lable at ScienceDirect

Journal of Cleaner Production 108 (2015) 232e246

Contents lists avai

Journal of Cleaner Production

journal homepage: www.elsevier .com/locate/ jc lepro

New network data envelopment analysis approaches: an applicationin measuring sustainable operation of combined cycle power plants

Gholam Reza Faramarzi a, Mohsen Khodakarami a, Amir Shabani b,Reza Farzipoor Saen c, *, Fatemeh Azad a

a Young Researchers and Elites Club, Karaj Branch, Islamic Azad University, Karaj, Alborz, Iranb Young Researchers and Elites Club, Science and Research Branch, Islamic Azad University, Tehran, Iranc Department of Industrial Management, Faculty of Management and Accounting, Karaj Branch, Islamic Azad University, P. O. Box: 31485-313, Karaj, Iran

a r t i c l e i n f o

Article history:Received 17 July 2014Received in revised form12 April 2015Accepted 14 June 2015Available online 22 June 2015

Keywords:SustainabilityNetwork data envelopment analysisMultiple objective linear programmingReturns to scaleCombined cycle power plants

* Corresponding author. Tel.: þ98 (26) 34418144 6E-mail addresses: grfaramarzi@yahoo.com (G.R.

chmail.ir (M. Khodakarami), shabani_dp@yahoo.coyahoo.com (R. Farzipoor Saen), azad.fatemeh@chmail

http://dx.doi.org/10.1016/j.jclepro.2015.06.0650959-6526/© 2015 Elsevier Ltd. All rights reserved.

a b s t r a c t

Nowadays, organizations deal with numerous economic, environmental, and social problems. To havesustainable operations, they have begun to incorporate environmental and social concerns into con-ventional economic objectives. A combined cycle power plant (CCPP) is a good instance of an opensystem with multistage processes and interconnected activities. Efficiency evaluation of CCPPs is acomplex task since there exist a variety of inputs (outputs) which enter into any stages of network.Additionally, there might be intermediate products which are consumed by the same power plants. Wecall such factors “loop” intermediate measures. To measure efficiency of CCPPs, network data envelop-ment analysis (NDEA) is used. This paper proposes new NDEA models to evaluate efficiency of CCPPs. Theproposed models calculate the efficiency of power plants and their sub-sectors under both CRS (constantreturns to scale) and VRS (variable returns to scale) assumptions. This paper provides a comprehensiveanalysis for returns to scale. We apply the new NDEA models to measure relative efficiency of CCPPs.

© 2015 Elsevier Ltd. All rights reserved.

1. Introduction

Organizations as open systems interact with their environment.Nowadays, organizations deal with numerous economic, environ-mental, and social problems. To be sustainable, they have begun toincorporate environmental and social concerns into conventionaleconomic objectives. Balancing economic, environmental, and so-cial operations to realize sustainable development is a majorobjective of many responsible organizations (Shabani et al., 2014;Jabbour and Jabbour, 2009). However, sustainability evaluation ofthe open system is a complex task, and many approaches formeasuring sustainability cannot deal with this multidimensionalperspective (Gerdessen and Pascucci, 2013).

A combined cycle power plant (CCPP) is a good instance of anopen system with multistage processes and interconnected activ-ities. The process of generating electric power includes differentactivities such as generation, transmission, distribution, and

; fax: þ98 (26) 34418156.Faramarzi), m.khodakarami@m (A. Shabani), farzipour@.ir (F. Azad).

retailing, which consumes large amounts of capital, labor, andfinancial resources (Vaninsky, 2006). Among these activities, thegeneration of electric power is at core of the production process.According to Yuzhi and Zhangna (2012), one of the features ofelectric power is that it is non-storable. Therefore, its production,transportation, sales, and consumption are done concurrently(Farzipoor Saen, 2010). Perishable nature of non-storable com-modities forces decision makers to be efficient to prevent losses(Tavassoli et al., 2015). From another point of view, power plants areone of the major users of fossil fuels in the world and their envi-ronmental impact such as pollution and global warming are sig-nificant. In the meantime, power plants influence societies.

Farrell (1957) proposed a method to evaluate technical effi-ciency of decision making units (DMUs), and determined an effi-cient frontier to measure efficiency of each DMU. The classical dataenvelopment analysis (DEA) model deals with multiple inputs andsingle output. Based on Farrell (1957), CCR (Charnes, Cooper, andRhodes) was developed to measure efficiency of DMUs with mul-tiple inputs and multiple outputs (Charnes et al., 1978). Theirapproach is called DEA. Subsequently, BCC (Banker, Charnes, andCooper) model was extended under VRS (variable returns to scale)assumption by Banker et al. (1984).

G.R. Faramarzi et al. / Journal of Cleaner Production 108 (2015) 232e246 233

In conventional applications of DEA, a DMU is generally treatedas a “black box” in which internal processes are not examined(Farzipoor Saen, 2009). In the conventional applications of DEA,initial inputs and final outputs are considered and productionsystem is assumed as awhole unit. However, in some situations, theDMU may have network structure. To overcome this shortcoming,F€are and Grosskopf (1996) were the first researchers who proposednetwork data envelopment analysis (NDEA) approach. To evaluateefficiency of DMUs with network structure, the NDEAmodel can beused. Therefore, the NDEA is a proper approach to evaluate effi-ciency of electric power plants. It deals with efficiency of divisionsas well as overall efficiency in a unified framework (Tone andTsutsui, 2009).

Most of previous studies on NDEA (e.g., Kao and Hwang, 2008;Liang et al., 2008; Chen et al., 2009) focus on pure serial processesin which the outputs of a stage are totally passed on to the nextstage as inputs. In other word, neither input nor output enter orleave the network at intermediate stages, while in most of real lifecases, there may be outputs from a given stage that leavenetwork. Also, there might be external inputs that enter in anystage of the network. Some studies have been done to rectify thisshortcoming (e.g., Tone and Tsutsui, 2009; Cook et al., 2010; Kao,2014; Lozano, 2015). As Chen et al. (2013) addressed, the problemwith the multiplier-based divisional efficiency under VRS is that itcannot be solved as a linear program. Cook et al. (2010) evaluatedthe efficiency of multistage processes with different types of in-puts and outputs through a multiplier-based NDEA model. Theydefined open multistage process in which each stage has its owninputs and two types of outputs. One type of output is as an inputto the next stage, and another type of output leaves the stage.However, their model works under constant return to scale (CRS)assumption. Furthermore, in multistage processes, there existintermediate measures that are consumed by the same network.We call such a factor as “loop” intermediate measure. For CCPPs inelectric power companies, for example, two gas power plants arearranged in parallel process whose generated electricity istransmitted to the network. Exhausted hot gas from two gasturbines is used to generate steam by passing it through heatrecovery steam generators (HRSGs). The generated steam byHRSGs is jointly used to feed a steam turbine. In CCPPs, thegenerated electricity by gas or steam “re-enter” as an input fordriving pumps, fans, and other equipment. Applying the NDEAmodels to determine performance of multistage processes we canreceive further insights from the obtained results and accordinglywe can make appropriate policy for performance improvement(Yu and Lin, 2008). In other words, employing the NDEA modelsdetermines not only inefficient DMUs, but also shows whichinefficient stage of the network causes the inefficiency. As aresult, to fill this research gap, and also to obtain returns to scaleanalysis of every stage of the network, this study proposes a newmodel based on multiplier divisional efficiency under VRSassumption.

Due to conflict objectives, decision making in manufacturing orservice organizations may become very complex and uncertain(Wong et al., 2009; Azadi et al., 2015). To deal with such multiplecriteria decision making (MCDM) problems, multi-objective pro-gramming methods including multiple objective linear program-ming (MOLP) models are introduced. Accordingly, this paperproposes new NDEA models based on MOLP concept to considernew inputs (outputs) which enter into (depart from) any stage ofthe network. This paper, first applies MOLP to propose a new linearNDEA model under CRS (constant returns to scale) assumption.Then, using this linear model, a new NDEA model under VRS(variable returns to scale) assumption is developed to measure theefficiency of both CCPPs and their sub-sectors. Furthermore, a

comprehensive analysis for returns to scale of every stage can beachieved by this model. The present study has several distinctiveinnovations in the fields of Operations Research and sustainabledevelopment. The main contributions of this paper are as follows:

� Employing MOLP concept, a new linear NDEA model under CRSassumption is proposed to measure the efficiency of both CCPPsand their sub-sectors.

� Using this new linear model and based on multiplier divisionalefficiency, a new NDEA model under VRS (variable returns toscale) assumption is developed.

� The proposed models are easy to implement and do not requirecomplex and time consuming calculations.

� In our proposed models, weights of stages are unknown andtheir optimal values are determined.

� This paper provides a comprehensive analysis on returns toscale. Utilizing this analysis, one can set more reasonablebenchmarks to help an inefficient DMU to become efficient.

� An extensive literature review of the most recent works onestimation of efficiency and sustainability of power plants isgiven.

� Applicability of proposed models is demonstrated through acase study. This paper for the first time estimates efficiency ofnetwork-structured power plants.

This paper is unfolded as follows. In Section 2 literature reviewis presented, and new NDEA models are developed in Section 3. Acase study is presented in Section 4. Concluding remarks are dis-cussed in Section 5.

2. Literature review

2.1. Employed techniques toward sustainability

World Commission on Environment and Development (WCED)defines sustainability as “development that meets the needs ofthe present without compromising the ability of future generationsto meet their own needs”. According to the United Nations defini-tion, themain components of sustainability are social development,economic development, and environmental protection, which are“three interdependent and mutually reinforcing pillars”.

Different methods have been employed to assess sustainability.Examples include analytic hierarchy process (AHP) (Chatzimouratidis and Pilavachi, 2009), fuzzy TOPSIS (Kannan et al.,2014), fuzzy AHP (Tasri and Susilawati, 2014; Deng et al., 2014).The problem with the aforementioned methods is that weights ofcriteria are often allocated in a subjective manner. This is a verychallenging task for decision makers as the numbers of criteria areincreased. DEA is a useful tool for allocating the weights to criteriaobjectively. A number of recent contributions of the DEA techniquein measuring sustainability can be seen in Lee and Farzipoor Saen(2012), Zhu et al. (2014), and Khodakarami et al. (2014).

