Selecting the optimal renewable energy using multi criteria decision making.
Yazdani-Chamzini, Abdolreza ; Fouladgar, Mohammad Majid ; Zavadskas, Edmundas Kazimieras 等
1. Introduction
Renewable energy is recognized as a key resource for future life
and plays a significant role in supplying energy and reducing air
pollutants and greenhouse gas emissions. Main renewable energy resources
are (Kaltschmitt et al. 2007): (i) solar radiation, (ii) wind energy,
(iii) hydropower, (iv) photosynthetically fixed energy, and (v)
geothermal energy. In 2009, about 16% of global final energy consumption
comes from renewable energies, with 10% coming from traditional biomass,
3.4% from hydropower, and 2.6% from all other renewable energies (REN21
2011). This is due to the negative effect of fossil fuels on the
environment, the precarious nature of dependency on fossil fuel imports,
and the advent of renewable energy alternatives (Cristobal et al. 2011).
These are environment-friendly and capable of replacing conventional
sources in a variety of applications at competitive prices
(Haralambopoulos, Polatidis 2003; Aras et al. 2004).
The selection of different energy investment projects is a multi
criteria decision making (MCDM) problem, because various criteria should
be analyzed and considered that are often in conflicting with each
other. These criteria affect the success of a renewable energy project.
For instance, two criteria that could be employed in renewable energy
selection might be power and operation and maintenance costs. There are
two conflicting criteria because an attempt in order to enhance power
possibly causes a growth in operation and maintenance costs. According
to the capability and effectively of MCDM and the need to incorporate
social, economic, technological, and environmental considerations in
energy issues, there is a vast MCDM literature on energy problems.
Beccali et al. (2003) applied the ELECTERE (ELimination Et Choix
Traduisant la Realite or Elimination and Choice Translating Reality)
method to determine regional level for the diffusion of renewable energy
technology. Heo et al. (2010) used fuzzy analytical hierarchy process
(FAHP) to analyze the assessment factors for renewable energy
dissemination program evaluation. Kahraman et al. (2010) applied a
comparative analysis for multi attribute selection among renewable
energy alternatives using fuzzy axiomatic design and FAHP.
Evans et al. (2009) employed sustainability indicators to assess
renewable energy technologies. They indicators include price of
generated electricity, greenhouse gas emissions during the full life
cycle of the technology, availability of renewable sources, efficiency
of energy conversion, land requirements, water consumption and social
impacts. In this study, each indicator was assumed to have equal
importance to sustainable development and utilized to rank the renewable
energy technologies against their impacts.
Lee et al. (2009) utilized the FAHP technique in order to
prioritize energy technologies against high oil prices. The results show
that building technology is the most preferred technology in the sector
of energy technologies against high oil prices, and the coal technology
and transportation technology are located in the second and third place,
respectively.
Cavallaro (2005) set out the application of PROMETHEE to assess
sustainable energy options. Oberschmidt et al. (2010) developed the
modified PROMETHEE approach for assessing energy technologies. Sola et
al. (2011) proposed a multi-criteria model using the PROMETHEE II
method, with the aim of ranking alternatives for induction motors
replacement. Lee et al. (2011) used a fuzzy AHP approach to prioritize
the weights of hydrogen energy technologies in the sector of the
hydrogen economy. Virtanen (2011) developed the PROMETHEE II method to
select the optimal energy system for buildings and districts. In order
to achieve the renewable energy policy goals, Shen et al. (2011) showed
how different policy goals lead to corresponding renewable energy
sources. In this paper, the relative importance of each goal was
evaluated by using AHP.
Anagnostopoulos et al. (2007) developed a logic-based fuzzy multi
criteria decision support system using the ideal and the anti-ideal
solutions in order to assess the sustainability of renewable energy
policies. Braune et al. (2009) presented a review of the recent
literature to analyze the potential of multi criteria decision analysis
for real world applications. The Multi-Attribute Utility Theory (MAUT)
is utilized for the evaluation of renewable energy alternatives by I.
Kaya and Kahraman (2011).
Doukas et al. (2009) developed a linguistic TOPSIS (technique for
order preference by similarity ideal solution) model to evaluate the
sustainability of renewable energy options. Kabir and Shihan (2003) used
the AHP method for selection of renewable energy sources. Nigim et al.
(2004) proposed two multi-criteria decision-making (MCDM) tools for
prioritizing local viable renewable energy sources. The first tool is
AHP and the second is sequential interactive model for urban
sustainability (SIMUS). In this paper, AHP is based on community
participation in the decision-making process through data collection and
elicitation of expert opinions, and SIMUS uses mathematical linear
programming manipulation, which also and primarily relies on elicitation
of expert opinions, but in a less subjective and more objective manner.
Axiomatic design (AD) methodology is proposed for the selection
among renewable energy alternatives under fuzzy environment by Kahraman
et al. (2010). T. Kaya and Kahraman (2011) proposed a modified fuzzy
TOPSIS methodology for the selection of the best energy technology
alternative. Kahraman and Kaya (2010) proposed a fuzzy multicriteria
decision-making methodology for the selection among energy policies. The
proposed method is based on the analytic hierarchy process (AHP) under
fuzziness.
Yi et al. (2011) developed an AHP method based on benefit,
opportunity, cost, and risk (BOCR) in order to select sustainable
renewable energy source for energy assistance to North Korea. Kaya and
Kahraman (2010) proposed an integrated VIKOR-AHP methodology to the
selection of the best energy policy and production site. They applied
pairwise comparison matrices of AHP for determining the weights of the
evaluation criteria. Cristobal (2011) applied the VIKOR method and the
AHP technique for the selection of a renewable energy project
corresponding to the renewable energy plan launched by the Spanish
Government. The AHP method is employed to weight the importance of the
various evaluation criteria, which allows decision-makers to determine
these values based on their preferences.
Balezentiene et al. (2013) proposed a MCDM framework for
prioritization of energy crops based on fuzzy MULTIMOORA method which
enables to tackle imprecise information. Streimikiene and Balezentis
(2013) developed a MCDM methodology for climate change mitigation
policies ranking in Lithuania based on priorities of sustainable energy
development. Streimikiene et al. (2012) developed a multi-criteria
decision support framework based on MULTIMOORA and TOPSIS for choosing
the most sustainable electricity production technologies.
