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Energy 36 (2011) 6398e6405

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Energy

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Measuring efficiency and productivity change in power electric generationmanagement companies by using data envelopment analysis: A case study

Alireza Fallahi a,*, Reza Ebrahimi b, S.F. Ghaderi c

a Iran Power Generation, Transmission and Distribution Management Co., Tavanir, Tehran, IranbDepartment of Industrial Engineering, Iran University of Science and Technology, Tehran, IrancDepartment of Industrial Engineering, College of Engineering, University of Tehran, Iran

a r t i c l e i n f o

Article history:Received 17 February 2011Received in revised form21 September 2011Accepted 22 September 2011Available online 21 October 2011

Keywords:Power electric generationData envelopment analysisEfficiencyProductivityIran

* Corresponding author. Tel.: þ98 21 27935463; faxE-mail addresses: fallahi@tavanir.org.ir, fallahi.ir@g

0360-5442/$ e see front matter � 2011 Elsevier Ltd.doi:10.1016/j.energy.2011.09.034

a b s t r a c t

This paper provides an empirical analysis of the determinants of energy efficiency in 32 power electricgeneration management companies over the period 2005e2009. The study uses non-parametric DataEnvelopment Analysis (DEA) to estimate the relative technical efficiency and productivity change of thesecompanies. In order to verify the stability of our DEA model and the importance of each input variable,a stability test is also conducted. The results of the study indicate that average technical efficiency ofcompanies decreased during the study period. Nearly half of the companies (14) are below this averagelevel of 88.7% for five years. Moreover, it is shown that the low increase of productivity changes is morerelated to low efficiency rather than technology changes.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

In the long run, improved thermal efficiency of power genera-tion through building more energy efficient plants helps to reducesystem capacity requirements and energy costs. Electricityproducers have therefore treated thermal efficiency as a measure ofmanagement or economic performance such as profitability [1].Electricity production in Iran has been linked to the extraction offossil fuels and the use of renewable resources. Most electricity isproduced in thermal power plants and they make around 97% fromtotal electricity energy in Iran (Annual operation statistics, TavanirCompany, www.tavanir.org.ir). In this regard, it is essential for Iranto improve the operational performance of thermal power plantsand analyze the critical variables of the existing utilities in order tomaintain its domestic demand and economic growth. However, theimportant issue how to improve the efficiency of these powerplants has been less attention up to now. The efficiency of a powerplant is generally defined as the electricity produced per energyinput. This ratio takes only the heating value of fuels into account,while neglecting other variables such as installed capacity andelectricity used [2]. Golany [3] suggested an alternative method to

: þ98 21 88644979.mail.com (A. Fallahi).

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measure the efficiency of a power plant using Data EnvelopmentAnalysis (DEA), a technique originally proposed by Charnes et al. [4]for evaluating the relative efficiency of decision-making units(DMUs).

In this study, the DEA method is applied to the performanceevaluation of Iran’s power electric generation management (PEGM)companies. That is a methodological strength in investigatingenergy studies. Because an important feature of DEA is that it doesnot need any specification of any production and/or cost function.The use of the DEA approach not only allows us to compare indi-vidual firms to best practice firms, but also to identify sources ofinefficiency. The innovative content of the paper is to apply DEA tothese companies for the first time and use a stability test to verifythe stability of our DEA model and the importance of each inputvariable. Finally, we hope that the results of this study can beregarded as one of the resources for making policy suggestions andmanagement strategy for Iran electricity sector.

The paper is organized as follows: Section 2 providesa summarization of power generation in Iran. Section 3 reviewsliterature on the application of DEA for performance measurementof electricity production sector in the recent years. In Section 4, themethodology that we follow to measure efficiency and productivitychanges is presented. Section 5 describes the data and measuringefficiency and productivity change. Finally, in Section 6, theconclusions are derived.

A. Fallahi et al. / Energy 36 (2011) 6398e6405 6399

2. Structure of power generation in Iran

In general, power plants are divided into two main typesincluding thermal and non-thermal (hydro, renewable or newenergies). Thermal power plants are an important source of elec-tricity generation in Iran due to cheap and abundant fossil fuels.From the total energy generated in 2009, the share of thermalplants was 96.6 per cent and non-thermal plants’ share was 3.4 percent (Electric Power Industry in Iran, TAVANIR Company, 2009). So,the power plants chosen for analysis had 96.6 per cent share in thetotal amount of the electricity generated in Iran. Although anincrease in the contribution of renewable energy is necessary anda matter of high priority, large scale power plants will continue toplay an important role within this mix and will remain indispens-able for the next few decades. It is therefore of outstandingimportance to increase the energy efficiency of such power plants.Iran`s PEGM companies, composed of one or more thermal powerplants, were established in 1995. In 2009, the number of themreached to 32 companies. They are public and act under thesupervision of TAVANIR Company (Iran power, Generation, Trans-mission and Distribution Management Company). We prefer totake these companies because their data was more complete thanpower plants. The measurement of energy efficiency in PEGMcompanies is much less problematic than in the case of industrialenergy efficiency. This is due to the fact that the output of theproduction process, namely electricity, is highly homogenous. Asa result, it is easier to compare performance of PEGM companiessince there is no concern about the issue of output quality.