To recognize variables of efficiency and sustainability evaluationof power plants, here we review recent papers from 2010 to 2014.The outcome of the review is displayed in Table 1. As is seen, allinputs, outputs, and intermediate variables are categorized underthe three dimensions of sustainability, including economic, envi-ronmental, and social pillars. Furthermore, for variables whichoverlap with each other, we classify them under the most commonused term.

2.2. NDEA approach

The CCR model works under CRS assumption. Under CRSassumption an increase in inputs of a DMU causes the same

Table 1Factors for sustainable operations assessment.

References

Variables (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) Category

Economic Environmental Social

1 e Allocated budget ✓ ✓ ✓ ✓

2 e Auditing & reviewing ✓ ✓ ✓ ✓

3 e Capacity usage ratio ✓ ✓ ✓

4 e Consumption, electricity (Wh) ✓ ✓ ✓ ✓ ✓ ✓ ✓

5 e Consumption, fuel (J or Liter or Ton) ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓

6 e Consumption, heating value of total fuels (Calories) ✓ ✓ ✓ ✓

7 e Consumption, total energy ✓ ✓ ✓ ✓

8 e Cost of generated power ($/Wh) ✓ ✓

9 e Cost, fuel ✓ ✓ ✓

10 e Cost, investment or capital ✓ ✓ ✓ ✓ ✓

11 e Cost, maintenance ✓ ✓ ✓ ✓ ✓

12 e Cost, operational ✓ ✓ ✓ ✓ ✓ ✓ ✓

13 e Cost, unit or total ✓ ✓ ✓ ✓ ✓ ✓

14 e Emission, CH4 ✓ ✓ ✓ ✓

15 e Emission, CO2 & CO ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓

16 e Emission, N2O ✓ ✓ ✓ ✓

17 e Emission, NMVOC & Dust ✓ ✓ ✓

18 e Emission, NOx ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓

19 e Emission, SO2 ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓

20 e Employees, Operational & Nonoperational ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓

21 e Employees, Potential Job Creation (job/Wh) ✓ ✓

22 e Evaluation and risk management ✓ ✓ ✓ ✓

23 e GDP supported by power ✓ ✓

24 e Generation, Gross (W h) ✓ ✓ ✓ ✓ ✓

25 e Generation, Net (Wh) ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓

26 e Generation, Capacity (W) ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓

27 e Implementation & Monitoring ✓ ✓ ✓ ✓

28 e Leadership & Commitment ✓ ✓

29 e Number of units ✓ ✓

30 e Operational time ✓ ✓

31 e Organization, resources, documentation ✓ ✓ ✓ ✓

32 e Planning ✓ ✓ ✓ ✓

33 e Policy and strategic objective ✓ ✓ ✓ ✓

34 e Thermal efficiency ✓ ✓

35 e Total revenuexðtÞij ✓ ✓

36 e Training (man-hours or $) ✓ ✓ ✓

Year of publication 2010 2011 2012 2013 2014

(1) S€ozen et al. (2010); (2) Liu et al. (2010); (3) Farzipoor Saen (2010); (4) Sueyoshi and Goto (2011); (5) Azadeh et al. (2012); (6) S€ozen et al. (2012); (7) Lins et al. (2012); (8) Rezaee et al. (2012); (9) Sueyoshi and Goto (2012a);(10) Sueyoshi and Goto (2012b); (11) Sueyoshi and Goto (2012c); (12) Sueyoshi and Goto (2012d); (13) Sueyoshi and Goto (2012e); (14) Liu andWen (2012); (15) Sueyoshi and Goto (2013); (16) Sueyoshi et al. (2013); (17)Wanget al. (2013); (18) Zhou et al. (2013); (19) Shakouri et al. (2014).

G.R.Faram

arziet

al./Journal

ofCleaner

Production108

(2015)232

e246

234

G.R. Faramarzi et al. / Journal of Cleaner Production 108 (2015) 232e246 235

proportionate increase in outputs. The BCC model was extendedunder VRS assumption. Under VRS assumption, an increase in in-puts does not usually cause a proportional change in outputs. UnderVRS assumption there are three statuses including increasing,decreasing, and constant returns to scale. Traditional DEA tech-niques consider a DMU as a “black-box”. Traditional models takeinto account initial inputs and final outputs of a DMU. This is notacceptable from managerial perspective because internal in-teractions of DMUs are disregarded by the traditional models. Toovercome this shortcoming, a new approach is proposed thatconsiders the DMUs as networks. In this new look, internal in-teractions of a DMU are considered in performance evaluation. Anumber of studies have focused on DMUs that have two-stages.Chiou and Chen (2006) and Karlaftis (2004) developed two con-ventional DEA models to measure efficiency of first and secondstages, separately. Such models that separately evaluate efficiencyof each stage are suffering from a significant drawback. Improve-ment solutions are usually inconsistent in intermediate measures.In other words, assume a situation in which a given intermediateoutput/input of the first stage is decreased to improve the effi-ciency, and at the same time the intermediate output/input isincreased to get a better efficiency score for the second stage.Assuming constant intermediate outputs/inputs, Keh et al. (2006)estimated efficiency of the first stage by input-oriented DEAmodels and the efficiency of the second stage by output-orientedDEA models. Although this kind of approach does not lead toconflicting improvement strategies, the DMU is supposed to bedivided into two autonomous departments. It means performanceof one department is completely unrelated to another department.Apparently, from organizational point of view, this is called into thequestion.

Tone and Tsutsui (2009) combined the two-step procedure ofKeh et al. (2006) in a single model in which the intermediatemeasures are kept unchanged. The structure of the model is called“fixed link”. A fixed link approach does not deal with links amongstages. In this case all the intermediate products are considered asnon-discretionary factors that are out of management's control,whereas there is no reason to consider all intermediate measures asnon-discretionary factors.

Novel approaches have been developed to model the interme-diate measures (Kao and Hwang, 2008; Liang et al., 2008; Chenet al., 2009). These approaches consider the intermediate mea-sures as discretionary factors since the linking activities are freelydetermined. In such cases there are “free links”. Although the two-stage approaches of Kao and Hwang (2008), Liang et al. (2008), andChen et al. (2009) can be extended for multistage networks, thenetwork should be a closed-system. In other words, only the firststage has its independent inputs and only the last stage has finaloutputs. However, in real world, there might be new inputs (out-puts) that enter (leave) any stage.

Tone and Tsutsui (2009) proposed a slacks-based NDEA modelentitled network SBM. Using their model one can evaluate stageefficiencies along with overall efficiency of networks. Their

Fig. 1. A multi-sta

proposed model can be utilized to deal with open systems inwhich some outputs from a given stage may leave the networkand new inputs that enter at any stage of network. Despite, theoverall efficiency is expressed as a weighted average of compo-nents (stages) efficiencies, where weights are exogenouslyimposed to reflect importance of components. Cook et al. (2010)examined a general problem of an open multistage network.They calculated radial measure of efficiency that can be decom-posed into a convex combination of radial measures for individualcomponents. In their case the weights are variables. However,their NDEA method cannot evaluate efficiency of open-systemswith loop intermediate measures. The loop intermediate mea-sures are factors consumed by the same DMU which has gener-ated them. Moreover, the model proposed by Cook et al. (2010) isin CRS context.

Chen et al. (2013) addressed that the performance evaluation ofthe network can be discussed with respect to the determination ofdivisional efficiency, frontier type, and projections. They concludedthat current envelopment models are not able to calculate divi-sional efficiencies and hence it is important to develop newmultiplier-based divisional efficiency model under VRS. Multipliermodel proposed by Cook et al. (2010) can measure divisional effi-ciency scores. Nonetheless, it works under CRS assumption. Kaoet al. (2014) employed a fuzzy approach based on CRS and VRSassumptions which had several steps that may cause longcomputational processes. Lozano (2015) proposed a slacks-basedmeasure (SBM) model to consider the exogenous inputs and out-puts at system level instead of process level. To improve discrimi-nation power of the model, the paper relaxes the constraints forboth the fixed-link and the free-link cases. This paper develops newmultiplier-based divisional efficiency approaches which work un-der both CRS and VRS assumptions. Furthermore, the new NDEAmodels are able to overcome the challenges of loop intermediatemeasures. Also, interpretation of returns to scale in networkcontext is discussed.

3. New NDEA models

3.1. NDEA model under CRS assumption

In this subsection, we introduce a new NDEA model to evaluaterelative efficiency of DMUs with network structures. Fig. 1 is atypical network. This figure shows three successive stages as “tO, t,and tI”which represent internal divisions of a DMU. For instance, letus describe stage t. As is seen, the inputs of the stage t are xðtÞij andzðtO/tÞsj , respectively. zðtO/tÞ

sj is an intermediate vector which leavesthe stage tO and is passed on as an input to stage t. xðtÞij is an externalinput which enters stage t. Also, the output of the stage t is yðtÞrjwhich leaves the process. There are also two intermediate vectorsnamely zðt/tIÞ

sj and zðt/tÞsj . zðt/tIÞ

sj is an intermediate vector whichleaves the stage t and is passed on as an input to stage tI. z

ðt/tÞsj is the

other intermediate vector which leaves the stage t but re-enters asan input to the same stage (t).

ge network.

G.R. Faramarzi et al. / Journal of Cleaner Production 108 (2015) 232e246236

Assume that we have J DMUs (networks) (j ¼ 1,…,J) each con-structed from t (t ¼ 1,…,T) stages. Each stage consumes I(t) inputs(i ¼ 1,…,I(t)) to produce R(t) outputs (r ¼ 1,…,R(t)). There are also S(t)

intermediate output/inputs (s ¼ 1,…,S(t)) for the tth stage that canbe produced by the same or another stage and consumed by the

same or another stage. Moreover, xðtÞij and yðtÞrj denote the ith input of

tth stage of jth DMU and rth output of tth stage of jth DMU,

respectively. Here, zðtI/tOÞsj and zðt/tÞ

sj represent two types of inter-

mediate measures: sth intermediate (output/input) from tth stage

EOverallCRS

j ¼

PTt¼1

PSðtÞs¼1 w

ðt/tIÞs zðt/tIÞ

sj þPSðtÞs¼1 w

ðt/tÞs zðt/tÞ

sj þPRðtÞr¼1 u

ðtÞr yðtÞrj

!