It is clear that the MCDM methods have demonstrated their
capability and effectiveness as a problem-solving tool in energy issues.
COPRAS (COmplex PRoportional ASsessment) is an MCDM technique that
is employed by different researchers in order to solve many various
problems. This method has some advantages as follows: 1) COPRAS allows
simultaneous consideration of the ratio to the ideal solution and the
negative ideal solution, 2) simple and logical computations, and 3)
results are obtained in shorter time than other methods such as AHP and
ANP.
In order to calculate the importance weights of criteria,
analytical hierarchy process (AHP) can be employed since it is based on
pairwise comparisons. This technique provides an organized description
of the hierarchical interaction or connection among the elements
(impacts, criteria or alternatives) (Reza et al. 2011).
In this paper, an integrated AHP-COPRAS method is proposed to
select the most appropriate renewable energy project among the feasible
alternatives. In the proposed method, AHP computes the relative
importance of evaluation criteria. Then, the COPRAS method is used to
obtain the final ranking order of alternatives.
2. Analytical hierarchy process (AHP)
Analytical hierarchy process (AHP) was first introduced by Saaty
(1980). The AHP is a powerful tool that helps decision makers by
organizing perceptions and judgments into a multi-level hierarchic
structure. This technique decomposes a complex problem into a structure
of hierarchy and then aggregates the solutions of all the sub problems
into a conclusion (Saaty 1994). AHP uses pair-wise comparisons to obtain
the relative importance of a criterion with respect to other criterion
(Lashgari et al. 2011; Azimi et al. 2011; Fouladgar et al. 2012 a, b, c;
Yazdani-Chamzini, Yakhchali 2012; Lashgari et al. 2012). The importance
of pairwise comparisons in decision making is caused to the AHP
technique be a popular method for determining weights in multi criteria
problems.
3. COPRAS (COmplex PRoportional ASsessment) method
COPRAS is an MCDM method that was developed by Zavadskas and
Kaklauskas (1996). This method assumes that the significance and
priority of the investigated versions depend directly on and are
proportional to a system of criteria adequately describing the
alternatives and to the values and weights of the criteria (Banaitiene
et al. 2008). This technique allows simultaneous consideration of the
ratio to the ideal solution and the negative ideal solution. The ideal
solution is a solution that minimizes the cost criteria and maximizes
the benefit criteria; whereas, the negative ideal solution maximizes the
cost criteria and minimizes the benefit criteria. The COPRAS technique
is employed by different researchers to model decision making problems.
4. Proposed model
The proposed model for ranking renewable energy, composed of AHP
and COPRAS techniques, has following three steps:
1. Criteria identification.
2. Criteria weight calculation.
3. Evaluation and selection of renewable energies with COPRAS.
Schematic diagram of the proposed model for selecting the optimal
renewable energy is depicted in Fig. 1.
[FIGURE 1 OMITTED]
4.1. Criteria identification
In the first step, renewable energy sources and the evaluation
criteria which will be used in decision making process are identified
and the decision hierarchy is organized. The AHP model is constructed
such that the first level comprises the overall goal, the second level
contains of criteria, and the last level includes alternatives.
4.2. Criteria weight calculation
In this step, pair-wise comparison matrices are established to
obtain the weights of evaluation criteria. Decision makers make their
evaluations using the scale presented in Table 1, to assign the values
of the elements of pair-wise comparison matrix. The relative weights of
the evaluation criteria are computed based on this matrix.
4.3. Evaluation of renewable energies with COPRAS
In the last step, evaluation of alternatives is accomplished by
using COPRAS approach. Prioritizing renewable energies is determined
based on the values of [N.sub.i] derived by COPRAS. In the last phase of
this step, the most appropriate alternative with the top value of 100%
is selected.
5. Case analyses
An example in three different cases considered to demonstrate and
validate the proposed method. Cristobal (2011) proposed VIKOR method for
selection of a renewable energy investment project. This example problem
is related with selection of a suitable renewable energy for the
Renewable Energy Plan launched by the Spanish Government in 2005.
Proposed model is applied to rank renewable energies in three various
cases.
These cases are as follows:
Case 1: The weights of criteria are similar to the weights used by
Cristobal (2011);
Case 2: The weights of two criteria (selected as randomly) are
inflated by keeping those of the remaining criteria constant;
Case 3: The weights of three criteria (selected as randomly) are
inflated by keeping those of the remaining criteria constant.
Case 1
The application is based on the steps provided in previous section
and described as following.
Step 1: criteria identification
In this step, criteria to be used in the model include Power (P),
Investment Ratio (IR), Implementation Period (IP), Operating Hours (OH),
Useful Life (UL), Operation and Maintenance Costs (O&M) and tons of
emissions of C[O.sub.2] avoided per year (tC[O.sub.2]/y). In this
problem, P, OH, UL, and tC[O.sub.2]/y are benefit criteria whereas IR,
IP, and O&M are cost criteria.
There are 13 alternative renewable energy projects as presented in
Table 2. The performance ratings of alternatives with respect to each
criterion are given in Table 3. Thus, the result of decision hierarchy
is depicted in Fig. 2.
[FIGURE 2 OMITTED]
Decision hierarchy includes three levels; the overall goal of the
decision process is in the first level, the second level of the
hierarchy comprises the evaluation criteria and renewable energy
projects are located in the last level of the hierarchy.
Step 2: criteria weight calculation
In this step, the relative importance of evaluation criteria with
respect to the goal is calculated. To achieving the aim, one has to form
a pairwise comparison matrix based on scale presented in Table 1. For
example, when P and IR are pairwise compared, P is judged as five time
important than IR. Table 4 presents the results of pairwise comparison
of evaluation criteria.