3. Literature survey

Since the early 1960s, there has been a growing interest inmeasuring the productivity and efficiency of the power sector.While the theoretical concept of global technical efficiency conceptwas introduced by Debreu [5] and Farrell [6], its practical imple-mentation has developed later along two main methodologicallines. The first one is non-parametric approach (mainly the DEAapproach), which makes use of linear and non-linear programmingtechniques; the second one is parametric approach, which makesuse mainly of statistical and econometric techniques.

The first group of methods is developments of the DEA methodwhich stems, historically, from the DebreueFarrell efficiencyconcept. The first DEA methods were developed by authors such asCharnes et al. [4], Banker [7], Banker et al. [8], Färe et al. [9] amongothers. It aims at evaluating global efficiencies of productionsystems, as revealed through microeconomic (generally cross-sectional) data. The DEA analyzes each decision-making unit(DMU) separately and identifies those that exhibit best practice.A frontier of these units is then constructed, and the efficiency levelof each DMU is determined relative to this best practice frontier. Theuse of the DEA approach not only allows us to compare individualDMUs to the best-practicing DMU, but also to identify the sources ofinefficiency. Some of the recent studies in this research area are asfollows: Sarica and Or [10] analyzed and compared the performanceof electricity generationplants inTurkey, and they showed that coal-fired plants have lower efficiency values than natural gas-fired ones.Operational performance efficiencyof the public thermal plantswassignificantly lower than their private counterparts. Liu et al. [2]evaluated the power generation efficiency of major thermal powerplants in Taiwan during 2004e2006 using the DEA approach.A stability test was conducted to verify the stability of the DEAmodel. According to the their results, all studied power plantsachieved acceptable overall operational efficiencies during2004e2006, and the combined cycle power plants were the mostefficient among all plants. Sozen et al. [11] analyzed efficiency of the

eleven lignite-fired, one hard coal-fired and three natural gas-firedstate-owned thermal power plants used for electricity generationwere conducted through DEA. Two efficiency indexes, operationaland environmental performance, were defined and pursued.Constant returns to scale (CRS) and variable returns to scale (VRS)type DEA models were used in the analyses. The relationshipbetween efficiency scores and input/output factors was investi-gated. Employing the obtained results, the power plants wereevaluated with respect to both the cost of electricity generation andthe environmental effects. Yadav et al. [12] applied the DEAapproach to evaluate the relative performance of 29 ElectricityDistribution Divisions of an Indian hilly state. They used input-oriented DEA to evaluate the relative overall efficiency, technicalefficiencyand scale efficiency. Their results indicated that numerousdivisions had scope for improvement in overall efficiency. Most ofthe utilities were inefficient due to their scale inefficiency ratherthan technical inefficiency. This method was applied widely tomeasure efficiency in electricity generation (e.g. [13e18]).

The second group of methods is parametric approaches, whichreflect ‘‘average’’ or ‘‘central tendency’’ behavior of DMUs. Morerecently, several authors investigated the possibility of combiningDEA approaches to parametric models, by introducing into suchmodels DEA efficiencies as exogenous variables. For example, Bar-ros and Peypoch [19] analyzed the technical efficiency of Portu-guese thermoelectric power generating plants with a two-stageprocedure. In the first stage, the plants’ relative technical effi-ciency estimated with DEA to establish which plants perform mostefficiently. In the second stage, the Simar and Wilson bootstrappedprocedure is adopted to estimate the efficiency drivers. Theirresults show that the majority of the thermoelectric energy plantswere not operating within the efficient frontier. Lam and Shiu [20]also applied the DEA approach to measure the technical efficiencyof China’s thermal power generation based on cross-sectional datafor 1995 and 1996. Their results demonstrate that municipalitiesand provinces along the eastern coast of China and those with richcoal supplies achieved the highest levels of technical efficiency.They also found that fuel efficiency and the capacity factor signif-icantly affect the technical efficiency. In their second stage regres-sion analysis, they found that fuel efficiency and the capacity factorsignificantly affect technical efficiency. Provinces and autonomousregions that were not under the control of the State PowerCorporation (SPC) achieved higher levels of efficiency. Park andLesourd [21] determined the efficiencies of 64 conventional fuelpower plants operating in South Korea by DEA approaches, as wellas by a stochastic-frontier method. Their results showed that thenull hypothesis of equality of means between all fuel types could beaccepted. In addition, they found that the efficiency for the oldestplants is significantly smaller than the newer ones. A comparison ofthe plants’ efficiencies by geographical area revealed no significantdifference.

The comparison of DEA, of parametric methods allowing forstochastic behavior, and of so-called semi-parametric methodswhich are a combination of both these approaches, has been dis-cussed by several authors, including Simar [22]. It is clear that thisstudy belongs to the first research group where DEA is applied tothe performance evaluation of electric generation. The study ofrelated previous researches indicates that some various variablesare used. Based on the nature of DEA technique the number ofmodel variables affects the results. Given imperfect data,researchers are often required to make tradeoff in selecting inputand output variables. In this paper, in order to verify the stability ofDEA model, a stability test was conducted by changing the numberof inputs. To get a fuller picture of the evolution, six models aredeveloped for this test. The Spearman correlation coefficients arecalculated to assess the impact of individual variables left out on the

A. Fallahi et al. / Energy 36 (2011) 6398e64056400

results. Ultimately, the best model is selected for the evaluation ofthe efficiency and productivity.

