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A multi criteria data envelopment analysis model to evaluate the efficiency of the Renewable Energy technologies
Renewable Energy 36 (2011) 2742e2746
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Renewable Energy journal homepage: www.elsevier.com/locate/renene
A multi criteria data envelopment analysis model to evaluate the efficiency of the Renewable Energy technologies José Ramón San Cristóbal* University of Cantabria, Escuela Técnica Superior de Náutica, German Gamazo, s/n, Santander 39004, Spain
a r t i c l e i n f o
a b s t r a c t
Article history: Received 23 November 2010 Accepted 4 March 2011 Available online 2 April 2011
The growing concern in the negative effects of fossil fuels on the environment has forced a more intensive use of Renewable Energy sources which are considered an important solution to the large atmospheric pollution caused from fossil fuel combustion. In the electricity-generating industry, due to the high costs associated with the construction and operation of plants and the regulations that enforce productivity evaluations, efficiency is a key managerial concept. DEA is a non-parametric method which produces detailed information on the efficiency of a unit, to be measured without any assumptions regarding the functional form of the production function. In this paper, the efficiency of 13 Renewable Energy technologies is evaluated through a Multiple Criteria Data Envelopment Analysis (MCDEA) model. Two additional criterion, the minsum and minimax criterion, are included in the model which are the most restrictive than that defined in the classical DEA. The results show that the only Decision Making Unit rated as efficient is the Windpower 10 P 50 MW technology and it can be considered the only non-dominated solution. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Renewable Energies Efficiency Multi criteria data envelopment analysis
1. Introduction A more intensive use of Renewable Energy Sources (RES) is considered an important solution to the large atmospheric pollution caused from fossil fuel combustion, upon which current energy production and use patterns throughout the world still rely heavily [1]. The growing concern in the negative effects of fossil fuels on the environment and the precarious nature of dependency on fossil fuel imports has forced many countries, specially the developed ones, to use RES, which are environment-friendly and capable of replacing conventional sources in a variety of applications at competitive prices [2,3]. The Kyoto Protocol, the EU Renewable Directive 2001/77/EC, and the European Biomass Action Plan are examples of political goals fostering the use of theses RES. In the electricity industry efficiency is a key managerial concept. The electricity-generating industry has always been at the focus of attention for productivity-efficiency measurement. This has been motivated basically by two factors. First, most of these companies have been publicly owned subject to regulations that enforce productivity evaluations, and second, the cost associated with the construction and operation of the electricity-generating facilities constitute a significant portion of the Gross National Product in
* Tel.: þ34 33 942 202267; fax: þ34 33 942 201303. E-mail address: [email protected]. 0960-1481/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2011.03.008
most developed countries. In this context, even small improvements may result in large monetary benefits [4]. The contribution of management sciences to assessing efficiency has been intensified in recent years since the publication by Charnes et al. [6] and the introduction of Data Envelopment Analysis (DEA). DEA is a mathematical programming approach using linear programming to assess the comparative efficiency of a set of Decision Making Units (DMUs) which, through distinct production processes and technologies, take a given level of inputs to produce a given quantity of outputs. In this paper, the efficiency of 13 Renewable Energy technologies is evaluated with a Multiple Criteria Data Envelopment Analysis (MCDEA) model under three different criteria, each of one is an independent objective function and so it defines a particular concept of efficiency. The paper is organized as follows. In the next section the MCDEA model is presented and, next, the model is applied to 13 different Renewable Energy technologies. Finally, a concluding section with the main results of the paper is presented. 2. DEA To estimate the efficiency scores of companies, various methods have been developed during the past two decades. These methods are generally classified as parametric and non-parametric methods. In the parametric methods, a cost of production function is estimated, whereas in the non-parametric methods, it is not
J.R. San Cristóbal / Renewable Energy 36 (2011) 2742e2746
necessary to estimate the cost or production function. Stochastic Frontier Analysis (SFA) and Data Envelopment Analysis (DEA) are the major parametric and non-parametric models respectively [5]. Charnes et al. [6] first introduced the DEA concept and many articles have since appeared that deal with various types of applications where the presence of multiple inputs and outputs makes comparison difficult. A non-parametric piecewise frontier (a best practice efficiency frontier) composed of DMUs, which own the optimal efficiency over the datasets is constructed by DEA for comparative efficiency measurement. Those DMUs located at the efficiency frontier have their maximum outputs generated among all DMUs by taking the minimum level of inputs, which are efficient DMUs and own the best efficiency among all DMUs. The existing gap from any DMUs to the efficiency frontier shows how far the DMUs should be further improved to reach the optimal efficiency level. DEA produces detailed