In order to obtain the vector W = ([W.sub.1], [W.sub.2], ...,
[W.sub.N]) which indicates the importance weights of criteria, each
entry in column i of pairwise comparison matrix is divided by the sum of
the entries in column i to form the normalized matrix in which the sum
of the entries in each column is 1. Then the average of the entries in
row i of the normalized matrix is calculated to obtain the vector W. The
CR is found to be acceptable, that is, less than 0.1. Priority weights
form W = (0.319, 0.09, 0.026, 0.116, 0.134, 0.042, 0.273) vector.
It is observed that power (0.319) is the most important criterion
in renewable energy selection. It is followed by tons of emissions of
C[O.sub.2] avoided per year (0.273), useful life (0.134) operating hours
(0.116), operation and maintenance costs (0.042), implementation period
(0.026), and investment ratio (0.09).
Step 3: Evaluation of renewable energies with COPRAS
To apply the COPRAS method, the decision matrix presented in Table
3. Table 5 shows the weighted normalized decision matrix.
The values of [P.sub.j] and [R.sub.i] are presented in Table 5.
Next, the relative weight and the utility degree of each alternative are
computed. The final rank of alternatives is listed in the last column of
Table 5. Fig. 3 depicts the ranking of renewable energies according to
the [N.sub.i] values. According to the utility degree, the best
renewable energy is A12, i.e. N12 = 100%. The utility degree has the
highest value, meaning that the needs of the decision maker and the
project are satisfied the best (Banaitiene et al. 2008).
[FIGURE 3 OMITTED]
Often all the MCDM methods criticized for the fact that in some
cases using different methods, different results are obtained. These
differences across algorithms occur are caused by (Zavadskas, Turskis
2011):
- Using weights differently;
- Different selection of the best solution;
- Attempt to scale objectives;
- Introducing additional parameters that affect solution.
Hence the evaluation process should be carried out by different
methods. Based on the relative weights of the evaluation criteria
obtained by AHP, the five MCDM tools, including SAW (simple additive
weighting) (MacCrimmon 1968), TOPSIS (technique for order preference by
similarity to ideal solution) (Hwang, Yoon 1981), VIKOR
(VlseKriterijumska Optimizacija I Kompromisno Resenje) (Opricovic 1998),
ARAS (additive ratio assessment) (Zavadskas, Turskis 2010) and MOORA
(Multi-Objective Optimization on the basis of Ratio Analysis) (Brauers,
Zavadskas 2006) were adopted for evaluating and ranking the feasible
renewable energies in order to validate the capability and effectiveness
of the proposed model.
The performance ranking order of the thirteen renewable energies
using SAW, TOPSIS, VIKOR, ARAS, and MOORA is as follows:
SAW: A12 > A3 > A6 > A7 > A13 > A5 > A2 > A11
> A9 = A10 > A8 > A1 > A4,
TOPSIS: A12 > A3 > A7 > A6 > A13 > A2 > A5 >
A11 > A9 = A10 > A8 > A1 > A4,
VIKOR: A12 > A3 > A7 > A6 > A5 A2 > A13 > A11
> A4 > A9 = A10 > A8 > A1,
ARAS: A12 > A3 > A7 > A13 > A5 > A2 > A11 > A9
= A10 > A8 > A1 > A4,
MOORA: A12 > A3 > A13 > A6 > A7 > A2 > A5 >
A11 > A9 = A10 > A8 > A1 > A4.
The ranking orders of different methods are listed in Table 6.
From Table 6, all these methods suggest A12 (i.e. Biomass
(co-combustion in conventional central) P [less than or equal to] 50MW)
as the first choice and A3 (i.e. Wind power 10 [less than or equal to] P
[less than or equal to] 50MW) as the second choice. Thus, the present
method is validated.
The rankings of six methods are then compared with the final
ranking (the arithmetic average of each row) results using the
Spearman's rank correlation coefficients in order to demonstrate
the capability and effectiveness of each method. The Spearman's
rank correlation coefficients between the final ranking and the proposed
model, VIKOR, SAW, MOORA, ARAS and TOPSIS methods are 0.994, 0.885,
0.986, 0.96, 0.994 and 0.994 respectively. The results show that the
proposed model (AHP-COPRAS), TOPSIS and ARAS outperform other methods.
It is followed by SAW, MOORA and VIKOR methods. The high Spearman's
rank correlation coefficient between the proposed model and the final
ranking demonstrates the potential application of the proposed model.
Case 2
The new application is based on the steps provided in previous
section and described as following.
Step 1 for case 2 is identical to step 1 for case 1.
Step 2 for case 2 is similar to step 2 for case 1, but with this
difference that only the weights calculated by the AHP technique are
changed in order to establish a new condition to validate the proposed
model more comprehensive. The new weights are obtained by increasing
fifty percent in the weights of two criteria O&M and tC[O.sub.2]/y,
then normalizing the final weights. The results of the importance
weights of evaluation criteria are computed as W = (0.276, 0.078, 0.023,
0.1, 0.116, 0.055, 0.352).
Based on above assumptions, tons of emissions of C[O.sub.2] avoided
per year (0.352) is the most critical criterion in this case. It is
followed by power (0.276), useful life (0.116) operating hours (0.1),
investment ratio (0.078), operation and maintenance costs (0.055), and
implementation period (0.023).
Step 3: Evaluation of renewable energies with COPRAS
According to the weights of evaluation criteria derived from AHP in
previous step, the COPRAS technique is applied to rank the feasible
alternatives in order to select the best renewable energy among a pool
of possible alternatives. The decision matrix presented in Table 3 is
normalized, and the results are depicted in Table 7. Since the weights
of evaluation criteria are different, the weighted normalized decision
matrix results are shown in Table 8.
The values of [P.sub.j] and [R.sub.i] are listed in Table 8. Then,
the utility degree of each alternative is computed as depicted in Table
8 and Fig. 4. The final rank of alternatives is presented in the last
column of Table 8. According to the utility degree, the most appropriate
renewable energy is A3, i.e. N3 = 100%. It is followed by A12 (96.08%),
A13 (59%), A7 (55.85%), A2 (47.68%), A5 (39.34%), A11 (38.68%), A9 = A10
(37.22%), A8 (36.6%), A1 (35.6%) and A4 (25.55%).