4. Methodology

4.1. Measuring the technical efficiency

The DEA is a mathematical programming method for assessingthe comparative efficiencies of DMUs. This methodology is a non-parametric approach determining a linear efficiency frontieralong the most efficient utilities to derive relative efficiencymeasures of all other utilities. It produces detailed information onthe efficiency of each unit, not only relative to the efficiency frontierbut also to specific efficient units that can be identified as rolemodels or comparators [23]. DEA allows for efficient measurementof multiple outputs and inputs without pre-assigned weights andspecifying any functional form on the relationships between vari-ables [14]. Therefore, it is not only a non-parametric approach butalso a data-driven frontier analysis technique that floats a linearsurface to rest on empirical observations [24].

In the literature, two DEA models are commonly used. The firstmodel was suggested by Charnes, Cooper and Rhodes (CCR) [4].And the second model was developed by Banker, Charnes, Cooper(BCC) [8]. The CCR model is built on the assumption of constantreturns to the scale (CRS) of activities, but the BCC model is built onthe assumption of variable returns to the scale (VRS) of activities.Returns to scale refers to a technical property of production thatexamines changes in output subsequent to a proportional change inall inputs (where all inputs increase by a constant). If outputincreases by same proportional change then there are constantreturns to scale (CRS), sometimes referred to simply as returns toscale. If output increases by less than that proportional change,there are decreasing returns to scale (DRS). If output increases bymore than that proportion, there are increasing returns to scale(IRS). The measure of efficiency of a DMU is defined as the ratio ofa weighted sum of outputs to a weighted sum of inputs subject tothe condition that a corresponding ratio for each DMU be less thanor equal to one. The following section describes the modelemployed in the current study.

Charnes et al. [4] first introduced the DEA efficiency concept,which stems from the DebreueFarrell efficiency concept. Assuminga cross-sectional sample of N production units in a given industry,withm inputs and n outputs, let j0 (1� j0�N) be one of these units.In this case, the CCR efficiency Pj0 of production unit j0, withproducts (with r¼ 1,., n) and production factors xij0 (with i¼ 1,.,m), is defined as the solution of the following programmingproblem:

max pj0 ¼Pn

r¼1 urj0yrj0Pmi¼1 vij0xij0

(1)

Subject to

Pnr¼1

urj0yrj

Pmi¼1

vij0xij

� 1; j ¼ 1;.;N

urj0 ; vij0 � 0 r ¼ 1;.;n; i ¼ 1;.;m

where j0 is the decision-making unit (DMU) being evaluated in theset of j¼ 1, ., N DMUs; pj0 the measure of efficiency of DMU “j0”,the (DMU) in the set of j¼ 1, ., N (DMU)s rated relative to theothers; yrj0 the amount of output “r” produced by DMU “j0” duringthe period of observation; xij0 the amount of resource input “i” usedby DMU “j0” during the period of observation; yrj the amount of

service output “r” produced by DMU “j” during the period ofobservation; xij the amount of resource input “i” used by DMU “j”during the period of observation; urj0 theweight assigned to serviceoutput r computed in the solution to the DEA model vrj0 the weightassigned to resource input i computed in the solution to the DEAmodel. This maximization problem is a fractional programmingproblem, which may easily be linearized.

It is difficult to solve the above model because of its fractionalobjective function. If the ratio is forced to be equal to one, then theobjective function will become linear. Details of the linear form ofa CCR model may be found in Chapter 2 of Cooper [25]. The dual ofthe linear model is required as it reduces the number of constraintsand thereby makes the linear problem easier to solve. It is givenbelow [25,26].

minqj0 � 3

Xmi¼1

s�ij0 þXnr¼1

sþrj0

!(2)

Subject to

qj0Xij0 �PNj¼1

ljXij � s�ij0 ¼ 0; i ¼ 1;.;m

yrj0 �PNj¼1

ljyrj þ sþrj0 ¼ 0; r ¼ 1;.;n

lj; s�ij0 ; sþij0

� 0; ci; j; r

where qj0 is the measure of efficiency of DMU “j0”, the DMU in theset of j¼ 1, ., N DMUs rated relative to the others; 3an infinites-imal positive number used to make both the input and outputcoefficients positive; s�ij0 slack variables for input constraints, whichare all constrained to be non-negative; sþij0 slack variables for outputconstraints, which are all constrained to be non-negative; and lj thedual weight assigned to DMUs.

Banker et al. [8] developed a model (BCC) with variable returnsto scale (VRS). The BCC model has the same equation as employedin the CCR model, but it adds a convexity constraint for the modi-fication. The dual form of the BCC model is shown in Eq. (3).

min qj0 � 3

Xmi¼1

s�ij0 þXnr¼1

sþrj0

!(3)

Subject to

qj0xij0 �PNj¼1

ljxij � s�ij0 ¼ 0; i ¼ 1;.;m

yrj0 �PNj¼1

ljyrj þ sþrj0 ¼ 0; r ¼ 1;.;n

PNj¼1

lj ¼ 1

lj; s�ij0 ; sþij0

� 0; ci; j; r

The above CCR and BCC models can identify the relative efficiencyscores of all the DMUs. Efficiency scores are constructed bymeasuring how far a utility is from the frontier. In general, a DMU isefficient if it has a score of one, while a score of less than oneindicates that it is inefficient.

The reasons that a DMU is inefficient may result from inap-propriate operation of the DMU itself or from the inadequate scaleof the DMU’s operation. In this regard, the CCR and the BCC modelsare calculated in this study in order to report scale efficiencyinformation, which is the ratio of the two scores [10].