information on the efficiency of the unit, to be measured without any assumptions regarding the functional form of the production function, not only relative to the efficiency frontier, but also to specific efficient units which can be identified as role models [7e9]. Thus, DEA can be used by inefficient organizations to benchmark efficient and ‘best-practice’ organizations. Application of DEA in the electric power industry may be traced back to the publications of Cote [10], Hjalmarsson and Veiderpass [11], Miliotis [12], and Golany et al. [4]. Since then, DEA has been widely applied both to the distribution aspects of operations and to the electric generation. Bagdachioglo et al. [13], applied DEA to the analysis of impact of ownership on efficiency. Yunos and Hawdon [14] considered organizational efficiency comparisons at the international level and Goto and Tsutsui [15] used DEA model to measure overall cost efficiency and technical efficiency between Japanese and U.S. electricity utilities. Forsuad and Kittelsen [16] applied DEA efficiency scores to measure Malmquist productivity index in the Norwegian electricity distribution companies. Chitkara [17] evaluated the operational inefficiencies of Indian power plants and Sueyoshi and Goto [18] investigated the performance of electric power generation in Japan. Pacuda and de Guzman [19] researched productive efficiency of electricity distribution in the Philippines and Resende [20] used a non-parametric input-oriented DEA model for evaluation of Brazilian electricity distribution firms. Chen [21] presented an assessment of technical efficiency and cross-efficiency in Taiwan’s electricity distribution sector. Jamasb and Pollit [22] compared 63 electricity distribution utilities for six European countries and Korhonen and Syrjanen [23] analyzed cost efficiency in Finnish electricity distribution and Nemoto and Goto [24] the dynamic efficiency of electric power production in Japan. Pahwa et al. [25] and Sauhueza and Rudnick [26], evaluated the efficiency of electric distribution utilities based on their performances. Estache et al. [27] applied DEA and econometric methods for performance assessment and ranking of South American electricity units and Gianakis et al. [28] studied the service quality assessment of UK electricity distribution utilities. Jha and Shrestha [29] evaluated the efficiency of Hydropower plants in Nepal using DEA and Vaninski [30] used DEA estimated the efficiency of electric power generation in the U.S. for the period of 1991 through 2004. Azadeh et al. [31] presented and integrated hierarchical DEA-Principal Component Analysis approach for location of solar plants. Sadjadi and Omrani [5] presented a DEA model with uncertain data for performance assessment of Iranian electricity distribution companies. Jayanthi et al. [32] showed a DEA-based application to the U.S. photovoltaic industry to evaluate the potential of innovations occurring in various stages of the industry value chain in terms of its relative efficiency with respect to a best practices frontier. The classical DEA model for evaluating the efficiency of a DMU, denoted by DMU0 is as follows [6]:
max s:t: m P i¼1 s P
h0 ¼
s P r¼1
2743
ur yrj0
vi xij0 ¼ 1 ur yrj
r¼1 ur ; vi
0
m P i¼1
(1) vi xij0 0
where j is the DMU index (j ¼ 1,.,n); r the output index (r ¼ 1,.,s); i the input index (i ¼ 1,.m); xij the value of the ith input of the jth DMU; yrj the value of the rth output of the jth DMU; ur the weight given to the rth output; ni the weight given to the ith input; and h0 the relative efficiency of DMU0, the DMU under evaluation. In this model, DMU0 is efficient if and only if h0 ¼ 1. Lii and Reeves [33] extend the concept of relative efficiency and the method of efficiency evaluation from single criterion-based conventional approach to multiple criteria-oriented one. The authors argue that the resulting DEA models are more flexible and powerful in many aspects, particularly in discriminant analysis and weight restriction, showing three advantages. First, in classical DEA, if a DMU is efficient, its optimal (weight) solution is almost surely non unique. In this situation, a Linear Programming procedure returns the first optimal solution it finds usually giving solutions with extremely distributed weights. Second, Multi Objective Linear Programming (MOLP) solutions contains not only the solution that individually optimize each of the objectives, but also other non-dominated solutions that, while non optimal under any given criterion, provide alternative choices for the associated DMU. There may be situations where some of these non-dominated solutions are more preferred to those solutions optimizing individual objectives. Third, the total number of non-dominated solutions associated with a DMU often reflects the stability of a DMU’s efficiency scores relative to the changes in efficiency criteria. Model (1) can be expressed equivalently in the following deviational variable form:
min s:t: m P i¼1 s P r¼1
s P d0 or max h0 ¼ ur yrj0 r¼1
vi xij0 ¼1 ur yrj
(2) m P i¼1
vi xij0 þ dj ¼ 0
ur ; vi ; dj 0
where d0 is the deviation variable for DMU0 and dj the deviation variable for the jth DMU (appeared at the jth original inequality constraint). Under this model, DMU0 is efficient if and only if d0 ¼ 0 (or equivalently, h0 ¼ 1). If DMU0 is not efficient, its efficiency score is h0 ¼ 1d0. The quantity d0, which is bounded by the interval [0.1], can be regarded as a measure of inefficiency (other measures of inefficiency have been proposed by [34e36]). The smaller the value of d0, the less inefficient (and thus the more efficient) DMU0 is. In this sense, we say that classical DEA method (Model(1) or (2)) minimizes DMU0’s inefficiency, as measured by d0, under the constraint that the weighted sum of the outputs is less than or equal to the weighted sum of the inputs for each DMU. Lii and Reeves [33] propose a MCDEA model that is different form other models in that each criterion is an independent objective function. That is, each criterion defines a particular concept of efficiency and there is no prior preference among these efficiency criteria. The form of the proposed MCDEA model depends upon the efficiency criteria used. For a MCDEA problem that has the