[FIGURE 4 OMITTED]
Finally, according to the relative importance of the evaluation
criteria obtained in step 2, five MCDM tools, including SAW, TOPSIS,
VIKOR, ARAS and MOORA, are applied for ranking the feasible
alternatives. Based on these five methods, the alternatives are ranked
in the descending order indicating the most preferred and least
preferred renewable energy as shown below:
SAW: A12 > A3 > A13 > A6 > A7 > A2 > A5 > A11
> A9 = A10 > A8 > A1 > A4,
TOPSIS: A3 > A12 > A13 > A7 > A6 > A2 > A11 >
A9 = A10 > A8 > A5 > A1 > A4,
VIKOR: A3 > A12 > A13 > A7 > A6 > A2 > A11 >
A9 = A10 > A8 > A1 > A5 > A4,
ARAS: A3 > A12 > A13 > A7 > A6 > A2 > A5 > A11
> A9 = A10 > A8 > A1 > A4,
MOORA: A3 > A12 > A13 > A6 > A7 > A2 > A11 >
A5 > A9 = A10 > A8 > A1 > A4.
The ranking orders of six techniques are presented in Table 9.
As shown in Table 9, all of the methods (with exception of the SAW
method) suggest A3 (i.e. Wind power 10 [less than or equal to] P [less
than or equal to] 50MW) as the first choice. Whereas, the SAW method
proposes A12 (i.e. Biomass (co-combustion in conventional central) P
[less than or equal to] 50MW) as the best choice.
The Spearman's rank correlation coefficients between the final
ranking and the proposed model, VIKOR, SAW, MOORA, ARAS and TOPSIS
methods are 0.978, 0.923, 0.969, 0.975, 0.978 and 0.958 respectively.
According to the results obtained by different methods, the proposed
model and the ARAS technique outperform other methods. It is followed by
MOORA, SAW, TOPSIS and VIKOR methods. Based on the Spearman's rank
correlation coefficient, the performance of the VIKOR method is poorer
than other methods in selecting the optimum alternative. Despite the
fact that SAW is located in higher rank than TOPSIS and VIKOR, but based
on the consensus of the five methods, this method is the poorest method
in order to choose the optimum renewable energy. In this case, similar
to case 1, there is a high Spearman's rank correlation coefficient
between the proposed model and the final ranking. Therefore, the rank of
alternatives by using the present method is validated.
Case 3
The new case is implemented according to the steps described in
previous section as following.
Step 1 for case 3 is identical to step 1 for cases 1 and 2.
Step 2 for case 3 is similar to step 2 for case 1 and 2, but with
this difference that only the weights calculated by the AHP technique
are varied in order to establish a new condition to validate the
proposed model more precise and accurate. For this reason, the weights
of three criteria P, O&M and tC[O.sub.2]/y are changed by increasing
from 0.319 to 0.415 (increasing 30%), 0.042 to 0.063 (increasing 50%)
and 0.273 to 0.409 (increasing 50%) respectively; next the final weights
are normalized. Finally, the relative weights of evaluation criteria are
obtained as W = (0.331, 0.072, 0.021, 0.092, 0.107, 0.05, 0.327).
Based on what mentioned above, power criterion (0.331) is more
important than other criteria in case 3. It is followed by tons of
emissions of C[O.sub.2] avoided per year (0.327), useful life (0.107)
operating hours (0.092), investment ratio (0.072), operation and
maintenance costs (0.05), and implementation period (0.021).
Step 3: Evaluation of renewable energies with COPRAS
Similarly, COPRAS was applied to rank the renewable energies based
on the relative weights of the evaluation criteria by AHP in previous
step. After constructing the normalized decision matrix, the weighted
normalized decision matrix results are presented in Table 10.
The values of [P.sub.j] and [R.sub.i] are presented in Table 10.
Next, the utility degree of each alternative is shown in Table 10 and
Fig. 5. The ranking results of thirteen alternatives are listed in the
last column of Table 10. Based on the values of the utility degree, the
optimal renewable energy is A12, i.e. N3 = 100%. It is followed by A3
(96.8%), A7 (61.94%), A13 (54.32%), A6 (54.28%), A2 (45.73%), A5
(40.3%), A11 (36.42%), A9 = A10 (35.09%), A8 (34.52%), A1 (33.61%) and
A4 (24.43%).
[FIGURE 5 OMITTED]
In the end, five MCDM methods (SAW, TOPSIS, VIKOR, ARAS and MOORA)
are employed to prioritize the alternatives based on the weights of the
criteria calculated in step 2. By applying these five methods, the rank
orders of the alternatives are computed.
The results of different methods are presented in the following:
SAW: A12 > A3 > A6 > A7 > A13 > A5 > A2 > A11
> A9 = A10 > A8 > A1 > A4,
TOPSIS: A3 > A12 > A7 > A13 > A6 > A2 > A5 >
A11 > A9 = A10 > A8 > A1 > A4,
VIKOR: A12 > A3 > A2 > A7 > A6 > A13 > A5 >
A11 > A9 = A10 > A1 > A8 > A4,
ARAS: A12 > A3 > A7 > A6 > A13 > A2 > A5 > A11
> A9 = A10 > A8 > A1 > A4,
MOORA: A12 > A3 > A13 > A7 > A6 > A2 > A5 >
A11 > A9 = A10 > A8 > A1 > A4.
Table 11 shows the ranking orders of six methods.
As seen in Table 11, all of the methods (with exception of the
TOPSIS method) propose A12 (i.e. Biomass (co-combustion in conventional
central) P [less than or equal to] 50MW) as the best choice and A3 as
the second choice. Whereas, TOPSIS suggests A3 (i.e. Wind power 10 [less
than or equal to] P [less than or equal to] 50MW) as the first choice.
Therefore, the rank of alternatives by using the present method is
validated.