PTt¼1

PIðtÞi¼1 v

ðtÞi xðtÞij þPSðtÞ

s¼1 wðtO/tÞs zðtO/tÞ

sj þPSðtÞs¼1 w

ðt/tÞs zðt/tÞ

sj

! (2)

to the same stage of jth DMU, and sth intermediate (output/input)from tIth stage to tOth stage of jth DMU.

According to Cook et al. (2010) and Kao et al. (2014), the effi-ciency of tth stage of jth DMU is defined as follows:

EðtÞCRS

j ¼

PSðtÞs¼1w

ðt/tIÞs zðt/tIÞ

sj þPSðtÞs¼1w

ðt/tÞs zðt/tÞ

sj þPRðtÞr¼1u

ðtÞr yðtÞrj

! PIðtÞ

i¼1vðtÞi xðtÞij þPSðtÞ

s¼1wðtO/tÞs zðtO/tÞ

sj þPSðtÞs¼1w

ðt/tÞs zðt/tÞ

sj

!

(1)

Expression (1) is the ratio of weighted sum of outputs toweighted sum of inputs of tth stage of jth DMU. In Expression (1),the v

ðtÞi ;uðtÞr ;wðt/tIÞ

s ;wðtO/tÞs , and wðt/tÞ

s represent the weights of ithinput, rth output, sth intermediate (output/input) from stage t to

8>>>><>>>>:Max

0BBBB@

PSðtÞs¼1 w

ðt/tIÞs zðt/tIÞ

sk þXSðtÞs¼1

wðt/tÞs zðt/tÞ

sk þXRðtÞ

r¼1

uðtÞr yðtÞrk

! PIðtÞ

i¼1 vðtÞi xðtÞik þ

XSðtÞs¼1

wðtO/tÞs zðtO/tÞ

sk þXSðtÞs¼1

wðt/tÞs zðt/tÞ

sk

!1CCCCA ct

s:t:0BBBB@

PSðtÞs¼1 w

ðt/tIÞs zðt/tIÞ

sj þXSðtÞs¼1

wðt/tÞs zðt/tÞ

sj þXRðtÞ

r¼1

uðtÞr yðtÞrj

! PIðtÞ

i¼1 vðtÞi xðtÞij þ

XSðtÞs¼1

wðtO/tÞs zðtO/tÞ

sj þXSðtÞs¼1

wðt/tÞs zðt/tÞ

sj

!1CCCCA � 1; ct; j:

vðtÞi ; uðtÞr ; wðt/tÞ

s ;wðtO/tÞs ;wðt/tIÞ

s � ε; ci; r; s; t:

(3)

stage tI, sth intermediate (output/input) from stage tO to stage t andsth (loop) intermediate (output/input), respectively.

There are two approaches for measuring the overall efficiencyscore of a DMU. In the first approach, the overall efficiencyequals the ratio of weighted sum of outputs plus weighted

intermediate measures to weighted sum of inputs plus weightedintermediate measures (Cook et al., 2010). In the secondapproach, the overall efficiency equals the weighted sum of allstages' efficiencies. In this approach, the weight of any stage isdetermined by the decision maker and the summation of allstages' weight equals 1 (Kao et al., 2014). In fact, in the firstapproach there is no need to decision maker's subjectiveweights. Due to this fact, we employ the first approach tomeasure the overall efficiency score of DMUs. Thus, for the jthDMU we have:

Kao et al. (2014) proposed a multi-objective programmingmodel to calculate the divisional efficiencies (within an orga-nization) and the overall efficiency of the organization. It isobvious that in situations where the stages of DMUs have thesame importance and priority, if we try to maximize the effi-ciency of all divisions (stages), then the overall efficiency ismaximized. This statement originates from the fact that overallefficiency of DMUs depends on efficiency of its stages. Thisimplies that inputs and outputs of DMUs are summation ofcorresponding inputs and outputs of their stages. The DMU isefficient if and only if all stages are efficient. Thus, it can beconcluded that DMU's performance depends on stages' per-formance. The initial proposed model of Kao et al. (2014) forthe kth DMU (the DMU under evaluation) can be written asfollows:

where ε is a positive, non-Archimedean infinitesimal. Thereason of using ε is to prevent the stages' efficiency scores tobecome zero. Note that there are J DMUs (networks) (j ¼ 1,…,J).The stage efficiency is a value between (0, 1], and this is defined

G.R. Faramarzi et al. / Journal of Cleaner Production 108 (2015) 232e246 237

for the Model (3) by making the Expression (1) less than orequal to one for each stage. The objective function of the Model(3) can be transformed into the Expression (4). The Expression(4) is same as the objective function of the Model (3).

8>>>><>>>>:

Max

PRðtÞ

r¼1uðtÞr yðtÞrk

!ct

Min

PIðtÞi¼1

vðtÞi xðtÞik

!ct

8>>>><>>>>:

Max

PSðtÞs¼1

wðt/tÞs zðt/tÞ

sk

!ct

Min

PSðtÞs¼1

wðt/tÞs zðt/tÞ

sk

!ct

8>>>><>>>>:

Max

PSðtÞs¼1

wðt/tIÞs zðt/tIÞ

sk

!ct

MinPSðtÞs¼1

wðtO/tÞs zðtO/tÞ

sk ct

(4)

As Amirteimoori and Kordrostami (2012) and Du et al.(2010) addressed, the Expression (4) can be transformed asfollows:

8>>><>>>:

MaxPTt¼1

PRðtÞ

r¼1uðtÞr yðtÞrk

MinPTt¼1

PIðtÞi¼1

vðtÞi xðtÞik

8>>><>>>:

MaxPTt¼1

PSðtÞs¼1

wðt/tÞs zðt/tÞ

sk

MinPTt¼1

PSðtÞs¼1

wðt/tÞs zðt/tÞ

sk

8>>><>>>:

MaxPTt¼1

PSðtÞs¼1

wðt/tIÞs zðt/tIÞ

sk

MinPTt¼1

PSðtÞs¼1

wðtO/tÞs zðtO/tÞ

sk

(5)

It is obvious that in the network the intermediate (output/input)measures flow from one stage to next stage. Hence we have:

XTt¼1

XSðtÞs¼1

wðt/tIÞs zðt/tIÞ

sk ¼XTt¼1

XSðtÞs¼1

wðtO/tÞs zðtO/tÞ

sk (6)

To prevent elimination of the effect of intermediate (output/input) measures, wemake them equal to 1, and incorporate into themodel as a constraint. Thus, we have8>>>><>>>>:

MaxPTt¼1

PRðtÞ

r¼1uðtÞr yðtÞrk

MinPTt¼1

PIðtÞi¼1

vðtÞi xðtÞik

s:t:XTt¼1

XSðtÞs¼1

wðtO/tÞs zðtO/tÞ

sk

þXTt¼1

XSðtÞs¼1

wðt/tÞs zðt/tÞ

sk ¼ 1

(7)

Similar to the above-mentioned transformation, the integrationof Expression (7) and linear form of the Model (3) can be written asModel (8). Note that the objective function of the Model (8) followsthe same purpose of the Expression (5).

MaxPTt¼1

PRðtÞ

r¼1uðtÞr yðtÞrk �

XTt¼1

XIðtÞi¼1

vðtÞi xðtÞik

s:t:PTt¼1

PSðtÞs¼1

wðtO/tÞs zðtO/tÞ

sk þXTt¼1

XSðtÞs¼1

wðt/tÞs zðt/tÞ

sk ¼ 1;

PSðtÞs¼1

wðt/tIÞs zðt/tIÞ

sj þXRðtÞ

r¼1

uðtÞr yðtÞrj �XIðtÞi¼1

vðtÞi xðtÞij þ

XSðtÞs¼1

wðtO/tÞs zðtO/tÞ

sj ; c

vðtÞi ;uðtÞr ;wðt/tÞ

s ;wðtO/tÞs ;wðt/tIÞ

s � ε; ci; r; s; t:

After running the Model (8) and getting optimal weights ofvðtÞ*i ; uðtÞ*r ; wðt/tÞ*

s ;wðtO/tÞ*s , and wðt/tIÞ*

s , we can calculatecomponent efficiencies through Eq. (1). To compute overall effi-ciencies of the Model (8), we may also use Eq. (2).

Definition 1. Under CRS condition, the efficiency score for stage t is avalue between (0, 1]. Stage t is said to be efficient, if and only ifEðtÞ

CRS*

j ¼1. Otherwise, it is an inefficient stage.

Definition 2. Under CRS condition, the efficiency score for DMUj is avalue between (0, 1]. DMUj is said to be overall efficient, if and only if

EOverallCRS*

j ¼ 1, i.e. all stages of DMUj become efficient. It means that

EðtÞCRS*

j ¼1 (t ¼ 1,2,…,T). Otherwise, DMUj is an inefficient DMU.

The NDEAModel (8) measures relative efficiency of DMUs underCRS assumption. However, this may be true only over some ranges,in which case one might say that the production function hasconstant returns over that range. Therefore, to estimate other be-haviors of the production function, in following subsection weextend the Model (8) under VRS condition.

3.2. Variable returns to scale (VRS) assumption

In previous subsection, the CRS NDEA model measured effi-ciency of DMU and its components (stages). However, it did notprovide information on whether DMU's scale of operation isoptimal or not. It is important for decision makers to have a clearimage on their production processes and estimate which scale ofoperation is useful for their network. Therefore, in this subsection, anew model is presented to measure the network performance

t; j;

(8)

G.R. Faramarzi et al. / Journal of Cleaner Production 108 (2015) 232e246238

under VRS assumption. To this end, we first obtain dual formulation(envelopment form) of the Model (8) as follows:

Min q

s:t:PJj¼1

lðtÞj xðtÞij � xðtÞik ; t ¼ 1;…; T ; i ¼ 1;…; I

PJj¼1

lðtÞj yðtÞrj � yðtÞrk ; t ¼ 1;…; T ; r ¼ 1;…;R

PJj¼1

�lðtIÞj � l

ðtÞj

�zðt/tIÞsj � qzðt/tIÞ

sk ; t ¼ 1;…; T; s ¼ 1;…; S

qzðt/tÞsk � 0; t ¼ 1;…; T ; s ¼ 1;…; S

lðtÞj � 0; cj; t

(9)

where lðtÞj is intensity of DMU loadings for the DMU under evalu-

ation, and q is a dual variable related to constraint of the Model (8).