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J.R. San Cristóbal / Renewable Energy 36 (2011) 2742e2746
following three criteria, i.e., minimizing d0, minimizing the sum of the deviations, and minimizing the maximum deviation, the MCDEA model can be specified as follows:
min
s P d0 or max h0 ¼ ur yrj0 n P
min
j¼1
r¼1
dj
min M s:t: m P vi xij0 ¼1 i¼1 s P
r¼1
ur yrj
(3) m P i¼1
vi xij0 þ dj ¼ 0
M dj 0 ur ; vi ; dj 0
The first objective of model (3) is identical to the objective of model (1) or (2). The second objective function is a straightforward representation of the deviation sum and the variable M in the third objective represents the maximum quantity among all deviation variables dj (j ¼ 1,.,n). Notice that the feasible region for decision variables ur and ni in model (3) is the same as that in models (1) and (2). The effect of added constraints, Mdj 0 is to make M the maximum deviation. They do not change the feasible region of decision variables. Model (3) is a MOLP and, in a MOLP problem it is generally impossible to find a solution that optimizes all objectives simultaneously. Therefore, the task of a MOLP solution process is not to find an optimal solution but, instead, to find non-dominated solutions (in multiple criteria terminology, a non-dominated solution is also called an efficient solution) and to help select a most preferred one. One fact to point out is that a non-dominated solution set for a MOLP problem will always contain, but is not limited to the optimal solutions obtained by individually optimizing each of the objectives in the MOLP problem under the setting of single objective linear programming. The solution that optimizes the first objective function of model (3) is equivalent to the optimal solution of model (1) or (2). That is, DMU0 is efficient (in the classical sense) if and only the value of d0 corresponding to the solution that optimizes the first objective function of model (3) is zero. In the same way, it can be defined a DMU’s relative efficiency corresponding to the second and third objective criteria in the following way: DMU0 is minsum efficient and minimax efficient if and only if the value of d0 corresponding to the solution that minimizes the second and third objective function
of model (3) is zero. In all the three above definitions, no matter is DMU0 is efficient or not, its DEA efficiency scores is 1d0. Efficiencies defined under minsum and minimax criterion are most restrictive than that defined in the classical DEA and these two criteria generally yield fewer efficient DMUs. That is, it is more difficult for a DMU to achieve minsum or minimax efficiency that to achieve classical DEA efficiency. More precisely, if DMU0 is minsum or minimax efficient, it must also be DEA efficient, because by definition, minsum or minimax efficiency requires d0 ¼ 0. However, if DMU0 is DEA efficient, it may or may not be minsum or minimax P dj is efficient, because d0 does not necessarily imply that M or minimized. Including these new criteria in a DEA model will result in the improvement in discriminating power. On the other hand, P since M or dj are functions of all deviation variables and each P deviation variable is related to a constraint, minimizing M or dj is, in some sense, equivalent to improving tighter constraints on weight variables. 3. Application In this section, the MCDEA model is applied for evaluating the efficiency of 13 RE technologies included in the Renewable Energy Plan approved by the Spanish Government on 2005 [37] for the following areas: Windpower, Hydroelectric, Solar, Biomass, Biogas and Biofuels. The input and output data used to perform the analysis, shown in Table 1, are defined as follows:
Inputs
n1 n2 n3
Investment ratio (Euro103/Kw) Implement period (years) Operating and maintenance costs (Euro103/Kwh)
Outputs u1 u2 u3 u4
Power (MW103) Operating hours(Hours103/year) Useful life (years) Tons of CO2avoided (tCO2106/year)
The results of classical DEA method, solved by LP are given in Table 2. Using model (3), the results obtained are shown in Tables 3e5, corresponding to the three criteria respectively (minimizing d0, minimizing the sum of the deviations, and minimizing the maximum deviation). Efficiency scores in Tables 2 and 3 are identical since they are obtained under the same criterion. As we can see, all DMUs except DMU7 (Solar Thermo-electric P 10 MW) are efficient. However, we can easily observe differences between
Table 1 Input and Output data for the 13 DMUs. DMU
DMU1 DMU2 DMU3 DMU4 DMU5 DMU6 DMU7 DMU8 DMU9 DMU10 DMU11 DMU12 DMU13
Input weights
Windpower P 5 MW Windpower 5 P 10 MW Windpower 10 P 50 MW Hydroelectric P 10 MW Hydroelectric 10 P 25 MW Hydroelectric 25 P 50 MW Solar Thermo-electric P 10 MW Biomass (energetic cultivations) P 5 MW Biomass (forest and agricultural wastes) P 5 MW Biomass (farming industrial wastes) P 5 MW Biomass (forest industrial wastes) P 5 MW Biomass (Co-combustion in conventional central) P 50 MW Biofuels P 2 MW
Output weights
n1
n2
n3
u1
u2
u3
u4
0.937 0.937 1.500 0.700 0.601 5.000 1.803 1.803 1.803 1.803 1.803 0.856 1.503
1 1 1 1.5 2 2.5 2 1 1 1 1 1 1.5
1.47 1.47 1.51 1.45 0.70 0.60 4.2 7.11 5.42 5.42 2.81 4.56 2.51
0.5 1.0 2.5 0.5 2.0 3.5 5.0 0.5 0.5 0.5 0.5 5.6 0.2
2.35 2.35 2.35 3.10 2.00 2.00 2.59 7.50 7.50 7.50 7.50 7.50 7.00
20 20 20 25 25 25 25 15 15 15 15 20 20
1.93 3.22 9.65 0.47 0.26 0.26 0.48 2.52 2.52 2.52 2.52 4.84 5.91
J.R. San Cristóbal / Renewable Energy 36 (2011) 2742e2746 Table 2 Classical DEA results. DMU