Based on the results obtained by different methods, the
Spearman's rank correlation coefficients between the final ranking
and the proposed model, VIKOR, SAW, MOORA, ARAS and TOPSIS methods are
0.994, 0.936, 0.97, 0.983, 0.994 and 0.987 respectively. According to
the Spearman's rank correlation coefficients, the proposed model
and the ARAS technique outperform other methods. It is followed by the
TOPSIS, MOORA, SAW and VIKOR methods. In this case, according to the
consensus of the five methods, the output of the TOPSIS method is the
poorest result in order to select the best alternative although its
Spearman's rank correlation coefficient is higher than three
methods MOORA, SAW and VIKOR. The high Spearman's rank correlation
coefficient between the proposed model and the final ranking
demonstrates that the proposed model outperform other methods.
6. Discussions
This research conducted a renewable energy selection problem using
the MCDM methods. AHP and COPRAS techniques were applied in decision
making process for obtaining the relative weights of evaluation
criteria, ranking the feasible alternatives and selecting the optimum
renewable energy among a pool of alternatives, respectively.
Furthermore, five MCDM analytical methods (i.e. SAW, MOORA, TOPSIS, ARAS
and VIKOR) were employed in decision making problem for the validation
of the proposed model. Based on the results of the computations, some
essential findings were discussed as follows.
In this study, AHP is used to calculate the relative importance of
the evaluation criteria of the renewable energies based on pairwise
comparison matrix. As presented in Table 5, the result of the AHP method
reveals that the "power" criterion is the most important
evaluation criterion. This is because the performance of renewable
energy project is strongly connected with generating power. Furthermore,
based on environmental regulations in order to reduce greenhouse gas
emissions, the criterion of "tons of emissions of C[O.sub.2]
avoided per year" is ranked as the second most critical criterion.
Besides, the COPRAS method is employed to rank the renewable
energies in order to select the optimum alternative. Often the ranking
results of the different MCDM methods are not identical. Therefore
assessment should be accomplished by different methods to validate the
result obtained by the proposed model. Therefore this study adopted five
MCDM methods VIKOR, TOPSIS, ARAS, MOORA and SAW to evaluate the
alternatives of this problem. For achieving the aim, an example is
illustrated to show the capability of the proposed model. In order to
generate several different conditions for ranking the alternatives, the
weights of evaluation criteria are changed to make three various cases.
Hence, based on the relative weights of the evaluation criteria
obtained by AHP, the performance ranking order of the thirteen renewable
energies for three cases using COPRAS is presented in Table 12.
Similarly, the ranking order is fulfilled by TOPSIS, VIKOR, ARAS, MOORA
and SAW and the results derived from these methods in three various
cases are listed in Table 12.
Based on the ranking order of each method and the Spearman's
rank correlation coefficients between the final ranking and each method,
it can be found that the proposed model has a high potential in
selecting the best renewable energy. The output of the model for three
cases is better than four methods VIKOR, ARAS, SAW and MOORA.
According to the results derived from the proposed model for case
1, the performance of the proposed model, TOPSIS and ARAS are the best;
so that, the ranking orders of all alternatives are identical. For case
2, based on the results derived from both ARAS and the proposed model,
the ranking orders of all alternatives are the same. For case 2, the
results obtained by SAW are poorest output based on the consensus of the
five methods. For case 3, the results obtained by TOPSIS are the poorest
result because all other methods suggest A12 as the first choice;
whereas, TOPSIS proposes A3 as the best alternative.
However, it can be understood that the results of the proposed
model (COPRAS-based model) is more stable than TOPSIS and SAW
techniques. The output of the proposed model and ARAS are the best in
comparison with all other methods in this problem.
7. Conclusions
The rapid growth of demand for energy by the ever increasing
population and the need for reducing air pollutants and greenhouse gas
emissions generated by fossil fuel caused to the renewable energy
resources be developed. Renewable energies are different and each of
them have relative advantage and drawbacks; so that, it is found by
researchers that it is difficult to evaluate the different alternatives
and select the best alternative among all the feasible alternatives
because there are tangible and intangible criteria that affect decision
making.
The current study proposes an MCDM evaluation model for selecting
the most appropriate renewable energy. This method is formed based on
the AHP and COPRAS techniques, which AHP is applied for calculating the
weights of evaluation criteria and COPRAS is used to rank the existing
alternatives. The proposed model can help decision makers in reducing
the decision failures. In this paper, an example in three different
cases is illustrated to demonstrate the potential application of the
proposed model. In order to validate the output of the model, it is
compared with five MCDM analytical tools, including VIKOR, SAW, TOPSIS,
ARAS and MOORA. It indicates that the final values of the proposed model
outperform VIKOR, SAW, TOPSIS and MOORA methods. The final values of the
thirteen alternatives obtained by ARAS and the proposed model are close
to each other. Therefore, the proposed model is found to be an
appropriate method of assessment to rank the renewable energies.
Likewise, the proposed model offers a general procedure that can be
applicable to diverse selection problems that incorporate complexity and
a number of evaluation criteria. The results derived from the proposed
model are logical and stable to fulfil when compared with the other MCDM
methods.
Caption: Fig. 1. Schematic diagram of the proposed model
Caption: Fig. 2. Decision hierarchy
Caption: Fig. 3. The utility degrees of alternatives obtained by
AHP-COPRAS (Case 1)
Caption: Fig. 4. The utility degrees of alternatives obtained by
AHP-COPRAS (Case 2)
Caption: Fig. 5. The utility degrees of alternatives obtained by
AHP-COPRAS (Case 3)
doi: 10.3846/16111699.2013.766257
Received 31 October 2012; accepted 10 January 2013
References
Anagnostopoulos, K.; Doukas, H.; Psarras, J. 2007. A logic-based
fuzzy multicriteria decision support system using the ideal and the
anti-ideal solutions: assessing the sustainability of renewable energy
policines, Advances in Fuzzy Sets and Systems 2(3): 239-266.
Aras, H.; Erdogmus, S.; Koc, E. 2004. Multi-criteria selection for
a wind observation station location using analytic hierarchy process,
Renew Energy 23(13): 83-92.
Azimi, R.; Yazdani-Chamzini, A.; Fouladgar, M. M.; Zavadskas, E.