There are two versions for either the CCR or the BCC model. Oneversion of these models aims to minimize inputs while satisfying atleast the given output levels. This is called the input-oriented

A. Fallahi et al. / Energy 36 (2011) 6398e6405 6401

model. The other version of the models attempts to maximize theoutput without requiring more of any of the observed input values.That is called the output-oriented model [25]. In this paper, we usethe input-oriented DEA model to evaluate the efficiency of Iran’sPEGM companies.

4.2. Measuring and decomposing the changes in productivity

Due to the multiple output and multiple input characteristics ofthe electricity supply industry, the non-parametric DEA approachprovides an attractive option. Consequently, productivity change isanalyzed in this study on the basis of changes in a frontierproduction function estimated by means of DEA. Productivitymeasurement has a long history, and the earliest approach wasbased on single or partial factor productivity measurement.Although it is easy to calculate, in practice this index is too simpleand could give a misleading picture of performance, when there ismore than a single output or a single input. In the real world firmsusually use multiple inputs to get multiple outputs, so themeasuring of productivity must be done using total factorproductivity (TFP) measurement. Thus, TFP is a generalization ofsingle factor productivity measurement. TFP growth refers to thechange in productivity over a period of time. There are severalapproaches to productivity measurement [27]. In order to take intoaccount the contribution of efficiency change to productivitychange, we use a non-parametric frontier approach.

In the case of non-parametric frontier production functions, totalfactor productivity (TFP) measurement based on the Malmquistindex is a natural approach; the index requires neither profitmaximization nor cost minimization, only quantity data. TheMalmquist index is calculated on the basis of the efficiencymeasures derived from the DEA model. In recent years, the Malm-quist index has become the standard approach to productivitymeasurement over time within the non-parametric literature.Malmquist indiceswere introduced by Caves et al. [28]. They namedthese indices after Malmquist, who had earlier proposed con-structing input quantity indices as ratios of distance functions. TheMalmquist index was only treated theoretically until its enhance-ment by Färe et al. [29]. A major contribution of this paper was toaccount for the existence of inefficiency in DMUs’ activity and toprovide DEA models for the calculation of the distance functions.Färe et al. [29] defined an input-oriented productivity index as thegeometric mean of the two Malmquist indices developed by Caveset al. [28], referring to the technologies at time periods t and tþ 1,yielding the following Malmquist-type measure of productivity:

Mt;tþ1i

�xtþ1;ytþ1;xt ;yt

�¼"Dti

�xtþ1;ytþ1�Dti ðxt ;ytÞ

�Dtþ1i

�xtþ1;ytþ1�

Dtþ1i ðxt ;ytÞ

#1=2

(4)

Another achievement of Färe et al. [29] was to show how todecompose the index Mt;tþ1

i into an index reflecting the change intechnical efficiency and an index reflecting the change in thefrontier of the production possibility set (i.e., an index of techno-logical change). These components are obtained by rewriting theindex in (2) as follows:

Mt;tþ1i

�xtþ1; ytþ1; xt ; yt

�¼Dtþ1

i

�xtþ1; ytþ1�

Dti ðxt ; ytÞ

�"

Dti

�xtþ1; ytþ1�

Dtþ1i

�xtþ1; ytþ1

�� Dt

i

�xt ; yt

�Dtþ1i ðxt ; ytÞ

#1=2¼ Etþ1

i � Ttþ1i ð5Þ

The ratio outside the bracket measures the input technicalefficiency change ðEtþ1

i Þ between time periods t and tþ 1. The

geometric mean of the two ratios inside the bracket captures thetechnological change ðTtþ1

i Þ or shift in technology between the twoperiods, evaluated at the input -output levels (xt,yt) at time period tand the levels (xtþ1, ytþ1) at time period tþ 1. In relation to thereturns to scale assumption used for the estimation of the distancefunctions, constant returns to scale (CRS) should be used in the firstinstance, as the Malmquist index provides an inaccurate produc-tivity measure when it is evaluated under variable returns to scale(VRS). Subsequently, Färe et al. [29] proposed an even largerdecomposition of this index, when they distinguished between fulltechnical efficiency and changes in scale efficiency within the termthat takes the change in technical efficiency, ðEtþ1

i Þ:

Etþ1i ¼ Dtþ1

i ðYtþ1;Xtþ1ÞDti ðYt ;XtÞ

¼"Dtþ1i ðYtþ1;Xtþ1ÞDti ðYt ;XtÞ

#VRS

�"Dtþ1i ðYtþ1;Xtþ1ÞCRS=Dtþ1

i ðYtþ1;Xtþ1ÞVRSDti ðYt ;XtÞCRS=Dt

i ðYt ;XtÞVRS

#

¼ ETPtþ1 � EStþ1i (6)

This distinction enables us to contemplate those situations wherea productive unit can be technically efficient, as the productionvolume uses the least quantity of factors; however, it is not situatedin the optimum production scale, because it is not adequately sized.Therefore, the changes in productivity that are strictly related totechnical efficiency appear in ETPtþ1

i , while these related to theproductive unit size appear in EStþ1

i .