DMU1 DMU2 DMU3 DMU4 DMU5 DMU6 DMU7 DMU8 DMU9 DMU10 DMU11 DMU12 DMU13
Efficiency
1 1 1 1 1 1 0.78 1 1 1 1 1 1
Table 5 Minimax DEA results. Input weights
Output weights
DMU
n1
n2
n3
u1
u2
u3
u4
0.14 0.29 0 0.10 0.45 0 0 0 0 0 0 0 0.08
0.40 0.38 0.44 0.32 0.31 0.33 0.20 1.00 1.00 1.00 0.12 0.20 0.12
0.32 0.23 0.37 0.26 0.08 0.28 0.15 0 0 0 0.31 0.17 0.28
0 0 0.38 0.01 0.07 0.28 0.14 0 0 0 0.07 0.18 0.07
1.31 1.30 0 1.05 0 0 0 1.33 1.33 1.33 1.24 0 1.30
3.46 3.44 0 2.70 3.45 0 0.27 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0.01 0 0.01
Table 3 Minimizing d0 results. DMU
DMU1 DMU2 DMU3 DMU4 DMU5 DMU6 DMU7 DMU8 DMU9 DMU10 DMU11 DMU12 DMU13
Efficiency
1 1 1 1 1 1 0.78 1 1 1 1 1 1
Input weights
Output weights
n1
n2
n3
u1
u2
u3
u4
0.10 0 0 0 0 0 0 0 0 0 0 0 0
9.02 7.89 7.84 5.67 4.70 3.83 3.62 3.01 3.61 3.61 6.15 4.02 5.11
0 0.14 0.14 0.10 0.08 0.07 0.07 0.10 0.12 0.12 0.12 0.13 0.09
0 0.06 0.06 0.04 0.04 0.03 0.03 0.02 0.03 0.03 0.05 0.03 0.04
0 0.54 0.54 0.39 0.32 0.26 0.25 0.48 0.57 0.57 0.45 0.64 0.35
5 3.64 3.62 2.62 2.17 1.77 1.67 1.37 1.65 1.65 3.05 1.83 2.36
0 0 0 0 0 0 0 0 0 0 0 0 0
the solutions shown in both Tables. The input and output weights obtained by the MOLP procedure in Table 3 are distributed more evenly than those obtained by classical DEA in Table 2. Table 4 lists the efficiency scores for each DMU under the Minsum criteria. Under this criteria the only DMUs rated as efficient are DMU1 (Windpower P 5 MW), DMU2 (Windpower 5 P 10 MW), DMU3 (Windpower 10 P 50 MW)and DMU11 (Biomass forest industrial wastes P 5 MW). Table 5 lists the efficiency scores for each DMU under the Minimax criterion. In particular, only DMU3 (Windpower 10 P 50 MW) and DMU12 (Biomass Co-combustion in conventional central P 50 MW) are rated as efficient, while the rest of the DMUs, rated as efficient by classical DEA and by
Table 4 Minsum DEA results. DMU
DMU1 DMU2 DMU3 DMU4 DMU5 DMU6 DMU7 DMU8 DMU9 DMU10 DMU11 DMU12 DMU13
Efficiency
1 1 1 0.88 0.67 0.54 0.36 0.53 0.65 0.65 1 0.80 0.86
2745
Input weights
Output weights
n1
n2
n3
u1
u2
u3
u4
0 0 0 0 0 0 0.10 0.06 0.08 0 0.15 0 0
8.51 8.51 8.48 5.98 4.80 3.89 1.10 1.10 1.34 3.61 3.26 1.80 5.56
0.10 0.10 0.10 0.07 0.06 0.05 0.06 0.11 0.13 0.12 0.14 0.18 0.07
0 0 0 0 0 0 0 0.02 0.03 0.03 0 0.02 0
0.67 0.67 0.67 0.47 0.38 0.31 0.38 0.54 0.70 0.57 0.86 1.64 0.44
4.21 4.21 4.19 2.96 2.37 1.92 1.04 0.74 0.91 1.65 2.36 1.28 2.75
0 0 0 0 0 0 0 0 0 0 0 0 0
DMU1 DMU2 DMU3 DMU4 DMU5 DMU6 DMU7 DMU8 DMU9 DMU10 DMU11 DMU12 DMU13
Efficiency
0.88 0.91 1 0.79 0.68 0.60 0.62 0.58 0.70 0.70 0.82 1 0.72
Input weights
Output weights
n1
n2
n3
u1
u2
u3
u4
0.10 0 0 0 0 0 0 0 0 0 0 0 0
9.02 7.89 7.84 5.67 4.70 3.83 3.62 3.01 3.61 3.61 6.15 4.02 5.11
0 0.14 0.14 0.10 0.08 0.07 0.07 0.10 0.12 0.12 0.12 0.13 0.09
0 0.06 0.06 0.04 0.04 0.03 0.03 0.02 0.03 0.03 0.05 0.03 0.04
0 0.54 0.54 0.39 0.32 0.26 0.25 0.48 0.57 0.57 0.45 0.64 0.35
5 3.64 3.62 2.62 2.17 1.77 1.67 1.37 1.65 1.65 3.05 1.83 2.36
0 0 0 0 0 0 0 0 0 0 0 0 0
Minsum criteria, are no longer efficient with respect to the Minimax criteria. As we can see, the only DMU rated as efficient under the three criteria is DMU3 (Windpower 10 P 50 MW) and it can be considered the only non-dominated solution. 4. Conclusions To find a non-dominated solution, also called an efficient solution in multiple criteria terminology, and to select the most preferred one is the main task of a MOLP. In this paper, a MCDEA is applied under three different criteria, (minimizing d0, minimizing the sum of the deviations, and minimizing the maximum deviation) each of one is an independent objective function and so it defines a particular concept of efficiency, a key managerial concept in the electricity-generating industry. As we can see, including more restrictive criteria than that defined in the classical DEA entails that, technologies that are efficient under classical DEA, prove to be inefficient under the MCDEA model. Decision-makers should participate in developing target setting or policy making scenarios that would enable managers to consider simultaneously inputs and outputs in the assessment of targets with the aim of increasing efficiency. References [1] Madlener R, Antunes CH, Dias LC. Assessing the performance of biogas plants with multi-criteria and data envelopment analysis. European Journal of Operations Research 2006;197:1084e94. [2] Aras H, Erdogmus S, Koc E. Multi-criteria selection for a wind observation station location using analytic hierarchy process. Renewable Energy 2004;23: 1383e92. [3] Haralambopoulos DA, Polatidis H. Renewable energy projects: structuring a multicriteria group decision-making framework. Renewable Energy 2003; 28:961e73. [4] Golany B, Roll Y, Ryback D. Measuring efficiency of power plants in Israel by data envelopment analysis. IEEE Transactions on Engineering Management 1994;41(3):291e301. [5] Sadjadi SJ, Omrani H. Data envelopment analysis with uncertain data: a application for Iranian electricity distribution companies. Energy Policy 2008;36:4247e54. [6] Charnes A, Cooper WW, Rhodes E. Measuring the efficiency of decisionmaking units. European Journal of Operational Research 1978;2:429e44. [7] Athanassopoulos AD, Lambropoulos N, Seiford L. Data envelopment scenario analysis for setting targets to electricity generating plants. European Journal of Operations Research 1999;15:413e28. [8] Hu JL, Kao CH. Efficient energy-savings targets for APEC economies. Energy Policy 2007;35:373e82. [9] Hu JL, Wang SC, Yeh FY. Total-factor water efficiency of regions in China. Resources Policy 2006;31:217e30. [10] Cote DO. Firm efficiency and ownership structure-the case of U.S. electric utilities using panel data. Annals of Public and Cooperative Economics 1989; 60(4):431e50. [11] Hjalmarsson L, Veiderpass A. Efficiency and ownershipin Swedish electricity retail distribution. The Journal of Productivity Analysis 1992;3(1/2):7e23.