K.; Basiri, M. H. 2011. Ranking the strategies of mining sector through
ANP and TOPSIS in a SWOT framework, Journal of Business Economics and
Management 12(4): 670-689.
http://dx.doi.org/10.3846/16111699.2011.626552
Balezentiene, L.; Streimikiene, D.; Balezentis, T. 2013. Fuzzy
decision support methodology for sustainable energy crop selection,
Renewable and Sustainable Energy Reviews 17(1): 83-93.
http://dx.doi.org/10.10167j.rser.2012.09.016
Banaitiene, N.; Banaitis, A.; Kaklauskas, A.; Zavadskas, E. K.
2008. Evaluating the life cycle of a building: a multivariant and
multiple criteria approach, Omega 36: 429-441.
http://dx.doi.org/10.10167j.omega.2005.10.010
Beccali, M.; Cellura, M.; Mistretta, M. 2003. Decision-making in
energy planning. Application of the Electre method at regional level for
the diffusion of renewable energy technology, Renewable Energy 28(13):
2063-2087. http://dx.doi.org/10.1016/S0960-1481(03)00102-2
Brauers, W. K. M.; Zavadskas, E. K. 2006. The MOORA method and its
application to privatization in a transition economy, Control and
Cybernetics 35(2): 443-468.
Braune, I.; Pinkwart, A.; Reeg, M. 2009. Application of
mulit-criteria analysis for the evaluation of sustainable energy systems
- a review of recent literature, in 5th Dubrovnic Conference on
Sustainable Development of Energy, Water and Environment Systems. ISBN
978-953-6313-97-6.
Cavallaro, F. 2005. An Integrated multi-criteria system to assess
sustainable energy options: an application of the Promethee method. FEEM
Working Paper No. 22 [online], [cited 11 October 2012]. Available from
Internet: http://ssrn.com/abstract=666741
Cristobal, J. R. S. 2011. Multi-criteria decision-making in the
selection of a renewable energy project in Spain: the Vikor method,
Renewable Energy 36: 498-502.
http://dx.doi.org/10.1016/j.renene.2010.07.031
Doukas, H.; Karakosta, Ch.; Psarras, J. 2009. A linguistic TOPSIS
model to evaluate the sustainability of renewable energy options,
International Journal of Global Energy Issues 32(1-2): 102-118.
http://dx.doi.org/10.1504/IJGEI.2009.027976
Evans, A.; Strezov, V.; Evans, T. J. 2009. Assessment of
sustainability indicators for renewable energy technologies, Renewable
and Sustainable Energy Reviews 13(5): 1082-1088.
http://dx.doi.org/10.1016/j.rser.2008.03.008
Fouladgar, M. M.; Yazdani-Chamzini, A.; Zavadskas, E. K.;
Yakhchali, S. H.; Ghasempourabadi, M. H. 2012a. Project portfolio
selection using fuzzy AHP and VIKOR techniques, Transformations in
Business & Economics 11(25): 213-231.
Fouladgar, M. M.; Yazdani-Chamzini, A.; Lashgari, A.; Zavadskas, E.
K.; Turskis, Z. 2012b. Maintenance strategy selection using AHP and
COPRAS under fuzzy environment, International Journal of Strategic
Property Management 16(1): 85-104.
http://dx.doi.org/10.3846/1648715X.2012.666657
Fouladgar, M. M.; Yazdani-Chamzini, A.; Zavadskas, E. K.; Moini, S.
H. H. 2012c. A new hybrid model for evaluating the working strategies:
case study of construction company, Technological and Economic
Development of Economy 18(1): 164-188.
http://dx.doi.org/10.3846/20294913.2012.667270
Haralambopoulos, D. A.; Polatidis, H. 2003. Renewable energy
projects: structuring a mul-ticriteria group decision-making framework,
Renew Energy 28(9): 61-73.
Heo, E.; Kim, J.; Boo, K. J. 2010. Analysis of the assessment
factors for renewable energy dissemination program evaluation using
fuzzy AHP, Renewable and Sustainable Energy Reviews 14(8): 2214-2220.
http://dx.doi.org/10.1016/j.rser.2010.01.020
Hwang, C. L.; Yoon, K. 1981. Multiple attribute decision making:
methods and applications, New York: Sprmger-Verlag.
http://dx.doi.org/10.1007/978-3-642-48318-9
Kabir, A. B. M. Z.; Shihan, S. M. A. 2003. Selection of renewable
energy sources using analytic hierarchy process, in Proceedings of the
International Symposium on Analytic Hierarchy Process ISAHP, August 7-9,
2003, Bali, Indonesia, 267-276.
Kahraman, C.; Cebi, S.; Kaya, I. 2010. Selection among renewable
energy alternatives using fuzzy axiomatic design: the case of Turkey,
Journal of Universal Computer Science 16(1): 82-102.
Kahraman, C.; Kaya, I. 2010. A fuzzy multicriteria methodology for
selection among energy alternatives, Expert Systems with Applications
37: 6270-6281. http://dx.doi.org/10.1016/j.eswa.2010.02.095
Kaya, I.; Kahraman, C. 2011. Evaluation of green and renewable
energy system alternatives using a multiple attribute utility model: the
case of Turkey, Soft Computing in Green and Renewable Energy Systems:
Studies in Fuzziness and Soft Computing 269: 157-182.
http://dx.doi.org/10.1007/978-3-642-22176-7_6
Kaya, T.; Kahraman, C. 2010. Multicriteria renewable energy
planning using an integrated fuzzy VIKOR and AHP methodology: the case
of Istanbul, Energy 35: 2517-2527.
http://dx.doi.org/10.1016/j.energy.2010.02.051
Kaya, T.; Kahraman, C. 2011. Multicriteria decision making in
energy planning using a modified fuzzy TOPSIS methodology, Expert
Systems with Applications 38: 6577-6585.
http://dx.doi.org/10.1016/j.eswa.2010.11.081
Kaltschmitt, M.; Streicher, W.; Wiese, A. 2007. Renewable energy:
technology, economics and environment. Springer-Verlag Berlin
Heidelberg.
Lashgari, A.; Fouladgar, M. M.; Yazdani-Chamzini, A.; Skibniewski,
M. J. 2011. Using an integrated model for shaft sinking method
selection, Journal of Civil Engineering and Management 17(4): 569-580.
http://dx.doi.org/10.3846/13923730.2011.628687
Lashgari, A.; Yazdani-Chamzini, A.; Fouladgar, M. M.; Zavadskas, E.