5. Measuring efficiency and productivity change

5.1. Data and models

The particular DEA methods mentioned above (with referenceto both constant returns to scale, and variable returns to scaletechnologies) were applied to the 32 PEGM companies operating inIran in 2005e2009. The choice of variables was based on theavailability of data, and on our previous discussion of the currentliterature. One output and five inputs are used in calculations. Theoutput is defined as the net electricity produced. Each PEGMcompany is considered as producing this output by using labor andother inputs. The labor is measured as the number of employees percompany. Only physical measure of capital, namely installedcapacity is used. Fuel and Electricity used are included as additionalinputs variable, since these may be the cost most directly control-lable by the manager of the companies. Finally, average operationaltime is considered as input in calculation. The specification isdescribed in Table 1. All data used in this paper were obtained fromthe annual operation statistics (Tavanir Company, www.tavanir.org.ir). The combination of the measured indicators ensures adherenceto the DEA convention that the minimum number of DMU obser-vations should be greater or equal to three times the number ofinputs plus outputs [30]. In our study, 160 observations are greaterthan three times the sum of the input and output variables(160� 3(5þ1)).

Due to the nature of the DEA technique, several factors includingthe relationship between sample size and number of model vari-ables may affect the results. Given imperfect data, researchers areoften required to make tradeoffs in selecting input and outputvariables. Changing the number of inputs or outputs is one of themethods to implement the stability and sensitivity analysis in DEA[2,31e33]. In order to verify the stability of our DEA model, thestability test was conducted by omitting one or more inputs vari-ables at a time. To get a fuller picture of the evolution, six modelsare considered for this test. The technical efficiency scores are

Table 1Definition of the variables.

Variable Unit Define

InputInstalled capacity (MW) Maximum design load of generated

electricity per monthFuel (106 calories) Sum of the heat value of fossil fuels

that used in a companyLabor The number of equivalent workersElectricity used (MWh) Electricity consumption by equipments

within the companyAverage operational

time(h) The amount of time that the power plants

of an company are in operation in a year

OutputNet electricity

produced(MWh) Sum of generated electricity without

electric energy consumed by company

A. Fallahi et al. / Energy 36 (2011) 6398e64056402

calculated for each company for each model. Results of the stabilitytest are shown in Table 2. The main model is model 1, whichincludes all output and input variables. The Spearman correlationcoefficients are calculated to assess the impact of individual vari-ables left out on the results obtained from Model 1 under the CCRmodel. Model 2 is calculated to observe the impact of the alterna-tive definition of labor on the results. The correlation coefficient of98% suggests that the new definition hasn’t a noticeable effect onthe results. Dropping the electricity used from the calculation hasa less important effect on the results, indicated by the correlationcoefficient of 98% in model 3. Model 4 is calculated by excludingother input “average operational time” from the original model. Thecorrelation coefficient of 96% suggests that excluding this variablefrom the calculation has a relatively small effect on the results.Models 5 and 6 are representatives of models that two and threeinputs are omitted respectively. Dropping the electricity used andaverage operational time from the calculation has a less importanteffect on the results, indicated by the correlation coefficient of 96%in Model 5. Model 6 is calculated by omitting three inputs averageoperational time, electricity used and labor from the originalmodel. The correlation coefficient of 91% and mean efficiency scoreof 83% suggests that excluding these variables from the calculationhas a relatively small effect on the results. Also the effect of removalof installed capacity and fuel investigated that obtained values for

Table 2Results of six models from stability test.

Variable Model 1 Model 2 Model 3 Model 4 Model 5 Model 6

OutputNet electricity

produced (MWh)U U U U U U

InputsInstalled

capacity (MW)U U U U U U

Fuel (MCal) U U U U U U

Labor U e U U U e

Expert labors e U e e e e

Inexpert labors e U e e e e

Electricity used(MWh)

U U e U e e

Average operationaltime (h)

U U U e e e

SCC with model 1 e 0.977 0.978 0.955 0.957 0.913Mean efficiency score 0.870 0.879 0.857 0.847 0.840 0.825Minimum efficiency

score0.565 0.565 0.523 0.512 0.512 0.512

Number of efficientcompanies

9 9 9 6 6 5

All correlation coefficients are significant at a level of significance¼ 0.001; SCC,Spearman correlation coefficients.

the correlation coefficient and mean efficiency score are 74% and0.47 respectively. These values indicated the importance of theseinputs. According to these results, Model 1 is used for the evalua-tion of the technical and scale efficiency in the following section.Table 3 presents the descriptive statistics of the variables used inthis model.

5.2. Application results and discussion

The DEA index can be calculated in several ways. In this study,we estimated an input-oriented, technically efficient (TE) DEAindex, assuming that PEGM companies aim to minimize the costsresulting from their activity. Because the amount of overall elec-tricity generated is based on policies and distribution regulationsfrom the authorities. Companies are very unlikely to increase theelectricity production simply to promote the efficiency. The resultsin terms of both CRS and VRS efficiencies are given in Table 4.

Here, we can observe that in CRS model only 9 companies(Montazeri, Ahvaz, Gilan, Khyam, Kerman, Persian Gulf, Shazand,Ghom and Bisetoon) among 32 companies have unit efficiency in2009. These companies can be offered as references to others forimproving their efficiency.

The operational efficiencies (CCR efficiency) of the surveyedcompanies in 2009 are between 0.565 and 1.000. These scores indi-cate, however, that thementionedcompaniescannonetheless reducethe inputs by up to 28%, while achieving the same productivity.