To considerVRSassumption, the convexity constraint ðPJj¼1l

ðtÞj ¼

1; ctÞ should be added into the Model (9). Thus, following envel-opment form of the NDEA model is obtained under VRS condition:

MaxPTt¼1

PRðtÞ

r¼1uðtÞr yðtÞrk �

XIðtÞi¼1

vðtÞi xðtÞik þ qðtÞ

!;

s:t:PTt¼1

PSðtÞs¼1

wðtO/tÞs zðtO/tÞ

sk þXTt¼1

XSðtÞs¼1

wðt/tÞs zðt/tÞ

sk ¼ 1;

PSðtÞs¼1

wðt/tIÞs zðt/tIÞ

sj þXRðtÞ

r¼1

uðtÞr yðtÞrj

!þ qðtÞ �

XIðtÞi¼1

vðtÞi xðtÞij þ

XSðtÞs¼1

wðtO/tÞs

vðtÞi ; uðtÞr ; wðt/tÞ

s ;wðtO/tÞs ;wðt/tIÞ

s � ε; c i; r; s; t

EOverallVRS

j ¼

PTt¼1

PSðtÞs¼1 w

ðt/tIÞ*s zðt/tIÞ

sj þPSðtÞs¼1 w

ðt/tÞ*s zðt/tÞ

sj þPRðtr¼

PTt¼1

PIðtÞi¼1 v

ðtÞ*i xðtÞij þPSðtÞ

s¼1 wðtO/tÞ*s zðtO/tÞ

sj þPSðtÞs¼1 w

EðtÞVRS

j ¼

PSðtÞs¼1 w

ðt/tIÞ*s zðt/tIÞ

sj þPSðtÞs¼1 w

ðt/tÞ*s zðt/tÞ

sj þPRðtÞr¼1 u

ðtÞ*r yðtÞrj PIðtÞ

i¼1 vðtÞ*i xðtÞij þPSðtÞ

s¼1 wðtO/tÞ*s zðtO/tÞ

sj þPSðtÞs¼1 w

ðt/tÞ*s zðtsj

Min q

s:t:PJj¼1

lðtÞj xðtÞij � xðtÞik ; t ¼ 1;…; T ; i ¼ 1;…; I

PJj¼1

lðtÞj yðtÞrj � yðtÞrk ; t ¼ 1;…; T; r ¼ 1;…;R

PJj¼1

�lðtIÞj � l

ðtÞj

�zðt/tIÞsj � qzðt/tIÞ

sk ; t ¼ 1;…; T ; s ¼ 1;…; S

qzðt/tÞsk � 0; t ¼ 1;…; T ; s ¼ 1;…; SPJ

j¼1lðtÞj ¼ 1; t ¼ 1;…; T

lðtÞj � 0; cj; t:

(10)

The convexity constraint ensures that the region specified by aset of points (DMUs) forms a convex set. It means that each com-posite DMU is a convex combination of reference DMUs. The dual ofModel (10) is a novel linear programming model which is as fol-lows:

zðtO/tÞsj

!; t ¼ 1;…; T ; j ¼ 1;…; J

(11)

where qðtÞ is an unrestricted in sign variable which indicatesthe status of returns to scale for tth stage of DMUk. Let anoptimal solution of the Model (11) to be(vðtÞ*i ; uðtÞ*r ; wðt/tÞ*

s ;wðtO/tÞ*s ;wðt/tIÞ*

s ). Hence, to measure effi-ciency of tth stage of jth DMU, we can use Eq. (12). Also, Eq.(13) computes the overall efficiency of jth DMU. These twomeasures have to be positive values; therefore, this conditionshould be considered in the Model (11)

Þ1 u

ðtÞ*r yðtÞrj þ qðtÞ

!

ðt/tÞ*s zðt/tÞ

sj

! ; j ¼ 1;…; J (13)

þ qðtÞ!

/tÞ! ; t ¼ 1;…T ; (12)

Table 2Results of the proposed Models (8) and (11).

DMU Model (11)-BCC Model (8)-CCR

Division 1 Division 2 Division 3 Overall efficiency Division 1 Division 2 Division 3 Overall efficiency

A 0.501 0.644 0.977 0.730 0.410 0.688 0.972 0.570B 0.043 0.820 1.000 0.504 0.211 0.339 1.000 0.383C 1.000 1.000 0.998 1.000 1.000 1.000 0.999 1.000D 0.254 1.000 1.000 0.935 0.225 0.705 1.000 0.828E 0.049 1.000 0.959 0.751 0.167 0.501 0.955 0.478F 0.686 0.668 0.985 0.718 0.470 0.656 0.984 0.598G 4.62E-06 1.000 0.985 0.878 0.551 0.717 0.983 0.762H 0.454 0.922 1.000 0.819 0.711 0.697 0.585 0.705I 0.224 1.000 0.992 0.997 0.245 1.000 0.990 0.995J 0.202 0.704 1.000 0.534 0.249 0.644 0.997 0.408

Table 3Results of Kao et al. (2014) model (fixed link).

DMU BCC CCR

Division 1 Division 2 Division 3 Overall efficiency Division 1 Division 2 Division 3 Overall efficiency

A 0.448 0.538 0.691 0.563 0.410 0.445 0.620 0.501B 0.177 0.650 0.678 0.472 0.211 0.348 0.579 0.386C 0.840 0.840 0.840 0.840 0.718 0.718 0.717 0.718D 0.254 1.000 1.000 0.702 0.225 0.942 0.942 0.655E 0.202 1.000 0.959 0.664 0.167 0.549 0.524 0.386F 0.541 0.687 0.593 0.591 0.470 0.452 0.678 0.550G 0.627 0.881 0.914 0.793 0.480 0.753 0.857 0.686H 0.733 0.859 0.932 0.838 0.469 0.385 0.544 0.482I 0.470 0.555 0.984 0.693 0.245 1.000 0.990 0.694J 0.225 0.733 0.857 0.579 0.249 0.418 0.579 0.415

Table 4Spearman's rho correlation coefficients.

Kao et al. (2014)

BCC division 1 BCC division 2 BCC division 3 BCC overall efficiency CCR division 1 CCR division 2 CCR division 3 CCR overall efficiency

Proposedmodels

BCC Division 1 0.552BCC Division 2 0.629BCC Division 3 0.113BCC overallefficiency

0.842b

CCR Division 1 0.964b

CCR Division 2 0.729a

CCR Division 3 0.460CCR overallefficiency

0.930b

a Correlation coefficient is significant at 0.05 level (2-tailed).b Correlation coefficient is significant at 0.01 level (2-tailed).

G.R. Faramarzi et al. / Journal of Cleaner Production 108 (2015) 232e246 239

Definition 3. Under VRS condition, the efficiency score for stage t is avalue between (0, 1]. Stage t is said to be efficient, if and only if

EðtÞVRS*

j ¼ 1. Otherwise, it is an inefficient stage.

Definition 4. Under VRS condition, the efficiency score for DMUj is avalue between (0, 1]. DMUj is said to be overall efficient, if and only ifEOverall

VRS*

j ¼ 1, i.e. all stages of DMUj become efficient. It means that

EðtÞVRS*

j ¼ 1 (t ¼ 1,2,…,T). Otherwise, DMUj is an inefficient unit.

The Model (11) estimates status of returns to scale for both theDMU and its stages. In the Model (11),

PTt¼1q

ðtÞ represents returnsto scale of whole network and q(t) represents returns to scale ofstage t. Thus, to know which scale of operation for network is

optimal, one can utilize following triple statuses in which super-script “*” means optimal solution:

Definition 5.

8>>>>>>>><>>>>>>>>:

ifPTt¼1

qðtÞ* <0; then jth DMU is decreasing returns to scale

ifPTt¼1

qðtÞ* ¼ 0; then jth DMU is constant returns to scale

ifPTt¼1

qðtÞ* >0; then jth DMU is increasing returns to scale

G.R. Faramarzi et al. / Journal of Cleaner Production 108 (2015) 232e246240

Similarly, to know which scale of operation for tth stage of jthnetwork is optimal, following triple statuses can be used:

Definition 6.

8>>><>>>:

if qðtÞ* <0; then tth stage of jth DMU is decreasing returns to scale

if qðtÞ* ¼ 0; then tth stage of jth DMU is constant returns to scale

if qðtÞ* >0; then tth stage of jth DMU is increasing returns to scale

Given the results obtained from the Model (11), we can estimatefollowing measures:

a) Returns to scale of each stage embedded in network thatshows which alternative of expansion, contraction, or sta-bility is more useful for the stage.

b) Returns to scale of whole network that shows which alter-native of expansion, contraction, or stability is more usefulfor the network.

c) Technical efficiency of each stage of network under VRScondition, which is useful for finding the closest benchmarksto stage under evaluation.

d) Technical efficiency of whole network under VRS condition,which is useful for finding the closest benchmarks to thenetwork under evaluation.

3.3. Numerical example

Kao et al. (2014) proposed a four-step method for solving MOLPModel (3) and applied their method in two case studies. Here, weuse their first case study. For the sake of brevity, we do not repeattheir data set. Table 2 depicts the results using the Models (8) and(11). Table 3 displays the results of the model proposed by Kao et al.(2014).

Stage1

(Gas power plant)

Fuel Cost

Mean annual air temperature

Hours of operation

Labor Cost

Internal consumption

Total Hours of T

Mean produced s

CO2 emission

Gross generation

Stage 2

(Gas power plant)

Internal consumption

Fuel Cost

Labor Cost

Mean annual air temperature

Hours of operation

Mean produced s

CO2 emission

Gross generation

Total Hours of T

Mean annual air

Hours

Fig. 2. Network of a combi

Table 4 shows Spearman's correlation coefficient between themodel proposed by Kao et al. (2014) and our proposed model.

Table 2 shows that our proposed model can identify efficientDMUs under both CRS and VRS assumptions. However, the modelproposed by Kao et al. (2014) cannot determine efficient DMUs indivision 1 and overall efficiency of fixed-link approach. Table 4shows that there is a significant correlation between the resultsof Kao et al. (2014) and our proposed model.