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Renewable Energy journal homepage: www.elsevier.com/locate/renene
A multi criteria data envelopment analysis model to evaluate the efficiency of the Renewable Energy technologies José Ramón San Cristóbal* University of Cantabria, Escuela Técnica Superior de Náutica, German Gamazo, s/n, Santander 39004, Spain
a r t i c l e i n f o
a b s t r a c t
Article history: Received 23 November 2010 Accepted 4 March 2011 Available online 2 April 2011
The growing concern in the negative effects of fossil fuels on the environment has forced a more intensive use of Renewable Energy sources which are considered an important solution to the large atmospheric pollution caused from fossil fuel combustion. In the electricity-generating industry, due to the high costs associated with the construction and operation of plants and the regulations that enforce productivity evaluations, efficiency is a key managerial concept. DEA is a non-parametric method which produces detailed information on the efficiency of a unit, to be measured without any assumptions regarding the functional form of the production function. In this paper, the efficiency of 13 Renewable Energy technologies is evaluated through a Multiple Criteria Data Envelopment Analysis (MCDEA) model. Two additional criterion, the minsum and minimax criterion, are included in the model which are the most restrictive than that defined in the classical DEA. The results show that the only Decision Making Unit rated as efficient is the Windpower 10 P 50 MW technology and it can be considered the only non-dominated solution. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Renewable Energies Efficiency Multi criteria data envelopment analysis
1. Introduction A more intensive use of Renewable Energy Sources (RES) is considered an important solution to the large atmospheric pollution caused from fossil fuel combustion, upon which current energy production and use patterns throughout the world still rely heavily [1]. The growing concern in the negative effects of fossil fuels on the environment and the precarious nature of dependency on fossil fuel imports has forced many countries, specially the developed ones, to use RES, which are environment-friendly and capable of replacing conventional sources in a variety of applications at competitive prices [2,3]. The Kyoto Protocol, the EU Renewable Directive 2001/77/EC, and the European Biomass Action Plan are examples of political goals fostering the use of theses RES. In the electricity industry efficiency is a key managerial concept. The electricity-generating industry has always been at the focus of attention for productivity-efficiency measurement. This has been motivated basically by two factors. First, most of these companies have been publicly owned subject to regulations that enforce productivity evaluations, and second, the cost associated with the construction and operation of the electricity-generating facilities constitute a significant portion of the Gross National Product in
* Tel.: þ34 33 942 202267; fax: þ34 33 942 201303. E-mail address: [email protected]. 0960-1481/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2011.03.008
most developed countries. In this context, even small improvements may result in large monetary benefits [4]. The contribution of management sciences to assessing efficiency has been intensified in recent years since the publication by Charnes et al. [6] and the introduction of Data Envelopment Analysis (DEA). DEA is a mathematical programming approach using linear programming to assess the comparative efficiency of a set of Decision Making Units (DMUs) which, through distinct production processes and technologies, take a given level of inputs to produce a given quantity of outputs. In this paper, the efficiency of 13 Renewable Energy technologies is evaluated with a Multiple Criteria Data Envelopment Analysis (MCDEA) model under three different criteria, each of one is an independent objective function and so it defines a particular concept of efficiency. The paper is organized as follows. In the next section the MCDEA model is presented and, next, the model is applied to 13 different Renewable Energy technologies. Finally, a concluding section with the main results of the paper is presented. 2. DEA To estimate the efficiency scores of companies, various methods have been developed during the past two decades. These methods are generally classified as parametric and non-parametric methods. In the parametric methods, a cost of production function is estimated, whereas in the non-parametric methods, it is not
J.R. San Cristóbal / Renewable Energy 36 (2011) 2742e2746
necessary to estimate the cost or production function. Stochastic Frontier Analysis (SFA) and Data Envelopment Analysis (DEA) are the major parametric and non-parametric models respectively [5]. Charnes et al. [6] first introduced the DEA concept and many articles have since appeared that deal with various types of applications where the presence of multiple inputs and outputs makes comparison difficult. A non-parametric piecewise frontier (a best practice efficiency frontier) composed of DMUs, which own the optimal efficiency over the datasets is constructed by DEA for comparative efficiency measurement. Those DMUs located at the efficiency frontier have their maximum outputs generated among all DMUs by taking the minimum level of inputs, which are efficient DMUs and own the best efficiency among all DMUs. The existing gap from any DMUs to the efficiency frontier shows how far the DMUs should be further improved to reach the optimal efficiency level. DEA produces detailed information on the efficiency of the unit, to be measured without any assumptions regarding the functional form of the production function, not only relative to the efficiency