In VRS model, that the technical efficiency is calculated withoutconsidering the effect of scale, 17 companies are efficient. However,in CRS model, in which the technical efficiency contains the scaleeffect, only nine companies have unit efficiency. Therefore, it can beperceived that the only reason why those eight companies in VRSshow the efficiency lower than one is their inadequate scale. Theaverage of efficiency score in VRS in 2009 is 0.923 that companieslike Ghaem, Khorasan, Fars, etc. are inefficient. This indicates thatthere are potential benefits in renovating the managementmeasures of these low technical efficiency companies.

Many companies like Rey, Zarand, Firoozi, etc. are inefficient intheir operational scales, and can increase their returns byenhancing the scales. It means that they have a good potential toimprove their efficiencies by resizing the operational scales tooptimize their productivity. 65% of the companies that don’t workin an optimum scale have increasing return to scale. So, thesecompanies have the potential to extend their working distinct forexpense regulation and improve the efficiency scores.

As seen from Table 4, the performance of evaluated companies in2005e2009 can be divided into three groups. First, the CRS, VRS, andscale efficiency scores of Montazeri, Ahvaz, Gilan, Khyam, Kerman,Persian Gulf, Shazand and Ghom companies all are close to or equalto 1.000. So they are at the optimal production frontier and couldhave a steady operational performance. Thismay be affected because

Table 3Descriptive statistics of the variables, 2005e2009.

Variables Minimumvalue

Maximumvalue

Mean Standarddeviation

InputsElectericity used (MWh) 771 866,950 228,372 234,670Average operational

time (h)3068 24,021 10,168 4,538

Fuel (MCal) 298,652 33,381,876 12,692,865 7,765,734Labor 40 789 300 176Installed capacity (MW) 50 3367 1111 679

OutputNet electricity

produced (MWh)103,148 13,661,357 5,152,018 3,347,684

Table 4Efficiency results for PEGM companies.

Firm TE CCR TE BCC SE RS

2005 2009 Mean 2005 2009 Mean 2005 2009 Mean 2005 2009

Rajaei 0.949 0.956 0.953 1.000 1.000 1.000 0.949 0.956 0.953 drs drsGhaem 0.900 0.857 0.891 0.959 0.901 0.924 0.938 0.951 0.964 drs drsKhorasan 0.954 0.826 0.868 0.956 0.838 0.878 0.998 0.985 0.989 irs irsMontazeri 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 crs crsFars 1.000 0.950 0.972 1.000 0.960 0.980 1.000 0.990 0.992 crs drsAhvaz 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 crs crsJonoob-e-Fars 1.000 0.910 0.936 1.000 1.000 1.000 1.000 0.910 0.936 crs drsSalimi 1.000 0.971 0.990 1.000 1.000 1.000 1.000 0.971 0.990 crs drsDamavand 1.000 0.708 0.854 1.000 0.720 0.944 1.000 0.984 0.909 crs drsSistan 0.690 0.598 0.671 0.709 0.621 0.690 0.974 0.963 0.972 irs irsGilan 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 crs crskhayyam 0.998 1.000 0.995 1.000 1.000 0.996 0.998 1.000 0.998 drs crsHormozgan 0.804 0.724 0.802 0.804 0.730 0.806 1.000 0.992 0.995 crs drsRey 0.810 0.565 0.697 0.889 1.000 0.950 0.912 0.565 0.742 irs irsAz.Sharghi 0.735 0.737 0.768 0.755 0.801 0.797 0.973 0.921 0.964 drs drsKerman 1.000 1.000 0.996 1.000 1.000 0.998 1.000 1.000 0.998 crs crsEsfahan 0.872 0.838 0.882 0.905 0.889 0.903 0.963 0.942 0.976 irs irsPersian Gulf 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 crs crsShazand 1.000 1.000 0.996 1.000 1.000 0.996 1.000 1.000 1.000 crs crsMofatteh 0.766 0.811 0.789 0.810 0.857 0.828 0.947 0.946 0.953 irs irsAbadan 1.000 0.923 0.978 1.000 1.000 1.000 1.000 0.923 0.978 crs irsYazd 1.000 0.848 0.893 1.000 0.898 0.927 1.000 0.944 0.963 crs irsGhom 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 crs crsToos 0.958 0.905 0.927 0.976 0.956 0.952 0.982 0.947 0.973 irs irsAz.Gharbi 0.967 0.807 0.898 1.000 0.864 0.943 0.967 0.935 0.951 irs irsKurdistan 0.862 0.835 0.878 1.000 1.000 0.994 0.862 0.835 0.884 irs irsBisetoon 0.954 1.000 0.925 0.982 1.000 0.984 0.971 1.000 0.940 irs crsMashhad 0.765 0.721 0.755 0.801 0.748 0.791 0.955 0.964 0.954 irs irsZarand 0.678 0.737 0.734 1.000 1.000 0.998 0.678 0.737 0.736 irs irsBeheshti 0.886 0.699 0.780 0.913 0.803 0.856 0.970 0.870 0.908 irs irsFiroozi 0.704 0.780 0.706 1.000 1.000 1.000 0.704 0.780 0.706 irs irsBesat 0.876 0.895 0.850 0.931 0.950 0.946 0.942 0.942 0.901 irs irs

Mean 0.910 0.863 0.887 0.950 0.923 0.940 0.959 0.936 0.945 e e

Minimum 0.678 0.565 0.671 0.709 0.621 0.690 0.678 0.565 0.706 e e

SD 0.107 0.125 0.103 0.082 0.105 0.080 0.076 0.092 0.077 e e

NECs 13 9 5 19 17 10 14 9 6 e e

TE: technical efficiency; SE: scale efficiency; RS: Return to scale; irs: increasing returns to scale; drs: decreasing returns to scale; crs: constant returns to scale; NECs = Numberof efficient companies.