4. Case study

The concept of sustainability is regularly portrayed by threeoverlapping circles, including social, economic, and environmentaldimensions. The social dimension implies developing human livingstandards. The economic dimension signifies a system of gener-ating, distributing, and consuming wealth to satisfy needs of peo-ple. The environmental dimension represents protecting theecosystem (Herremans and Reid, 2002). Meanwhile, companiesseem to be major players on the societal path toward sustainability.Thus, it is essential to discover practical approaches for sustainabledevelopment inside the companies (Koplin et al., 2007). CCPPs playa significant role in Iran's power industry and sustainable operationof CCPPs is an important topic for policy makers.

According to Iranian government figures, in 2011, CCPPs gener-ated 30.3 percent of total electricity energy. As the world's secondlargest natural gas reserves, Iran is one of the most hydrocarbon-rich areas in the world. Thus, the country has a great potentialityfor operating those kinds of power plants. To demonstrate appli-cability of the proposed CRS and VRS NDEA models a case study ispresented.

In CCPPs, fuel (natural gas or gasoil) is consumed to generateelectricity. In some CCPPs, the exhausted hot gases from two gasturbines are used to generate steam by passing it through theHRSGs. The generated steam is then used to feed a steam turbine.Each gas turbine and each steam turbine have their own inde-pendent electricity generator and the electricity generated by gas or

raining

team

team

raining

Stage 3(Steam power plant)

Internal consumption

temperature

of operation

Labor Cost

Sewage

Gross generation

Total Hours of Training

ned cycle power plant.

Table 6Stage (2) (Second gas power plant).

DMU(power plant)

Inputs Outputs Intermediate outputs/inputs

Fuel cost(1000 USD)

Labor cost(1000 USD)

Hours ofoperation (h)

Mean annual airtemperature (�C)

Grossgeneration(Mwh)

Total hours oftraining (h)

CO2 emission(1000 Ton)

Internalconsumption(Mwh)

Mean producedsteam (kg/s)

Damavand 1 103,906 44 7820 9 863,973 124 779.79 4552 63.78Damavand 2 95,573 47 7770 9 861,979 132 862.38 4050 64.21Damavand 3 95,924 50 7443 9 851,329 110 958.72 3786 63.72Damavand 4 36,877 46 4265 9 436,392 76 918.84 2807 63.4Fars 1 43,835 49 7668 18 659,680 108 1219.35 1888 49.89Fars 2 52,012 54 7246 18 626,240 95 1239.7 1809 49.78Fars 3 59,214 55 8065 18 707,020 129 1237.5 1916 49.92Kazeroon 1 60,527 46 7738 22 762,819 123 564.87 3605 54.33Kazeroon 2 55,809 50 5812 22 715,796 90 539 4197 65.18Kazeroon 3 51,139 45 6115 22 741,817 100 543.21 2573 65.27Kerman 1 95,489 52 7501 16 788,752 107 1471.8 3201 60.61Kerman 2 82,303 51 7267 16 788,704 100 1453.14 3090 60.68Kerman 3 127,615 54 6289 16 723,488 97 1480.05 3859 61.03Kerman 4 105,180 53 7897 16 872,024 108 1407.78 3085 60.49Khoy 112,427 46 7962 10 701,970 122 3733.56 3002 49.14Montazerghaem 1 47,987 43 6988 16 561,070 131 1617 1690 49.68Montazerghaem 2 72,353 46 7218 16 609,270 87 1688.34 1904 49.73Montazerghaem 3 56,825 43 8150 16 667,592 77 1521.33 9832 49.84Neyshabur 1 64,888 47 8495 15 707,505 112 202.46 6524 50.21Neyshabur 2 59,778 49 7313 15 613,829 131 197.6 4922 49.99Neyshabur 3 39,799 45 7202 15 584,783 102 202.28 4464 49.98Qom 1 51,318 41 6835 17 671,369 122 1211.58 4453 52.71Qom 2 83,157 42 7433 17 750,450 115 1217.7 2638 52.46Sanandaj 97,506 47 7179 12 755,704 120 1857.93 3941 62.61Shahid Rajaei 1 49,982 47 6796 13 581,030 72 306.28 3224 48.31Shahid Rajaei 2 83,185 49 7680 13 658,430 133 348.84 4190 48.42Shahid Rajaei 3 85,020 49 7913 13 692,680 100 326.48 4262 97.26Shariati 53,526 40 7497 14 657,802 94 3612.56 1929 52.03Yazd 1 73,287 42 7423 19 680,821 121 745.71 4457 51.15Yazd 2 95,061 49 6791 19 751,210 93 804.27 11,985 63.68

Table 5Stage (1) (First gas power plant).

DMU(Power plant)

Inputs Outputs Intermediate outputs/inputs

Fuel cost(1000 USD)

Labor cost(1000 USD)

Hours ofoperation (h)

Mean annual airtemperature (�C)

Grossgeneration(Mwh)

Total hours oftraining (h)

CO2 emission(1000 Ton)

Internalconsumption(Mwh)

Mean producedsteam (kg/s)

Damavand 1 97,762 47 7583 9 835,882 130 795.08 4191 63.78Damavand 2 95,463 50 7539 9 826,832 83 846.41 2906 64.21Damavand 3 44,903 46 5362 9 575,776 134 873.12 3204 63.72Damavand 4 44,277 48 4342 9 430,424 130 918.84 3082 63.40Fars 1 42,513 52 7264 18 616,960 78 1219.35 1784 49.89Fars 2 38,913 50 6079 18 527,320 97 1172.08 1541 49.78Fars 3 52,373 52 7898 18 692,130 86 1147.5 1924 49.92Kazeroon 1 28,833 47 5534 22 543,624 80 564.87 2782 54.33Kazeroon 2 44,351 46 5988 22 728,244 75 529.2 2917 65.18Kazeroon 3 67,426 51 6870 22 804,669 133 524.15 3483 65.27Kerman 1 132,819 55 7856 16 821,515 88 1418.28 3742 60.61Kerman 2 130,659 53 7501 16 812,816 126 1399.32 3507 60.68Kerman 3 40,256 49 6043 16 650,356 95 1506.96 4262 61.03Kerman 4 59,050 46 6592 16 701,248 88 1329.57 2278 60.49Khoy 94,105 43 7623 10 669,420 117 3802.7 3321 49.14Montazerghaem 1 70,389 49 7913 16 652,826 118 1499.4 3826 49.68Montazerghaem 2 26,565 47 6535 16 531,785 102 1688.34 3246 49.73Montazerghaem 3 78,008 46 8295 16 672,135 90 1670.48 2750 49.84Neyshabur 1 62,065 44 8196 15 712,465 72 206.28 5333 50.21Neyshabur 2 39,413 52 6248 15 524,260 91 205.2 4117 49.99Neyshabur 3 18,048 50 4563 15 369,286 121 210.06 3164 49.98Qom 1 94,373 44 8385 17 843,603 120 1303.02 29,888 52.71Qom 2 99,530 45 7990 17 809,167 79 1150.05 27,368 52.46Sanandaj 101,516 42 7384 12 792,880 84 1894.36 3808 62.61Shahid Rajaei 1 49,270 44 7640 13 658,160 114 323.95 1774 48.31Shahid Rajaei 2 74,491 47 7527 13 643,480 88 324.36 2034 48.42Shahid Rajaei 3 80,064 48 7822 13 678,080 74 320.32 396 97.26Shariati 51,919 49 7988 14 706,104 73 3548.05 2201 52.03Yazd 1 28,381 47 5805 19 511,604 87 787.92 248 51.15Yazd 2 94,909 45 6880 19 757,939 108 761.94 13,424 63.68

G.R. Faramarzi et al. / Journal of Cleaner Production 108 (2015) 232e246 241

G.R. Faramarzi et al. / Journal of Cleaner Production 108 (2015) 232e246242

steam power plants is transmitted to electrical network via high-voltage transmission lines. In CCPPs, the generated electricity bysteam power plant can be used as an input for driving pumps, fans,and other equipments. Typically, the two gas turbines are linked toone steam turbine. Thus, a module of a CCPP consists of two gaspower plants and one steam power plant. Fig. 2 depicts network ofa combined cycle power plant.

4.1. Data set

The data set adopted from annual published figures of Iran po-wer industry for the year 2011. This data set consists of 30 CCPPslocated in Iran. As mentioned before, CCPPs consist of three-stagesincluding two gas power plants and one steam power plant (seeFig. 2). Tables 5e7 depict the data set of three stages. In general, gaspower plants consume natural gas and gasoil to generate electricity.The first input to stage 1 and 2 represents the fuel cost. Similarly,the second input of these stages and the first input of stage 3 standfor labor cost. Since we wish to assess sustainable operation ofindependent units of power plants, cost of operational labors thatdirectly involve in generating power is taken into account. Opera-tional labors are directly engaged in day-to-day operations of thepower plant. In fact, they carry out primary activities of the powerplants. Cost of operational labors implies to paid wages to labors.Also, the third input represents total hours that stages 1, 2, and 3 arein operation. Generally, in cooler climates, gross generation ofelectricity is increased. Thus, we consider mean annual air tem-perature as an important input (fourth input) for all stages. The firstoutput of stages 1, 2, and 3 indicates gross electricity generationfrom the three power plants, respectively, which is transmitted toelectrical network via high-voltage transmission lines. The second

Table 7Stage (3) (Steam power plant).