frontier, but also to specific efficient units which can be identified as role models [7e9]. Thus, DEA can be used by inefficient organizations to benchmark efficient and ‘best-practice’ organizations. Application of DEA in the electric power industry may be traced back to the publications of Cote [10], Hjalmarsson and Veiderpass [11], Miliotis [12], and Golany et al. [4]. Since then, DEA has been widely applied both to the distribution aspects of operations and to the electric generation. Bagdachioglo et al. [13], applied DEA to the analysis of impact of ownership on efficiency. Yunos and Hawdon [14] considered organizational efficiency comparisons at the international level and Goto and Tsutsui [15] used DEA model to measure overall cost efficiency and technical efficiency between Japanese and U.S. electricity utilities. Forsuad and Kittelsen [16] applied DEA efficiency scores to measure Malmquist productivity index in the Norwegian electricity distribution companies. Chitkara [17] evaluated the operational inefficiencies of Indian power plants and Sueyoshi and Goto [18] investigated the performance of electric power generation in Japan. Pacuda and de Guzman [19] researched productive efficiency of electricity distribution in the Philippines and Resende [20] used a non-parametric input-oriented DEA model for evaluation of Brazilian electricity distribution firms. Chen [21] presented an assessment of technical efficiency and cross-efficiency in Taiwan’s electricity distribution sector. Jamasb and Pollit [22] compared 63 electricity distribution utilities for six European countries and Korhonen and Syrjanen [23] analyzed cost efficiency in Finnish electricity distribution and Nemoto and Goto [24] the dynamic efficiency of electric power production in Japan. Pahwa et al. [25] and Sauhueza and Rudnick [26], evaluated the efficiency of electric distribution utilities based on their performances. Estache et al. [27] applied DEA and econometric methods for performance assessment and ranking of South American electricity units and Gianakis et al. [28] studied the service quality assessment of UK electricity distribution utilities. Jha and Shrestha [29] evaluated the efficiency of Hydropower plants in Nepal using DEA and Vaninski [30] used DEA estimated the efficiency of electric power generation in the U.S. for the period of 1991 through 2004. Azadeh et al. [31] presented and integrated hierarchical DEA-Principal Component Analysis approach for location of solar plants. Sadjadi and Omrani [5] presented a DEA model with uncertain data for performance assessment of Iranian electricity distribution companies. Jayanthi et al. [32] showed a DEA-based application to the U.S. photovoltaic industry to evaluate the potential of innovations occurring in various stages of the industry value chain in terms of its relative efficiency with respect to a best practices frontier. The classical DEA model for evaluating the efficiency of a DMU, denoted by DMU0 is as follows [6]:
max s:t: m P i¼1 s P
h0 ¼
s P r¼1
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ur yrj0
vi xij0 ¼ 1 ur yrj
r¼1 ur ; vi
0
m P i¼1
(1) vi xij0 0
where j is the DMU index (j ¼ 1,.,n); r the output index (r ¼ 1,.,s); i the input index (i ¼ 1,.m); xij the value of the ith input of the jth DMU; yrj the value of the rth output of the jth DMU; ur the weight given to the rth output; ni the weight given to the ith input; and h0 the relative efficiency of DMU0, the DMU under evaluation. In this model, DMU0 is efficient if and only if h0 ¼ 1. Lii and Reeves [33] extend the concept of relative efficiency and the method of efficiency evaluation from single criterion-based conventional approach to multiple criteria-oriented one. The authors argue that the resulting DEA models are more flexible and powerful in many aspects, particularly in discriminant analysis and weight restriction, showing three advantages. First, in classical DEA, if a DMU is efficient, its optimal (weight) solution is almost surely non unique. In this situation, a Linear Programming procedure returns the first optimal solution it finds usually giving solutions with extremely distributed weights. Second, Multi Objective Linear Programming (MOLP) solutions contains not only the solution that individually optimize each of the objectives, but also other non-dominated solutions that, while non optimal under any given criterion, provide alternative choices for the associated DMU. There may be situations where some of these non-dominated solutions are more preferred to those solutions optimizing individual objectives. Third, the total number of non-dominated solutions associated with a DMU often reflects the stability of a DMU’s efficiency scores relative to the changes in efficiency criteria. Model (1) can be expressed equivalently in the following deviational variable form:
min s:t: m P i¼1 s P r¼1
s P d0 or max h0 ¼ ur yrj0 r¼1
vi xij0 ¼1 ur yrj
(2) m P i¼1
vi xij0 þ dj ¼ 0
ur ; vi ; dj 0
where d0 is the deviation variable for DMU0 and dj the deviation variable for the jth DMU (appeared at the jth original inequality constraint). Under this model, DMU0 is efficient if and only if d0 ¼ 0 (or equivalently, h0 ¼ 1). If DMU0 is not efficient, its efficiency score is h0 ¼ 1d0. The quantity d0, which is bounded by the interval [0.1], can be regarded as a measure of inefficiency (other measures of inefficiency have been proposed by [34e36]). The smaller the value of d0, the less inefficient (and thus the more efficient) DMU0 is. In this sense, we say that classical DEA method (Model(1) or (2)) minimizes DMU0’s inefficiency, as measured by d0, under the constraint that the weighted sum of the outputs is less than or equal to the weighted sum of the inputs for each DMU. Lii and Reeves [33] propose a MCDEA model that is different form other models in that each criterion is an independent objective function. That is, each criterion defines a particular concept of efficiency and there is no prior preference among these efficiency criteria. The form of the proposed MCDEA model depends upon the efficiency criteria used. For a MCDEA problem that has the