Table 5Malmquist TFP index: annual average.

Year EffCh TechCh PeCh SeCh TFPCh

2006 0.988 1.028 0.996 0.991 1.0142007 0.999 1.001 1.001 0.999 0.9982008 0.980 1.041 0.998 0.983 1.0202009 0.988 1.034 0.982 1.009 1.021

Annual average 0.989 1.026 0.994 0.995 1.013

EffCh, efficiency change; TechCh, technical change; PeCh, pure efficiency change;SeCh, scale efficiency change; TFPCh, total factor productivity change (Malmquistindex).

A. Fallahi et al. / Energy 36 (2011) 6398e6405 6403

all of them have only one power plant. Analyses and comparisons ofdata of these companies show that they have a power plant withhigh net electricity produced. So, their proportion of output to inputsis larger in comparison with other companies.

Second, Rajaei, Jonoob-e-Fars, Salimi, Abadan and Firoozicompanies have optimal VRS efficiency but lower scale efficiency.This indicates that they are already technically efficient; however;they have limited or inappropriate scales.

Third, the companies that their VRS efficiency and scale effi-ciency scores are not one. These companies can be divided into twogroups. At the first group there are six companies such as Dam-avand, Rey, Kurdistan, etc. that their VRS score is higher than thescale score. And at the second group there are 13 companies such asGhaem, Khorasan, Fars, etc. that their scale efficiency is higher thanVRS score. In clarity; companies in group one not only shouldincrease their technical efficiency but also should make theirproduction scale optimum. Inverse, the production scale of groupsecond companies should be made optimum, moreover; theyshould attend more to their technical efficiency.

Some other points are derived from analyzes. Firstly, in2005e2009 Montazeri, Ahvaz, Gilan, Kerman, Persian Gulf,Shazand and Ghom companies have a value close to or equal to theunit for their CRS index. It shows that they maintained theirefficiency toward other companies and are on the efficient frontier.Also, Khayyam and Bisetoon companies enhanced their efficiencyand, compared with other companies, had an ascending procedurein moving to the efficient frontier. In verse, the efficiency of

Kurdistan, Az.Gharbi, Yazd, Abadan, Rey, Hormozgan and Khorasancompanies had a descending procedure. They should increase theirefficiency by making proper decisions. Other companies had anirregular procedure. It should be mentioned that companies whichform the reference set that are placed on the efficient frontier hadnot any special change in this five-year period. So, the efficientfrontier in this period hadn’t a far change. Secondly, best practicecalculations indicate that 13 companies in 2005 and 9 in 2009 inCRS and 19 companies in 2005 and 17 in 2009 in VRS are on theefficient frontier, showing that the number of efficient companiesin both models declined in 2009 rather than 2005. Thirdly, theoverall average of efficiency in CRS reduced from 0.910 in 2005 to0.863 in 2009, also, in VRS reduced from 0.950 to 0.923. Fourthly,the average efficiency is 0.863 for CRS and 0.923 for VRS in 2009.It means that if we use available possibilities without any

Table 6Malmquist TFP index: average results by company: 2005e2009.

Firm EffCh TechCh PeCh SeCh TFPCh

Rajaei 1.002 1.007 1.000 1.002 1.009Ghaem 0.990 1.005 0.987 1.005 0.993Khorasan 0.966 1.029 0.969 0.997 0.993Montazeri 1.000 1.012 1.000 1.000 1.012Fars 0.988 1.010 0.991 0.998 0.998Ahvaz 1.000 1.027 1.000 1.000 1.027Jonoob-e-Fars 0.979 1.046 1.000 0.979 1.020Salimi 0.993 1.022 1.000 0.993 1.015Damavand 0.918 1.042 0.930 1.007 0.957Sistan 0.977 1.008 0.979 0.998 0.984Gilan 1.000 1.002 1.000 1.000 1.002khayyam 1.001 1.008 1.000 1.000 1.009Hormozgan 0.976 1.008 0.978 0.998 0.982Rey 0.914 1.090 1.033 0.889 0.996Az.Sharghi 1.007 1.005 1.018 0.987 1.010Kerman 1.000 1.124 1.000 1.000 1.126Esfahan 0.992 1.015 0.997 0.995 1.006Persian Gulf 1.000 1.114 1.000 1.000 1.114Shazand 1.000 1.008 1.000 1.000 1.008Mofatteh 1.018 1.002 1.016 1.000 1.019Abadan 0.981 1.029 1.000 0.981 1.010Yazd 0.965 1.037 0.978 0.986 0.994Ghom 1.000 0.997 1.000 1.000 0.997Toos 0.986 1.015 0.996 0.991 1.001Az.Gharbi 0.958 1.043 0.965 0.992 0.994Kurdistan 0.995 1.050 1.000 0.997 1.040Bisetoon 1.014 1.011 1.005 1.010 1.027Mashhad 0.991 1.016 0.987 1.002 1.006Zarand 1.023 1.017 1.000 1.023 1.040Beheshti 0.959 1.006 0.974 0.976 0.964Firoozi 1.035 1.014 1.000 1.035 1.048Besat 1.014 1.017 1.007 1.016 1.030

Mean 0.989 1.026 0.994 0.995 1.013SD 0.026 0.031 0.018 0.023 0.034

EffCh, efficiency change; TechCh, technical change; PeCh, pure efficiency change;SeCh, scale efficiency change; TFPCh, total factor productivity change (Malmquistindex).