K.; Shafiee, S.; Abbate, N. 2012. Equipment selection using fuzzy multi
criteria decision making model: key study of Gole Gohar iron mine,
Inzinerine Ekonomika - Engineering Economics 23(2): 125-136.
Lee, S. K.; Mogi, G.; Kim, J. W. 2009. Decision support for
prioritizing energy technologies against high oil prices: a fuzzy
analytic hierarchy process approach, Journal of Loss Prevention in the
Process Industries 22(6): 915-920.
http://dx.doi.org/10.1016/j.jlp.2009.07.001
Lee, S. K.; Mogi, G.; Lee, S. K.; Kim, J. W. 2011. Prioritizing the
weights of hydrogen energy technologies in the sector of the hydrogen
economy by using a fuzzy AHP approach, International Journal of Hydrogen
Energy 36(2): 1897-1902.
http://dx.doi.org/10.1016/j.ijhydene.2010.01.035
MacCrimmon, K. R. 1968. Decision making among multiple-attribute
alternatives: a survey and consolidated approach. RAND Memorandum,
RM-4823-ARPA.
Nigim, K.; Munier, N.; Green, J. 2004. Pre-feasibility MCDM tools
to aid communities in prioritizing local viable renewable energy
sources, Renewable Energy 29(11): 1775-1791.
http://dx.doi.org/10.1016/j.renene.2004.02.012
Oberschmidt, J.; Geldermann, J.; Ludwig, J.; Schmehl, M. 2010.
Modified PROMETHEE approach for assessing energy technologies,
International Journal of Energy Sector Management 4(2): 183-212.
http://dx.doi.org/10.1108/17506221011058696
Opricovic, S. 1998. Multicriteria optimization of civil engineering
systems. Belgrade: Faculty of Civil Engineering (in Serbian).
Renewable Energy Policy Network for the 21st Century (REN21). 2011.
Renewables 2011: global status report. 17 p.
Reza, B.; Sadiq, R.; Hewage, K. 2011. Sustainability assessment of
flooring systems in the city of Tehran: an AHP-based life cycle
analysis, Construction and Building Materials 25: 2053-2066.
http://dx.doi.org/10.1016/j.conbuildmat.2010.11.041
Saaty, T. L. 1980. The analytic hierarchy process. New York:
McGraw-Hill.
Saaty, T. L. 1994. How to make a decision: the analytic hierarchy
process, Interfaces 24: 19-43. http://dx.doi.org/10.1287/inte.24.6.19
Shen, Y. Ch.; Chou, Ch. J.; Lin, G. T. R. 2011. The portfolio of
renewable energy sources for achieving the three E policy goals, Energy
36(5): 2589-2598. http://dx.doi.org/10.1016/j.energy.2011.01.053
Sola, A. V. H.; Mota, C. M. M.; Kovaleski, J. L. 2011. A model for
improving energy efficiency in industrial motor system using
multicriteria anglysi, Energy Policy 39(6): 3645-3654.
http://dx.doi.org/10.1016/j.enpol.2011.03.070
Streimikiene, D.; Balezentis, T. 2013. Multi-objective ranking of
climate change mitigation policies and measures in Lithuania, Renewable
and Sustainable Energy Reviews 18: 144-153.
http://dx.doi.org/10.1016/j.rser.2012.09.040
Streimikiene, D.; Balezentis, T.; Krisciukaitiene, I.; Balezentis,
A. 2012. Prioritizing sustainable electricity production technologies:
MCDM approach, Renewable and Sustainable Energy Reviews 16(5):
3302-3311. http://dx.doi.org/10.1016/j.rser.2012.02.067
Virtanen, M. 2011. Choosing the optimal energy system for buildings
and districts. Master's thesis, Lappeenranta University of
Technology.
Yazdani-Chamzini, A.; Yakhchali, S. H. 2012. Tunnel Boring Machine
(TBM) selection using fuzzy multicriteria decision making methods,
Tunnelling and Underground Space Technology 30: 194-204.
http://dx.doi.org/10.1016Zj.1ust.2012.02.021
Yi, S. K.; Sin, H. Y.; Heo, E. 2011. Selecting sustainable
renewable energy source for energy assistance to North Korea, Renewable
and Sustainable Energy Reviews 15: 554-563.
http://dx.doi.org/10.1016/j.rser.2010.08.021
Zavadskas, E. K.; Kaklauskas, A. 1996. Determination of an
efficient contractor by using the new method of multicriteria
assessment, in D. A. Langford, A. Retik (Eds.). International Symposium
for "The Organisation and Management of Construction". Shaping
Theory and Practice, vol. 2: Managing the Construction Project and
Managing Risk. CIB W 65. London, Weinheim, New York, Tokyo, Melbourne,
Madras. London: E and FN SPON: 94-104.
Zavadskas, E. K.; Turskis, Z. 2010. A new additive ratio assessment
(ARAS) method in multicriteria decision making, Technological and
Economic Development of Economy 16(2): 159-172.
http://dx.doi.org/10.3846/tede.2010.10
Zavadskas, E. K.; Turskis, Z. 2011. Multiple criteria decision
making (MCDM) methods in economics: an overview, Technological and
Economic Development of Economy 17(2): 397-427.
http://dx.doi.org/10.3846/20294913.2011.593291
Abdolreza Yazdani-Chamzini (1), Mohammad Majid Fouladgar (2),
Edmundas Kazimieras Zavadskas (3), S. Hamzeh Haji Moini (4)
(1, 2) Young Researchers Club, South Tehran Branch, Islamic Azad
University, Tehran, Iran
(3) Faculty of Civil Engineering, Vilnius Gediminas Technical
University, Sauletekio al. 11, LT-I0223 Vilnius, Lithuania
(4) Fateh Research Group, Department of Strategic Management, Milad
Building, Mini city, Aghdasieh, Tehran, Iran
E-mails: (1) manager@fatehidea.com; (2) a.yazdani@fatehidea.com;
(3) Edmundas.Zavadskas@vgtu.lt (corresponding author); (4)
smhpm85@yahoo.com
Abdolreza YAZDANI-CHAMZINI. Master of Science in the Department of
Mining Engineering, research assistant of Tehran University,
Tehran-Iran. Author of more than 46 research papers. In 2011, he
graduated from the Science and Engineering Faculty at Tarbiat Modares
University, Tehran-Iran. His research interests include decision making,
forecasting, modeling, and optimization.