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following three criteria, i.e., minimizing d0, minimizing the sum of the deviations, and minimizing the maximum deviation, the MCDEA model can be specified as follows:
min
s P d0 or max h0 ¼ ur yrj0 n P
min
j¼1
r¼1
dj
min M s:t: m P vi xij0 ¼1 i¼1 s P
r¼1
ur yrj
(3) m P i¼1
vi xij0 þ dj ¼ 0
M dj 0 ur ; vi ; dj 0
The first objective of model (3) is identical to the objective of model (1) or (2). The second objective function is a straightforward representation of the deviation sum and the variable M in the third objective represents the maximum quantity among all deviation variables dj (j ¼ 1,.,n). Notice that the feasible region for decision variables ur and ni in model (3) is the same as that in models (1) and (2). The effect of added constraints, Mdj 0 is to make M the maximum deviation. They do not change the feasible region of decision variables. Model (3) is a MOLP and, in a MOLP problem it is generally impossible to find a solution that optimizes all objectives simultaneously. Therefore, the task of a MOLP solution process is not to find an optimal solution but, instead, to find non-dominated solutions (in multiple criteria terminology, a non-dominated solution is also called an efficient solution) and to help select a most preferred one. One fact to point out is that a non-dominated solution set for a MOLP problem will always contain, but is not limited to the optimal solutions obtained by individually optimizing each of the objectives in the MOLP problem under the setting of single objective linear programming. The solution that optimizes the first objective function of model (3) is equivalent to the optimal solution of model (1) or (2). That is, DMU0 is efficient (in the classical sense) if and only the value of d0 corresponding to the solution that optimizes the first objective function of model (3) is zero. In the same way, it can be defined a DMU’s relative efficiency corresponding to the second and third objective criteria in the following way: DMU0 is minsum efficient and minimax efficient if and only if the value of d0 corresponding to the solution that minimizes the second and third objective function
of model (3) is zero. In all the three above definitions, no matter is DMU0 is efficient or not, its DEA efficiency scores is 1d0. Efficiencies defined under minsum and minimax criterion are most restrictive than that defined in the classical DEA and these two criteria generally yield fewer efficient DMUs. That is, it is more difficult for a DMU to achieve minsum or minimax efficiency that to achieve classical DEA efficiency. More precisely, if DMU0 is minsum or minimax efficient, it must also be DEA efficient, because by definition, minsum or minimax efficiency requires d0 ¼ 0. However, if DMU0 is DEA efficient, it may or may not be minsum or minimax P dj is efficient, because d0 does not necessarily imply that M or minimized. Including these new criteria in a DEA model will result in the improvement in discriminating power. On the other hand, P since M or dj are functions of all deviation variables and each P deviation variable is related to a constraint, minimizing M or dj is, in some sense, equivalent to improving tighter constraints on weight variables. 3. Application In this section, the MCDEA model is applied for evaluating the efficiency of 13 RE technologies included in the Renewable Energy Plan approved by the Spanish Government on 2005 [37] for the following areas: Windpower, Hydroelectric, Solar, Biomass, Biogas and Biofuels. The input and output data used to perform the analysis, shown in Table 1, are defined as follows:
Inputs
n1 n2 n3
Investment ratio (Euro103/Kw) Implement period (years) Operating and maintenance costs (Euro103/Kwh)
Outputs u1 u2 u3 u4
Power (MW103) Operating hours(Hours103/year) Useful life (years) Tons of CO2avoided (tCO2106/year)
The results of classical DEA method, solved by LP are given in Table 2. Using model (3), the results obtained are shown in Tables 3e5, corresponding to the three criteria respectively (minimizing d0, minimizing the sum of the deviations, and minimizing the maximum deviation). Efficiency scores in Tables 2 and 3 are identical since they are obtained under the same criterion. As we can see, all DMUs except DMU7 (Solar Thermo-electric P 10 MW) are efficient. However, we can easily observe differences between
Table 1 Input and Output data for the 13 DMUs. DMU
DMU1 DMU2 DMU3 DMU4 DMU5 DMU6 DMU7 DMU8 DMU9 DMU10 DMU11 DMU12 DMU13
Input weights
Windpower P 5 MW Windpower 5 P 10 MW Windpower 10 P 50 MW Hydroelectric P 10 MW Hydroelectric 10 P 25 MW Hydroelectric 25 P 50 MW Solar Thermo-electric P 10 MW Biomass (energetic cultivations) P 5 MW Biomass (forest and agricultural wastes) P 5 MW Biomass (farming industrial wastes) P 5 MW Biomass (forest industrial wastes) P 5 MW Biomass (Co-combustion in conventional central) P 50 MW Biofuels P 2 MW
Output weights
n1
n2
n3
u1
u2
u3
u4
0.937 0.937 1.500 0.700 0.601 5.000 1.803 1.803 1.803 1.803 1.803 0.856 1.503
1 1 1 1.5 2 2.5 2 1 1 1 1 1 1.5
1.47 1.47 1.51 1.45 0.70 0.60 4.2 7.11 5.42 5.42 2.81 4.56 2.51
0.5 1.0 2.5 0.5 2.0 3.5 5.0 0.5 0.5 0.5 0.5 5.6 0.2
2.35 2.35 2.35 3.10 2.00 2.00 2.59 7.50 7.50 7.50 7.50 7.50 7.00
20 20 20 25 25 25 25 15 15 15 15 20 20
1.93 3.22 9.65 0.47 0.26 0.26 0.48 2.52 2.52 2.52 2.52 4.84 5.91
J.R. San Cristóbal / Renewable Energy 36 (2011) 2742e2746 Table 2 Classical DEA results. DMU
DMU1 DMU2 DMU3 DMU4 DMU5 DMU6 DMU7 DMU8 DMU9 DMU10 DMU11 DMU12 DMU13
Efficiency
1 1 1 1 1 1 0.78 1 1 1 1 1 1