A. Fallahi et al. / Energy 36 (2011) 6398e64056404

development in power plants capacities, of course, in an optimumway, the produced electricity can be increased to 14% at the firstmodel and to 8% at the second. Fifthly, according to the averagescores for five years, Sistan Company had the worst performance inboth CCR and BCC models. Finally, on the basis of the BCC results,which measure pure technical efficiency accountable to manage-ment skills, the average score is higher than the CCR model resultsin the period. The rationale for interpreting BCC as management

0.900.920.940.960.981.001.021.041.061.081.101.12

Raj

aei

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Fig. 1. Average results of Malmquist TF

skills is based on the contrast between the CCR and BCC models.The CCRmodel identifies the overall technical inefficiency, whereasthe BCC differentiates between technical efficiency and scale effi-ciency [34]. Based on this differentiation, the ratio between CCRand BCC models enables the estimation of scale efficiency and,assuming that efficiency is due to managerial skills and scaleeffects, the BCC scores are interpreted as managerial skills. Thus,according to the BCC scores obtained, 17 companies analyzed areefficient in 2009. Therefore, the overall conclusion is that there isroom for management to improve the efficiency of companies.

Tables 5 and 6 show the total factor productivity changes by yearand by company, respectively. Table 5 shows that The TFP annualaverage variation is 1.3%. The changes in productivity were almostthe same within the years of the analyzed period except 2007. In2007, we can see a slight decline in the evolution of productivity. Itsresults in Table 5 indicate that the main source of factor produc-tivity change has been technological change, which is a situationspecific to this industry. Unlike telecommunications it hasn’t facedtechnological changes that are external to the firms; hence, it isfeasible to consider technological change as taking place within thecompany.

Table 6 and Fig. 1 show that 21 companies have experiencedincreases and 11 decreases in their total factor productivity. Thecompanies with the most positive significant changes are Kermanand Persian Gulf; inverse, Damavand and Beheshti are those withthe most negative significant changes. Kerman and Persian Gulfhave a similar situation. Both of them have a unit technical effi-ciency. So their high TFP is result of technological change. Kerman isa new company and had a TFP more than unit in all studied years,moreover, its installed capacity increased in 2008, and after that itsTFP increased more. It is possible that the expert labor of PersianGulf Company is the cause for its positive significant change.Deducing from the results of decomposition of the Malmquistindex reflect a problem of pure technical efficiency for Damavand,the company that had the worst scores, it can be perceived that thementioned problem led its unacceptable scores. This company canattain additional productivity increments if it increases pure tech-nical efficiency. Lastly, the level of pure technical inefficiency ofBeheshti is low, the same as it is derived from scale efficiency.

The decomposition of the Malmquist index shows that, atcompany level, almost all productivity increases are explained byimprovements in technological efficiency. All companies exceptGhom have a positive growth in technology efficiency. It meansthat; companies have improved their productivity by using modernfacility and equipments.

Kerm

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EffCh TechCh TFPCh

P index by company: 2005e2009.

A. Fallahi et al. / Energy 36 (2011) 6398e6405 6405

6. Conclusion

In this study, DEA was applied on the 32 PEGM companies inIran in order to measure their relative performances over theperiod 2005e2009. A stability test is applied to verify the stabilityof our DEA model and the importance of each input variable. To geta better picture of the evolution, six models are given in this test.The efficiency scores acrossmodels reveal that our results are stableacross all specifications.

The preceding analysis shows that all PEGM companies in Iranachieved acceptable overall operational efficiencies during2005e2009, with the range of average CCR efficiency from 0.671 to1.000. The average score for the BCC efficiency is 0.940 and that forthe scale efficiency is 0.945 for all evaluated companies. It meansthat if we utilize available capacities in handwithout any increasinggeneration capacities, the generated electricity can be increased.Also, Calculations show that the number of efficient companies andthe overall average of efficiency in both CRS and VRS modelsdeclined in 2009 comparing with year 2005. In general, theempirical evidence illustrate that technical efficiency of thecompanies should be increased.

With regard to the total factor productivity that the Malmquistindex reports for the 2005e2009 period, annual average variation is1.3%. There are 21 companieswhich have experienced increases andother 11 companies decreases in their total factor productivity. Thetotal factor productivity change shows that the low increase ofproductivity change is due to low efficiency change, and not tech-nology change. Technological change, which is a situation specific tothis industry, has been positive for all the companies except Ghom.

Renovation and modernization for achieving higher efficiencylevels needs to be pursued vigorously and all existing generationcapacity should be brought to acceptable performance standards. Incase of persistent poor efficiencies of companies, it is suggested thatalternate strategies including change of management may beconsidered.

This study revealed the conditions of Iran’s PEGM companies.The outcomes of investigation are beneficial for improving theefficiency, productivity and related policies for these companies. Itis tried to use maximum available data to enhance the validity ofthe model. However; there were some restrictions such as acces-sibility to cost information. Additional factors in such companiescould be pursued as a part of future works to offer a more insightfulsensitivity analysis.

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