the same output. After the slack evaluation, directions for improvement of the relatively ISSN: 2230-7818

inefficient units can be carried out. For this purpose BCC model has been used. The slack analysis results are shown in Table V in which only input slacks are shown, as input-oriented approach is used in this paper only input slacks are mentioned, as the model used in this paper is input-oriented. It is evident that slacks for efficient utilities with an efficiency score of 100 % are obviously zero. Even inefficient utilities, the slack

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values might not be present. There are 3 DMUs having slack in the installed capacity, 4 having slack in coal consumption, 1 in oil consumption, 3 in auxiliary consumption and 4 DMUs have input slack in energy losses. The results shown in the Table IV shows that some of the utilities are technically inefficient, which indicates excess resources are used by them than required to produce the given level of output. Slack evaluation for the input variables is carried out to determine the amount of inefficiencies.

S.No.

Utility

3) Evaluation of target values For each inefficient utility target value for input variable is calculated so as to make them efficient and shown in the

TABLE V SLACK ANALYSIS

Slack 1 (Installed capacity)

Slack 2 (Coal consumption)

Slack 3 (Oil consumption)

Slack 4 (auxiliary consumption)

Slack 5 (energy losses)

Haryana

247.534

Himachal Pradesh

Jammu & Kashmir

Punjab

Rajasthan

Uttar Pradesh

Uttrakhand

Delhi

Gujarat

Madhya Pradesh

2391.401

2899.024

Chhattisgarh

2001.218

82.782

Maharashtra

Goa

Andhra Pradesh

Karnataka

Kerala

Tamil Nadu

Puducherry

Bihar

Jharkhand

772.065

Orissa

West Bengal

Sikkim

Assam

55.919

63.548

1110.468

Manipur

19.54

0.332

114.264

Meghalaya

Nagaland

Tripura

Arunachal Pradesh

14.242

756.182

93.399

Mizoram

Table VI. The target values for installed capacity, coal consumption, oil consumption, auxiliary consumption, energy losses for Haryana, Madhya Pradesh, Chhattisgarh, Jharkhand, Manipur, and Arunachal Pradesh are lower than their respective original or actual values. Let us take the case of Haryana; the input installed capacity and coal consumption should be reduced by 17 % and 20 % respectively for making it technically efficient. The mean technical efficiency of all the utilities is 97.9 % which means utilities could reduce their inputs by 2.1 % without reducing their outputs.

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4) Summary of Peers For each inefficient utility, DEA identifies a set of efficient utilities that form a peer group for that inefficient utility. There are 26 utilities which have efficiency score of one and are technically efficient. The optimal input-output mix is given by the efficient utility that forms a peer for inefficient utility [2]. For example Gujarat, Punjab, Rajasthan, Puducherry and Delhi form the peer group for Haryana. For utilities having efficiency score of one, their peers are they themselves.

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TABLE VI INPUT TARGET EVALUATION

Original values

Target values

Coal consumptio n (000'MT)

Oil consumptio n (KL)

Auxiliary Consumptio n (GWh)

Energy losses (GWh)

Installed Capacit y (MW)

Coal consumptio n (000'MT)

Oil consumptio n (KL)

Auxiliary Consumptio n (GWh)

Energy losses (GWh)

3159

7819

38534

1168.1

8924.6

2610.7

6213.7

31842

965.3

7374.8

926

6.7

1026.6

6.7

1026.6

Haryana Himachal Pradesh Jammu & Kashmir

625

1718

5.1

5070.3

Punjab

4861

10994

16303

1623.8

8834.2

Rajasthan

4519

12339

22997

1983.2

12575.6

Uttar Pradesh

5077

16985

63082

2244

15036.4

Uttrakhand

1734

Delhi

932

1718

Gujarat

8351

22274

Madhya Pradesh

4483

11999

Chhattisgarh

2814

7994

Maharashtra

14580

39385

Goa

Andhra Pradesh

9452

17587

Karnataka

7625

7875

Kerala

2287

Tamil Nadu

10606

17476

Puducherry

Bihar

590

134

Jharkhand

1754

3796

Orissa

West Bengal

Sikkim

Assam

Manipur

Meghalaya

27 28

Utility

926.3

625.7

1718

5.1

5070.3

4861.3

10994

16303

1623.8

8834.2

4519.6

12339

22997

1983.2

12575.

5077.4

16985

63082

2244

15036.4 2624.5

17.82

2624.5

1734.8

17.8

11901

315.8

6556.3

932.4

1718

11901

315.8

6556.3

479022

3166.6

15650.8

8351.3

22274

479022

3166.6

15650.8

32274

1348.3

13066

3668.4

7425.2

26403

1103

7790.5

24136

926.5

4503

2265.8

4434.6

19431

663.1

3625.3

1124510

4704

28827.7

14580.4

39385

1124510

4704

28827.7

64247

7.19

684.8

78.05

64247

7.1

684.8

35782

2491.1

14110.8

9452

17587

35782

2491.1

14110.8

201647

1347.3

7960.9

7625.9

7875

201647

1347.3

7960.9

112394

64.1

2554.2

2287

112394

64.1

2554.2

621024

2401.4

12187.4

10606.2

17476

621024

2401.4

12187.4

16.3

129.7

32.52

16.3

129.7

3.7

4186

590.4

134

3.7

4186

5795

453.4

3432.4

1650.3

2799.5

5452

426.6

3229.6

S.No.