DMU(Power plant)

Inputs Outputs

Labor cost(1000 USD)

Hours ofoperation (h)

Mean annual airtemperature (�C)

Grossgeneration(Mwh)

Damavand 1 48 7793 9 733,789Damavand 2 49 7816 9 838,547Damavand 3 45 7569 9 685,912Damavand 4 49 2074 9 228,088Fars 1 45 8401 18 616,525Fars 2 52 8025 18 545,766Fars 3 54 8365 18 671,842Kazeroon 1 51 6703 22 654,401Kazeroon 2 52 6419 22 620,859Kazeroon 3 52 6604 22 667,132Kerman 1 52 3067 16 1001164Kerman 2 48 3074 16 973,185Kerman 3 45 2969 16 811,878Kerman 4 51 3072 16 941,318Khoy 46 8432 10 695,919Montazerghaem 1 40 8317 16 589,286Montazerghaem 2 44 7508 16 507,650Montazerghaem 3 43 8706 16 652,090Neyshabur 1 46 8411 15 735,501Neyshabur 2 40 8340 15 567,215Neyshabur 3 42 7247 15 512,295Qom 1 41 8572 17 700,129Qom 2 46 8278 17 699,635Sanandaj 47 2816 12 291,216Shahid Rajaei 1 41 7625 13 666,600Shahid Rajaei 2 44 8075 13 670,205Shahid Rajaei 3 48 8350 13 699,783Shariati 41 8406 14 719,824Yazd 1 44 7355 19 792,281Yazd 2 45 5070 19 608,613

output of the stages shows total hours of training to operationallabors. This variable is important because improving skills of laborsis vital for competitiveness of business. In addition to desirableoutputs such as generated electricity (economic factor) and totalhours of training (social factor), there are also undesirable outputslike CO2 emission and sewage (environmental factor) which areharmful to environment. As a result, the third output of stages 1 and2 (two gas power plants) signifies the CO2 emission. Also, the thirdoutput of stage 3 (steam power plant) represents the sewage (wastewater) which exits from steam power plant.

As mentioned before, in CCPP, some of the generated electricityfrom gas and steam power plants is used as input for drivingpumps, fans, and other equipments. These are in fact the loop in-termediate measures of stages. Thus, we consider internal con-sumption as the first intermediate measure of the problem. Thesecond intermediate output/input represents mean producedsteam by the HRSGs, which is used for driving a steam turbine,flowing from the first and second gas power plants to the thirdstage, respectively.

4.2. Results

After running the Model (8) and utilizing the Eq. (1), we obtainstage efficiency scores of power plants under CRS condition. Also,we compute overall efficiency of each power plant by Eq. (2).Outcomes are displayed in Table 8. To run the proposed models andobtain the results, we use Lingo software. The Model (8) yields fiveoverall efficient DMU (i.e., DMUs 1, 2, 3, 4,15, 22, 24, and 28). Ac-cording to the Definition 2, these DMUs achieved ENetworkCRS

j ¼ 1;therefore, these are DMUs whose stages are efficient, simulta-neously. Such DMUs, as a result, can be considered as “benchmark”

Intermediate outputs/inputs

Total hours oftraining (h)

Sewage(1000 m3)

Internalconsumption(Mwh)

Mean producedsteam stage 1(kg/s)

Mean producedsteam stage 2(kg/s)

112 265.405 38,540 63.775 63.78103 226.17 28,457 64.21 64.21114 134.05 26,592 63.72 63.7299 151.97 8478 63.4 63.479 254.24 27,556 49.885 49.89

106 170.212 27,654 49.78 49.7899 268.532 30,843 49.915 49.92

116 182.622 28,379 54.33 54.33126 179.64 29,268 65.18 65.1892 240.45 30,791 65.27 65.2784 235.68 36,147 60.61 60.61

134 232.531 35,262 60.68 60.6884 211.505 30,266 61.03 61.0380 164.8 35,507 60.49 60.49

131 236.313 23,088 49.14 49.14130 221.564 24,636 49.675 49.6880 202.585 25,600 49.725 49.73

117 223.965 26,560 49.835 49.84109 262.272 27,800 50.21 50.2193 206.184 25,656 49.985 49.99

108 118.638 22,922 49.975 49.98123 226.395 30,292 52.71 52.71133 239.7 30,878 52.455 52.46116 206.752 12,983 62.61 62.6178 198.64 26,686 48.31 48.31

103 248.391 26,927 48.42 48.4291 219.016 27,627 97.26 97.2694 239.64 26,326 52.03 52.0386 203.175 35,126 51.15 51.1591 227.04 34,920 63.68 63.68

Table 8Stage and overall efficiency score under CRS assumption.

No. DMU (Power plant) Eð1ÞCRS

j Eð2ÞCRS

j Eð3ÞCRS

j EOverallCRS

j

1 Damavand1 1.000 1.000 1.000 1.0002 Damavand 2 1.000 1.000 1.000 1.0003 Damavand 3 1.000 1.000 1.000 1.0004 Damavand 4 1.000 1.000 1.000 1.0005 Fars1 0.883 1.000 0.880 0.9106 Fars 2 0.834 0.886 0.539 0.7277 Fars 3 0.892 0.932 0.799 0.8518 Kazeroon1 1.000 0.991 0.648 0.8499 Kazeroon 2 1.000 1.000 0.599 0.83210 Kazeroon 3 1.000 1.000 0.642 0.86311 Kerman1 0.902 0.936 1.000 0.94812 Kerman 2 0.940 0.974 1.000 0.97213 Kerman 3 1.000 1.000 0.900 0.96914 Kerman 4 0.976 0.967 0.951 0.96415 Khoy 1.000 1.000 1.000 1.00016 Montazerghaem1 0.874 1.000 1.000 0.98317 Montazerghaem 2 1.000 0.802 0.583 0.77618 Montazerghaem 3 0.847 0.938 0.921 0.90819 Neyshabur1 0.983 0.928 1.000 0.99820 Neyshabur 2 0.834 0.958 0.854 0.89021 Neyshabur 3 1.000 1.000 0.612 0.82222 Qom1 1.000 1.000 1.000 1.00023 Qom 2 0.959 0.967 0.954 0.95724 Sanandaj 1.000 1.000 1.000 1.00025 Shahid Rajaei1 1.000 0.945 0.883 0.93626 Shahid Rajaei 2 0.826 0.935 0.946 0.92127 Shahid Rajaei 3 0.838 0.811 0.788 0.81128 Shariati 1.000 1.000 1.000 1.00029 Yazd 1 0.953 0.917 0.893 0.91730 Yazd 2 0.962 0.913 0.826 0.885

G.R. Faramarzi et al. / Journal of Cleaner Production 108 (2015) 232e246 243

for inefficient power plants. It is well-known that “the fewernumber of efficient DMUs, the higher benchmarking power of themodel” (Chiou et al., 2010). Therefore, the Model (8) has highbenchmarking power. The results of the Model (8) indicate that

Table 9The results obtained from the Model (11).

No. DMU (Power plant) Eð1ÞVRS

j Eð2ÞVRS

j Eð3ÞVRS

j

1 Damavand1 1.000 1.000 1.0002 Damavand 2 1.000 1.000 1.0003 Damavand 3 1.000 1.000 1.0004 Damavand 4 1.000 1.000 1.0005 Fars1 0.846 1.000 0.9066 Fars 2 0.770 0.854 0.4177 Fars 3 0.900 1.000 0.8458 Kazeroon1 1.000 1.000 0.5569 Kazeroon 2 1.000 1.000 0.52510 Kazeroon 3 1.000 1.000 0.74911 Kerman1 0.915 0.945 1.00012 Kerman 2 1.000 0.982 1.00013 Kerman 3 1.000 1.000 1.00014 Kerman 4 0.983 1.000 0.93315 Khoy 1.000 1.000 1.00016 Montazerghaem1 0.765 1.000 1.00017 Montazerghaem 2 1.000 0.557 0.81018 Montazerghaem 3 0.714 0.934 0.92619 Neyshabur1 0.999 0.933 1.00020 Neyshabur 2 0.826 0.959 1.00021 Neyshabur 3 1.000 1.000 0.94422 Qom 1 1.000 1.000 1.00023 Qom 2 0.948 1.000 1.00024 Sanandaj 1.000 1.000 1.00025 Shahid Rajaei 1 1.000 0.950 1.00026 Shahid Rajaei 2 0.812 0.965 0.94527 Shahid Rajaei 3 0.669 0.657 0.88528 Shariati 1.000 1.000 1.00029 Yazd 1 1.000 0.970 0.98130 Yazd 2 1.000 0.872 0.901

stage 1 of the DMUs 1, 2, 3, 4, 8, 9, 10, 13, 15, 17, 21, 22, 24, 25, and 28are efficient. Based on the Definition 1, they have E1

CRS

j ¼ 1. Also, thesecond stage of the DMUs 1, 2, 3, 4, 5, 9, 10, 13, 15, 16, 21, 22, 24, and28 are efficient. Moreover, the third stage of the DMUs 1, 2, 3, 4, 11,12, 15, 16, 19, 22, 24, and 28 are efficient.

While there are 17 DMUs with efficient stages 1 and 2, thirdstage of 11 DMUs are efficient, E3

CRS

j ¼ 1. This means thatmost of thesteam power plants operate inefficiently.

Because of the input-oriented Model (8), to improve the ef-ficiency of CCPPs, inefficient DMUs should decrease their inputvariables, while achieving the same amount of output variables.For example, the overall efficiency score of Kazeroon 1 in Table 8is 0.849. This implies that this DMU can decrease 15.1 percent ofits inputs including fuel cost, labor cost, etc, while achieving thesame output amounts. This feature can help inefficient DMUslike Kazeroon 1 to lie on the efficiency frontier and becomeefficient.

Now, we turn to the results obtained under VRS assumption.Given the outcomes of the Model (11), Table 9 depicts calculationsof formulas (13) and (14). Based on the Definition (3), the first stageof DMUs 1, 2, 3, 4, 8, 9, 10, 12, 13, 15, 17, 21, 22, 24, 25, 28, 29, and 30are efficient, since they attained E1

VRS

j ¼ 1. Regarding the secondstage, DMUs 1, 2, 3, 4, 5, 7, 8, 9,10, 13, 14,15, 16, 21, 22, 23, 24, and 28are relatively efficient.

The third stage of the DMUs 1, 2, 3, 4, 11, 12, 13, 15, 16, 19, 20,22, 23, 24, 25, and 28 are efficient, E3

VRS

j ¼ 1 and the third stage ofother DMUs are relatively inefficient. It means E3

VRS

j <1. Based onthe Definition 4, under VRS condition, DMUj is said to be overallefficient, if and only if EOverall

VRS*

j ¼ 1. It means that all stages ofDMUj are efficient. As can be seen in Table 9, DMUs 1, 2, 3, 4, 13, 15,22, 24, and 28 meet the terms of this definition. Thus, they areoverall efficient and archive EOverall

VRS

j ¼ 1. Note that the DMUswhich are overall efficient under CRS assumption are overallefficient under VRS assumption, as well.