Table 5 Minimax DEA results. Input weights
Output weights
DMU
n1
n2
n3
u1
u2
u3
u4
0.14 0.29 0 0.10 0.45 0 0 0 0 0 0 0 0.08
0.40 0.38 0.44 0.32 0.31 0.33 0.20 1.00 1.00 1.00 0.12 0.20 0.12
0.32 0.23 0.37 0.26 0.08 0.28 0.15 0 0 0 0.31 0.17 0.28
0 0 0.38 0.01 0.07 0.28 0.14 0 0 0 0.07 0.18 0.07
1.31 1.30 0 1.05 0 0 0 1.33 1.33 1.33 1.24 0 1.30
3.46 3.44 0 2.70 3.45 0 0.27 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0.01 0 0.01
Table 3 Minimizing d0 results. DMU
DMU1 DMU2 DMU3 DMU4 DMU5 DMU6 DMU7 DMU8 DMU9 DMU10 DMU11 DMU12 DMU13
Efficiency
1 1 1 1 1 1 0.78 1 1 1 1 1 1
Input weights
Output weights
n1
n2
n3
u1
u2
u3
u4
0.10 0 0 0 0 0 0 0 0 0 0 0 0
9.02 7.89 7.84 5.67 4.70 3.83 3.62 3.01 3.61 3.61 6.15 4.02 5.11
0 0.14 0.14 0.10 0.08 0.07 0.07 0.10 0.12 0.12 0.12 0.13 0.09
0 0.06 0.06 0.04 0.04 0.03 0.03 0.02 0.03 0.03 0.05 0.03 0.04
0 0.54 0.54 0.39 0.32 0.26 0.25 0.48 0.57 0.57 0.45 0.64 0.35
5 3.64 3.62 2.62 2.17 1.77 1.67 1.37 1.65 1.65 3.05 1.83 2.36
0 0 0 0 0 0 0 0 0 0 0 0 0
the solutions shown in both Tables. The input and output weights obtained by the MOLP procedure in Table 3 are distributed more evenly than those obtained by classical DEA in Table 2. Table 4 lists the efficiency scores for each DMU under the Minsum criteria. Under this criteria the only DMUs rated as efficient are DMU1 (Windpower P 5 MW), DMU2 (Windpower 5 P 10 MW), DMU3 (Windpower 10 P 50 MW)and DMU11 (Biomass forest industrial wastes P 5 MW). Table 5 lists the efficiency scores for each DMU under the Minimax criterion. In particular, only DMU3 (Windpower 10 P 50 MW) and DMU12 (Biomass Co-combustion in conventional central P 50 MW) are rated as efficient, while the rest of the DMUs, rated as efficient by classical DEA and by
Table 4 Minsum DEA results. DMU
DMU1 DMU2 DMU3 DMU4 DMU5 DMU6 DMU7 DMU8 DMU9 DMU10 DMU11 DMU12 DMU13
Efficiency
1 1 1 0.88 0.67 0.54 0.36 0.53 0.65 0.65 1 0.80 0.86
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Input weights
Output weights
n1
n2
n3
u1
u2
u3
u4
0 0 0 0 0 0 0.10 0.06 0.08 0 0.15 0 0
8.51 8.51 8.48 5.98 4.80 3.89 1.10 1.10 1.34 3.61 3.26 1.80 5.56
0.10 0.10 0.10 0.07 0.06 0.05 0.06 0.11 0.13 0.12 0.14 0.18 0.07
0 0 0 0 0 0 0 0.02 0.03 0.03 0 0.02 0
0.67 0.67 0.67 0.47 0.38 0.31 0.38 0.54 0.70 0.57 0.86 1.64 0.44
4.21 4.21 4.19 2.96 2.37 1.92 1.04 0.74 0.91 1.65 2.36 1.28 2.75
0 0 0 0 0 0 0 0 0 0 0 0 0
DMU1 DMU2 DMU3 DMU4 DMU5 DMU6 DMU7 DMU8 DMU9 DMU10 DMU11 DMU12 DMU13
Efficiency
0.88 0.91 1 0.79 0.68 0.60 0.62 0.58 0.70 0.70 0.82 1 0.72
Input weights
Output weights
n1
n2
n3
u1
u2
u3
u4
0.10 0 0 0 0 0 0 0 0 0 0 0 0
9.02 7.89 7.84 5.67 4.70 3.83 3.62 3.01 3.61 3.61 6.15 4.02 5.11
0 0.14 0.14 0.10 0.08 0.07 0.07 0.10 0.12 0.12 0.12 0.13 0.09
0 0.06 0.06 0.04 0.04 0.03 0.03 0.02 0.03 0.03 0.05 0.03 0.04
0 0.54 0.54 0.39 0.32 0.26 0.25 0.48 0.57 0.57 0.45 0.64 0.35
5 3.64 3.62 2.62 2.17 1.77 1.67 1.37 1.65 1.65 3.05 1.83 2.36
0 0 0 0 0 0 0 0 0 0 0 0 0
Minsum criteria, are no longer efficient with respect to the Minimax criteria. As we can see, the only DMU rated as efficient under the three criteria is DMU3 (Windpower 10 P 50 MW) and it can be considered the only non-dominated solution. 4. Conclusions To find a non-dominated solution, also called an efficient solution in multiple criteria terminology, and to select the most preferred one is the main task of a MOLP. In this paper, a MCDEA is applied under three different criteria, (minimizing d0, minimizing the sum of the deviations, and minimizing the maximum deviation) each of one is an independent objective function and so it defines a particular concept of efficiency, a key managerial concept in the electricity-generating industry. As we can see, including more restrictive criteria than that defined in the classical DEA entails that, technologies that are efficient under classical DEA, prove to be inefficient under the MCDEA model. Decision-makers should participate in developing target setting or policy making scenarios that would enable managers to consider simultaneously inputs and outputs in the assessment of targets with the aim of increasing efficiency. References [1] Madlener R, Antunes CH, Dias LC. Assessing the performance of biogas plants with multi-criteria and data envelopment analysis. European Journal of Operations Research 2006;197:1084e94. [2] Aras H, Erdogmus S, Koc E. Multi-criteria selection for a wind observation station location using analytic hierarchy process. Renewable Energy 2004;23: 1383e92. [3] Haralambopoulos DA, Polatidis H. Renewable energy projects: structuring a multicriteria group decision-making framework. Renewable Energy 2003; 28:961e73. [4] Golany B, Roll Y, Ryback D. Measuring efficiency of power plants in Israel by data envelopment analysis. IEEE Transactions on Engineering Management 1994;41(3):291e301. [5] Sadjadi SJ, Omrani H. Data envelopment analysis with uncertain data: a application for Iranian electricity distribution companies. Energy Policy 2008;36:4247e54. [6] Charnes A, Cooper WW, Rhodes E. Measuring the efficiency of decisionmaking units. European Journal of Operational Research 1978;2:429e44. [7] Athanassopoulos AD, Lambropoulos N, Seiford L. Data envelopment scenario analysis for setting targets to electricity generating plants. European Journal of Operations Research 1999;15:413e28. [8] Hu JL, Kao CH. Efficient energy-savings targets for APEC economies. Energy Policy 2007;35:373e82. [9] Hu JL, Wang SC, Yeh FY. Total-factor water efficiency of regions in China. Resources Policy 2006;31:217e30. [10] Cote DO. Firm efficiency and ownership structure-the case of U.S. electric utilities using panel data. Annals of Public and Cooperative Economics 1989; 60(4):431e50. [11] Hjalmarsson L, Veiderpass A. Efficiency and ownershipin Swedish electricity retail distribution. The Journal of Productivity Analysis 1992;3(1/2):7e23.
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