Installed Capacity (MW)

2650

1889

330.7

7358.9

2498.4

2650

1889

330.7

7358.9

6590

18184

36268

2610.3

7100.7

6590

18184

36268

2610.3

7100.7

0.01

151.5

44.11

151.5

446

1599.2

390.3

12.5

488.8

384

344.2

381

0.6

227.9

189

2.1

538.7

189

2.14

Nagaland

0.02

228.8

30.6

0.02

228.8

148

8.7

297.8

148.3

8.7

297.8

Tripura Arunachal Pradesh

1745

0.2

347.3

45.9

962

0.2

248.7

Mizoram

639

144.6

69.3

639

144.6

2498

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REFERENCES

[14]

[15] [16] [17] [18]

[19] [20] [21]

Tripta Thakur, S.G. Deshmukh, and S.C. Kaushik, .― Efficiency Evaluation of The State Owned Electric Utilities In India‖, Energy Policy, 34(17), 1187-1198, 2007. [2] D.K. Jha & R. Shrestha, ―Measuring Efficiency of Hydropower plants in Nepal using Data Envelopment Analysis‖ , IEEE Transactions on Power Systems, Vol. 21 , No 4 ,pp 1502-1511, November 2006. [3] M.Saleem, ― Technical Efficiency in Electricity Sector of PakistanThe impact of Private and Public Ownership.‖, PhD. [4] Tripta Thakur, S.G.Deshmukh, S.C.Kaushik, and Mukul Kulshrestha, ― Impact assessment of the Electricity Act 2003 on the Indian power sector.‖, Energy Policy, vol. 33, no. 9, pp. 1187-1198, 2005. [5] MoP , 2009. Ministry of Power website, http://powermin.nic.in/ [6] K.P.Kannan, N.V.Pillai, 2000. Plight of the Power Sector in India: SEBs and Their saga of inefficiency. Working Paper No. 308, November 2000. Centre For Development Studies, thiruvananthapuram. [7] D.K. Jha, N.Yorino ,and Y.Zoka, ― A Modified DEA Model for Benchmarking of Hydropower Plants.‖, PowerTech 2007 [8] P.Chitkara, ― A Data Envelopment analysis Approach to Evaluation of Opeartional Inefficiencies in Power Generating Units: A Case Study of Indian Power Plants.‖ IEEE Transactions on Power Systems, Vol. 14, no. 2, May 1999. [9] B. Golany, Y. Roll, and D. rybak,‖Measuring Efiiciency of Power Plants in Israel by Data Envelopment Analysis.‖ IEEE Transactions on Engineering Managrment, vol. 41, no. 3, pp. 291-301, Aug. 1994. [10] A. Vaninsky, ― Efficiency of electric power generation in the United States: Analysis and forecast based on data envelopment analysis.‖, Energy Economics, vol. 28, pp. 326-338, 2006. [11] All India Electricity Statistics , General Review 2009, Central Electricity Authority, New Delhi.

[1]

[13]

The mean CRS and VRS efficiencies are 84.8 % and 97.9 % respectively. All the utilities, with the exception of the best practices and and five Utilities –Sikkim, Assam, Manipur, Arunachal Pradesh and Mizoram, exhibited decreasing returns to scale suggesting that the utilities exceeded their most productive scale size. The numbers of utilities that appear as efficient entities are 11 in case of CRS while under VRS condition, it increased to 24. This VRS formulation ensures that similar sized utilities are benchmarked and compared with each other. It is evident that slacks for efficient utilities with an efficiency score of 100 % are obviously zero. The slack values might not be present even for inefficient utilities. There are 3 DMUs having slack in the installed capacity, 4 having slack in coal consumption, 1 in oil consumption, 3 in auxiliary consumption and 4 DMUs have input slack in energy losses. For each inefficient utility target value for input variable is calculated so as to make them efficient. The target values for installed capacity, coal consumption, oil consumption, auxiliary consumption, energy losses for Haryana, Madhya Pradesh, Chhattisgarh, Jharkhand, Manipur, and Arunachal Pradesh are lower than their respective original or actual values. The mean technical efficiency of all the utilities is 97.9 % which means utilities could reduce their inputs by 2.1 % without reducing their outputs.

M. Abbott, ― The productivity and efficiency of the Australian electricity supply industry.‖ ,Energy Economics, vol. 28, pp. 444-338, 2006. K. sarica and I. Or, ― Efficiency assessment of Turkish power plants using data envelopment analysis.‖ ,Energy, vol. 32, pp. 1484-1499, 2007. R. F. Lovado, ― Benchmarking the efficiency of Philippines Electric Cooperatives Using Stochastic Frontier Analysis and Data Envelopment Analysis‖,Third East West Center International Graduate Student Conference, Hawaii, Feb. 2004. T. Coelli, D.S. Prasado Rao, and George E. Battese, ― An Introduction to Efficiency and Productivity Analysis.‖ W.W. Cooper and K. Tone, ― Measures of inefficiency in data envelopment analysis and stochastic frontier estimation.‖, European Journal of Operational Research, 99(72-88), 1997. A. Charnes, W.W. Cooper and E. Rhodes, ― Mesauring the efficiency of decision making units‖, European Journal of Operational Research, vol. 2, no. 6, pp 429-444. R. Meenakumari and N. Kamraj, ― Measurement of Relative Efficiency of State Owned Electric Utilities in India Using Data Envelopment analysis.‖, Modern Applied Science, vol. 2, no. 5 , pp 6171, Sep 2008. V.K.Yadav, N.P. Padhy, and H.O.Gupta, ― Assessing the performance of electric utilities of developing countries: An intercountry comparison using DEA‖, IEEE Transaction. A. Pahwa, X. Feng, and d. Lubkeman, ― Performance evaluation of electric distribution utilities based on data envelopment analysis.‖ IEEE Transactions on Power Systems, Vol. 18, no. 1, pp. 400-405, Feb 2003. Tripta Thakur, ― Benchmarking study for the Indian Electric Electric utilities Data Envelopment Analysis‖, IEEE Transactions on Power Systems, pp 545-549, 2005.

[12]

V. CONCLUSIONS

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