EOverallVRS

j qð1Þ qð2Þ qð3ÞP3

t¼1qðtÞ

1.000 �3.560 �4.403 �6.505 �14.4671.000 �4.253 �2.447 �2.368 �9.0681.000 �0.197 �3.913 5.705 1.5941.000 4.301 0.608 8.507 13.4160.919 �2.573 �14.263 �7.990 �24.8260.644 �4.017 �1.917 �2.368 �8.3030.883 �3.917 �7.495 �11.646 �23.0580.822 2.280 �6.518 �2.368 �6.6060.780 �3.728 �1.051 �2.552 �7.3310.863 �5.201 �1.051 �12.329 �18.5800.958 �4.288 �3.271 �2.368 �9.9280.996 �14.662 �2.563 �2.955 �20.1811.000 �2.090 �3.714 24.191 18.3870.973 4.146 �3.314 �2.368 �1.5351.000 �5.380 0.061 �9.377 �14.6960.969 �9.014 �1.023 4.683 �5.3530.790 �11.511 �4.744 8.055 �8.2000.895 �4.291 �1.288 8.997 3.4180.987 8.677 �1.288 �12.267 �4.8780.984 �0.339 �12.767 67.619 54.5140.954 �5.038 �0.688 28.875 23.1491.000 �3.770 �0.495 8.997 4.7320.999 �2.749 134.190 �37.459 93.9821.000 �3.803 �0.562 �31.304 �35.6690.991 0.117 �0.101 16.876 16.8920.938 �0.630 �40.565 �8.682 �49.8770.817 �4.417 �4.790 8.590 �0.6181.000 �4.502 �0.396 8.598 3.7010.995 137.152 11.686 8.053 156.8900.994 199.138 �3.449 16.394 212.083

G.R. Faramarzi et al. / Journal of Cleaner Production 108 (2015) 232e246244

Although, efficiency scores of CCPPs provide better insight formanagers, they need to be equipped to more useful and detailedanalysis. Table 9 provides returns to scale of stages as well as wholenetworks. For example, q(1) ¼ 199.138 and q(3) ¼ 16.394 for theDMU#30 (Yazd 2), indicate that stages 1 and 3 have increasingreturns to scale (see Definition 6). This means that if the inputs ofthese stages are increased, their outputs are increased more pro-portionally. This result is ideal for improving production of thesestages. However, it increases CO2 emission and sewage amount.Therefore, to improve production, managers should consider howto reduce CO2 emission and sewage. This consideration also helpsthe DMU tomaintainmore sustainable production at the same levelof production. Additionally, increasing return to scale indicates thatan increase in inputs results in proportionally more increase inoutputs. Basically, DMUs which have increasing returns to scale canbe regarded by managers from three major aspects. The first aspectis to improve good outputs. In such conditions, they generate morebad outputs. They should apply technologies which decrease theamount of CO2 emission or sewage and lessen their impact. Recy-cling waste water and planting trees can be applied by managers.The second aspect is in situations that environmental pollution ishigh. In that situation they might deal with power shortage in thenetwork. Although this outcome is ideal from the environmentalperspective, it has an undesirable effect on production. In fact,DMUs with increasing returns to scale can decrease their envi-ronmental impact more easily, but they decrease their powergeneration as well. Finally, from investment aspect, such DMUs aresuitable as they produce more outputs.

On the other hand, stage 2 of this DMU obtained q(2) ¼ �3.449that reveals it has decreasing returns to scale. In decreasing returnsto scale, an increase in inputs results in proportionally less in-creases in outputs and vice versa. This situation is more useful for

0.5000.5500.6000.6500.7000.7500.8000.8500.9000.9501.000

Dam

avan

d1D

amav

and

2D

amav

and

3D

amav

and

4Fa

rs1

Fars

2Fa

rs 3

Kaz

eroo

n1K

azer

oon

2K

azer

oon

3K

erm

an1

Ker

man

2K

erm

an 3

Ker

man

4

Fig. 4. Overall efficiency score

0.5000.5500.6000.6500.7000.7500.8000.8500.9000.9501.000

Dam

avan

d1D

amav

and

2D

amav

and

3D

amav

and

4Fa

rs1

Fars

2Fa

rs 3

Kaz

eroo

n1K

azer

oon

2K

azer

oon

3K

erm

an1

Ker

man

2K

erm

an 3

Ker

man

4

Fig. 3. Overall efficiency score

managers who want less reduction in their production but moresaving in inputs. These DMUs are also improper points for furtherinvestment as they produce relatively less amount of output thaninvested capital.

Generally, returns to scale of whole network are summation ofall returns to scales of stages (see Definition 5). Thus, the value of212.083 for DMU #30 shows that it has increasing returns to scale.The same analysis can be conducted for other DMUs.

Comparing overall as well as stage efficiency scores obtainedfrom the Models (8) and (11), we realize that the NDEA modelunder CRS condition produces fewer efficient DMUs than theNDEA models under VRS condition. This is also shown in Figs. 3and 4. Note that the same holds in the case of stage efficiencyscores.

5. Concluding remarks

To determine sources of unsustainable operation in organiza-tions with multiple internal interactions, an in-depth managerialconsideration is required. Nowadays, organizations have begun toanalyze their internal interactions regarding economic, environ-mental, and social problems to create and maintain more sustain-able operation. To measure sustainability of DMUs, DEA is a well-established mathematical technique. Traditional DEA models,however, consider the DMUs as black boxes, ignoring their internalactivities. This paper sheds further light on the black box. To thisend, in this paper, two NDEA models were proposed. The proposedmodels were developed under assumption of CRS and VRS. Theproposed models help managers to evaluate not only DMUs (net-works) but also their associated stages. Additionally, this studyprovided a comprehensive interpretation to analyze returns toscale of network and its stages. The NDEA models then were

Kho

yM

onta

zerg

haem

1M

onta

zerg

haem

2M

onta

zerg

haem

3N

eysh

abur

1N

eysh

abur

2N

eysh

abur

3Q

om1

Qom

2Sa

nand

ajSh

ahid

Raj

aei1

Shah

id R

ajae

i 2Sh

ahid

Raj

aei 3

Shar

iati

Yaz

d 1

Yaz

d 2

s under VRS assumption.

Kho

yM

onta

zerg

haem

1M

onta

zerg

haem

2M

onta

zerg

haem

3N

eysh

abur

1N

eysh

abur

2N

eysh

abur

3Q

om1

Qom

2Sa

nand

ajSh

ahid

Raj

aei1

Shah

id R

ajae

i 2Sh

ahid

Raj

aei 3

Shar

iati

Yaz

d 1

Yaz

d 2

s under CRS assumption.

G.R. Faramarzi et al. / Journal of Cleaner Production 108 (2015) 232e246 245

applied to measure the efficiency of 30 CCPPs. Assuming CRS sit-uation, the obtained results revealed that five CCPPs were overallefficient. Similarly, fourteen CCPPs were overall efficient under VRSassumption. Therefore, discriminating power of VRS NDEAmodel islower than CRS NDEA model.

Managerial implications of this study are as follows: First, theNDEA models enable decision maker(s) to monitor their wholefirms as well as their corresponding stages. Most energy firmswhich are located in geographically separate regions consist of in-dividual units positioned side by side that work under the mainfirm. By measuring efficiency of individual units, managers cancompare specific stage of their firms with their competitors. Hence,based upon the obtained results, managers can set appropriatebenchmarks for inefficient DMUs and make suitable improvementpolicies for their organizations. Second, considering different stagesof a network, one can realize strengths and weaknesses of thenetwork. Finally, managers are concerned about operational andenvironmental efficiency of their firms. The weight and contribu-tion of each input in final output can help managers to improveboth operational and environmental efficiencies.

Here, a number of further research directions are proposed:

� Developing a NDEAmodel for open systems to gradually projectboth inefficient networks and its stages toward efficient frontieris an interesting topic.

� It is a good idea to develop similar models in the presence ofstochastic and/or imprecise data.

� The proposed models, with minor modifications, can be appliedin other areas of decision-making like assessing sustainability ofsupply chains and evaluating efficiency of production lines. Theexample of such modifications can be inclusion of imprecisedata, non-discretionary factors, and dual-role factors in theproblem.

Acknowledgments

The authors would like to thank two anonymous Reviewers fortheir valuable suggestions and comments.

References

Amirteimoori, A., Kordrostami, S., 2012. Production planning in data envelopmentanalysis. Int. J. Prod. Econ. 140 (1), 212e218.

Azadeh, A., Hasani Farmand, A., Jiryaei Sharahi, Z., 2012. Performance assessmentand optimization of HSE management systems with human error and ambi-guity by an integrated fuzzy multivariate approach in a large conventionalpower plant manufacturer. J. Loss Prev. Process Ind. 25 (3), 594e603.

Azadi, M., Shabani, A., Khodakarami, M., Farzipoor Saen, R., 2015. Planning infeasible region by two-stage target-setting DEA methods: an application ingreen supply chain management of public transportation service providers.Transp. Res. Part E Logist. Transp. Rev. 74, 22e36.

Banker, R., Charnes, A., Cooper, W.W., 1984. Some models for estimating technicaland scale inefficiencies in data envelopment analysis. Manag. Sci. 30 (9),1078e1092.

Charnes, A., Cooper, W.W., Rhodes, E., 1978. Measuring the efficiency of decisionmaking units. Eur. J. Oper. Res. 23 (1), 429e444.

Chatzimouratidis, A.I., Pilavachi, P.A., 2009. Technological, economic and sustain-ability evaluation of power plants using the analytic hierarchy process. EnergyPolicy 37 (3), 778e787.

Chen, Y., Liang, L., Zhu, J., 2009. Equivalence in two-stage DEA approaches. Eur. J.Oper. Res. 193 (2), 600e604.

Chen, Y., Cook, W.D., Kao, C., Zhu, J., 2013. Network DEA pitfalls: divisional efficiencyand frontier projection under general network structures. Eur. J. Oper. Res. 226(3), 507e515.

Chiou, Y.C., Chen, Y.H., 2006. Route-based performance evaluation of Taiwanesedomestic airlines using data envelopment analysis. Transp. Res. Part E Logist.Transp. Rev. 42 (2), 116e127.

Chiou, Y.C., Lawrence, W.L., Yen, B.T.H., 2010. A joint measurement of efficiency andeffectiveness for non-storable commodities: integrated data envelopmentanalysis approaches. Eur. J. Oper. Res. 201 (2), 477e489.

Cook, D., Zhu, J., Bi, G., Yang, F., 2010. Network DEA: additive efficiency decompo-sition. Eur. J. Oper. Res. 207 (2), 1122e1129.

Deng, Y., Xu, J., Liu, Y., Mancl, K., 2014. Biogas as a sustainable energy source inChina: regional development strategy application and decision making. Renew.Sustain. Energy Rev. 35, 294e303.

Du, J., Lianga, L., Yao, C., Bi, G.B., 2010. DEA-based production planning. Omega 38(1e2), 105e112.

F€are, R., Grosskopf, S., 1996. Intertemporal Production Frontiers: with Dynamic DEA.Kluwer Academic Publishers, Boston.

Farrell, M.J., 1957. The measurement of productive efficiency. J. R. Stat. Soc. Ser. A120 (3), 253e290.

Farzipoor Saen, R., 2009. Technology selection in the presence of imprecise data,weight restrictions, and nondiscretionary factors. Int. J. Adv. Manuf. Technol. 41(7e8), 827e838.

Farzipoor Saen, R., 2010. Performance measurement of power plants in the exis-tence of weight restrictions via slacks-based model. Benchmark. Int. J. 17 (5),677e691.

Gerdessen, J.C., Pascucci, S., 2013. Data envelopment analysis of sustainability in-dicators of European agricultural systems at regional level. Agric. Syst. 118,78e90.

Herremans, I.M., Reid, R.E., 2002. Developing awareness of the sustainabilityconcept. J. Environ. Educ. 34 (1), 16e20.

Jabbour, A.L.S., Jabbour, C.J.C., 2009. Are supplier selection criteria going green? Casestudies of companies in Brazil. Ind. Manag. Data Syst. 109 (4), 477e495.

Kannan, D., Beatriz Lopes de Sousa Jabbour, A., Jos�e Chiappetta Jabbour, C., 2014.Selecting green suppliers based on GSCM practices: using fuzzy TOPSIS appliedto a Brazilian electronics company. Eur. J. Oper. Res. 233 (2), 432e447.

Kao, C., 2014. Efficiency decomposition in network data envelopment analysis withslacks-based measures. Omega 45, 1e6.

Kao, C., Hwang, S.N., 2008. Efficiency decomposition in two-stage data envelop-ment analysis: an application to non-life insurance companies in Taiwan. Eur. J.Oper. Res. 185 (1), 418e429.

Kao, H.-Y., Chan, C.-Y., Wu, D.-J., 2014. A multi-objective programming method forsolving network DEA. Appl. Soft Comput. 24, 406e413.

Karlaftis, M.G., 2004. A DEA approach for evaluating the efficiency and effectivenessof urban transit systems. Eur. J. Oper. Res. 152 (2), 354e364.

Keh, H.T., Chu, S., Xu, J., 2006. Efficiency, effectiveness and productivity of marketingin service. Eur. J. Oper. Res. 170 (1), 265e276.

Khodakarami, M., Shabani, A., Farzipoor Saen, R., 2014. A new look at measuringsustainability of industrial parks: a two-stage data envelopment analysisapproach. Clean Technol. Environ. Policy 16 (8), 1577e1596.

Koplin, J., Seuring, S., Mesterharm, M., 2007. Incorporating sustainability into supplymanagement in the automotive industry e the case of the Volkswagen AG.J. Clean. Prod. 15 (11e12), 1053e1062.

Lee, K.H., Farzipoor Saen, R., 2012. Measuring corporate sustainability manage-ment: a data envelopment analysis approach. Int. J. Prod. Econ. 140 (1),219e226.

Liang, L., Cook, W.D., Zhu, J., 2008. DEA model for two-stage processes: gameapproach and efficiency decomposition. Nav. Res. Logist. 55 (1), 643e653.

Lins, M.E., Oliveira, L.B., da Silva, A.C.M., Rosa, L.P., Pereira Jr., A.O., 2012. Perfor-mance assessment of alternative energy resources in Brazilian power sectorusing data envelopment analysis. Renew. Sustain. Energy Rev. 16 (1),898e903.

Liu, X., Wen, Z., 2012. Best available techniques and pollution control: a case studyon China's thermal power industry. J. Clean. Prod. 23 (1), 113e121.

Liu, C.H., Lin, S.J., Lewis, C., 2010. Evaluation of thermal power plant operationalperformance in Taiwan by data envelopment analysis. Energy Policy 38 (2),1049e1058.

Lozano, S., 2015. Alternative SBM model for network DEA. Comput. Ind. Eng. 82,33e40.

Rezaee, M.J., Moini, A., Makui, A., 2012. Operational and non-operational perfor-mance evaluation of thermal power plants in Iran: a game theory approach.Energy 38 (1), 96e103.

Shabani, A., Farzipoor Saen, R., Torabipour, S.M.R., 2014. A new data envelopmentanalysis (DEA) model to select eco-efficient technologies in the presence ofundesirable outputs. Clean Technol. Environ. Policy 16 (3), 513e525.

Shakouri, G.H., Nabaee, M., Aliakbarisani, S., 2014. A quantitative discussion on theassessment of power supply technologies: DEA (data envelopment analysis)and SAW (simple additive weighting) as complementary methods for the“Grammar”. Energy 64, 640e647.

S€ozen, A., Alp, _I., Kilinc, C., 2012. Efficiency assessment of the hydro-power plants inTurkey by using Data Envelopment Analysis. Renew. Energy 46, 192e202.

S€ozen, A., Alp, _I., €Ozdemirc, A., 2010. Assessment of operational and environmentalperformance of the thermal power plants in Turkey by using data envelopmentanalysis. Energy Policy 38 (10), 6194e6203.

Sueyoshi, T., Goto, M., 2011. DEA approach for unified efficiency measurement:assessment of Japanese fossil fuel power generation. Energy Econ. 33 (2),292e303.

Sueyoshi, T., Goto, M., 2012a. Returns to scale and damages to scale on U.S. fossilfuel power plants: radial and non-radial approaches for DEA environmentalassessment. Energy Econ. 34 (6), 2240e2259.

Sueyoshi, T., Goto, M., 2012b. DEA environmental assessment of coal fired powerplants: methodological comparison between radial and non-radial models.Energy Econ. 34 (6), 1854e1863.

Sueyoshi, T., Goto, M., 2012c. Returns to scale, damages to scale, marginal rate oftransformation and rate of substitution in DEA environmental assessment.Energy Econ. 34 (4), 905e917.

G.R. Faramarzi et al. / Journal of Cleaner Production 108 (2015) 232e246246

Sueyoshi, T., Goto, M., 2012d. Environmental assessment by DEA radial mea-surement: U.S. coal-fired power plants in ISO (Independent System Operator)and RTO (Regional Transmission Organization). Energy Econ. 34 (3),663e676.

Sueyoshi, T., Goto, M., 2012e. DEA radial measurement for environmental assess-ment and planning: desirable procedures to evaluate fossil fuel power plants.Energy Policy 41, 422e432.

Sueyoshi, T., Goto, M., 2013. A comparative study among fossil fuel power plants inPJM and California ISO by DEA environmental assessment. Energy Econ. 40,130e145.

Sueyoshi, T., Goto, M., Sugiyama, M., 2013. DEA window analysis for environmentalassessment in a dynamic time shift: performance assessment of U.S. coal-firedpower plants. Energy Econ. 40, 845e857.

Tasri, A., Susilawati, A., 2014. Selection among renewable energy alternatives basedon a fuzzy analytic hierarchy process in Indonesia. Sustain. Energy Technol.Assess. 7, 34e44.

Tavassoli, M., Faramarzi, G.R., Farzipoor Saen, R., 2015. Ranking electricity distri-bution units using slacks-based measure, strong complementary slacknesscondition, and discriminant analysis. Int. J. Electr. Power Energy Syst. 64,1214e1220.

Tone, K., Tsutsui, M., 2009. Network DEA: a slacks-based measure approach. Eur. J.Oper. Res. 197 (1), 243e252.

Vaninsky, A., 2006. Efficiency of electric power generation in the United States:analysis and forecast based on data envelopment analysis. Energy Econ. 28 (3),326e338.

Wang, Y.S., Xie, B.C., Shang, L.F., Li, W.H., 2013. Measures to improve the perfor-mance of China's thermal power industry in view of cost efficiency. Appl. En-ergy 112, 1078e1086.

World Commission on Environment and Development (WCED), 1987. Our CommonFuture. Oxford University Press, Oxford, England.

Wong, B.Y.H., Luque, M., Yang, J.-B., 2009. Using interactive multiobjective methodsto solve DEA problems with value judgments. Comput. Oper. Res. 36 (2),623e636.

Yu, M.M., Lin, E.T.J., 2008. Efficiency and effectiveness in railway performance usinga multi-activity network DEA model. Omega 36 (6), 1005e1017.

Yuzhi, S., Zhangna, 2012. Study of the input-output overall performance evaluationof electricity distribution based on DEA method. Energy Procedia 16,1517e1525. Part C.

Zhou, Y., Xing, X., Fang, K., Liang, D., Xu, C., 2013. Environmental efficiency analysisof power industry in China based on an entropy SBM model. Energy Policy 57,68e75.

Zhu, Z., Wang, K., Zhang, B., 2014. Applying a network data envelopment analysismodel to quantify the eco-efficiency of products: a case study of pesticides.J. Clean. Prod. 69, 67e73.

本文献由“学霸图书馆-文献云下载”收集自网络，仅供学习交流使用。

学霸图书馆（www.xuebalib.com）是一个“整合众多图书馆数据库资源，

提供一站式文献检索和下载服务”的24 小时在线不限IP

图书馆。

图书馆致力于便利、促进学习与科研，提供最强文献下载服务。

图书馆导航：

图书馆首页 文献云下载 图书馆入口 外文数据库大全 疑难文献辅助工具