Mohammad Majid FOULADGAR. PhD student of future study in Amirkabir
University of Technology, Tehran-Iran. Author of 13 research papers. In
2007 he graduated from the science and engineering Faculty at Tarbiat
Modares University, Tehran-Iran. His research interests include decision
support system, fuzzy logic, water resource, and forecasting.
Edmundas Kazimieras ZAVADSKAS. Prof., the Head of the Department of
Construction Technology and Management at Vilnius Gediminas Technical
University, Lithuania. PhD in Building Structures (1973). Dr Sc. (1987)
in Building Technology and Management. A member of Lithuanian and
several foreign Academies of Sciences. Doctore Honoris Causa from
Poznan, Saint-Petersburg and Kiev universities. A member of
international organizations; a member of steering and programme
committees at many international conferences; a member of the editorial
boards of several research journals; the author and co-author of more
than 400 papers and a number of monographs in Lithuanian, English,
German and Russian. Research interests: building technology and
management, decision-making theory, automation in design and decision
support systems.
S. Hamzeh Haji MOINI. Master of Science of Project Management,
research assistant of Fateh Research Group, Tehran-Iran. He is the
author of 7 research papers. His interests include decision support
system, portfolio selection, and artificial intelligence.
Table 1. Pair-wise comparison scale
Definition Value
Equal importance 1
Weak importance 3
Essential importance 5
Demonstrated importance 7
Extreme importance 9
Intermediate values 2, 4, 6, 8
Table 2. Alternatives for electricity generation (Cristobal 2011)
Symbol Alternative
A1 Wind power P [less than or
equal to] 5MW
A2 Wind power 5 [less than or
equal to] P [less than or
equal to] 10MW
A3 Wind power 10 [less than or
equal to] P [less than or
equal to] 50MW
A4 Hydroelectric P [less than
or equal to] 10MW
A5 Hydroelectric 10 [less than
or equal to] P [less than
or equal to] 25MW
A6 Hydroelectric 25 [less than
or equal to] P [less than
or equal to] 50MW
A7 Solar Thermo-electric P
[greater than or equal to]
10MW
A8 Biomass (energetic
cultivations) P [less than
or equal to] 5MW
A9 Biomass (forest and
agricultural wastes) P
[less than or equal to] 5MW
A10 Biomass (farming industrial
wastes) P [less than or
equal to] 5MW
A11 Biomass (forest industrial
wastes) P [less than or
equal to] 5MW
A12 Biomass (co-combustion in
conventional central) P
[less than or equal to]
50MW
A13 Bio fuels P [less than or
equal to] 2MW
Table 3. Preference ratings of alternatives (Cristobal 2011)
P IR IP OH UL O&M tC[O.sub.2]/y
A1 5000 937 1 2350 20 1.47 1929936
A2 10000 937 1 2350 20 1.47 3216560
A3 25000 937 1 2350 20 1.51 9649680
A4 5000 1500 1.5 3100 25 1.45 472812
A5 20000 700 2 2000 25 0.7 255490
A6 35000 601 2.5 2000 25 0.6 255490
A7 50000 5000 2 2596 25 4.2 482856
A8 5000 1803 1 7500 15 7.106 2524643
A9 5000 1803 1 7500 15 5.425 2524643
A10 5000 1803 1 7500 15 5.425 2524643
A11 5000 1803 1 7500 15 2.813 2524643
A12 56000 856 1 7500 20 4.56 4839548
A13 2000 1503 1.5 7000 20 2.512 5905270
Table 4. Pairwise comparison matrix
P IR IP OH UL O&M tC[O.sub.2]/y
P 1 5 9 3 5 7 1
IR 1/5 1 5 1/3 1/3 5 1/3
IP 1/9 1/5 1 1/5 1/7 1/3 1/5
OH 1/3 3 5 1 1 3 1/5
UL 1/5 3 7 1 1 5 1/3
O&M 1/7 1/5 3 1/3 1/5 1 1/5
tC[O.sub.2]/y 1 3 5 5 3 5 1
Table 5. Analysis results
P IR IP OH UL O&M
Max Min Min Max Max Min
A1 0.0070 0.0042 0.0015 0.0044 0.0103 0.0016
A2 0.0140 0.0042 0.0015 0.0044 0.0103 0.0016
A3 0.0350 0.0042 0.0015 0.0044 0.0103 0.0016
A4 0.0070 0.0067 0.0023 0.0059 0.0129 0.0016
A5 0.0280 0.0031 0.0030 0.0038 0.0129 0.0008
A6 0.0490 0.0027 0.0038 0.0038 0.0129 0.0006
A7 0.0700 0.0222 0.0030 0.0049 0.0129 0.0045
A8 0.0070 0.0080 0.0015 0.0142 0.0077 0.0076
A9 0.0070 0.0080 0.0015 0.0142 0.0077 0.0058
A10 0.0070 0.0080 0.0015 0.0142 0.0077 0.0058
A11 0.0070 0.0080 0.0015 0.0142 0.0077 0.0030
A12 0.0783 0.0038 0.0015 0.0142 0.0103 0.0049
A13 0.0028 0.0067 0.0023 0.0132 0.0103 0.0027
tC [P.sub.i] [R.sub.i] [Q.sub.i] [N.sub.i]
[O.sub.2]/y
Max
A1 0.0142 0.0359 0.0073 0.0530 35.20
A2 0.0236 0.0524 0.0073 0.0694 46.14
A3 0.0709 0.1207 0.0073 0.1376 91.43
A4 0.0035 0.0292 0.0105 0.0410 27.25
A5 0.0019 0.0465 0.0069 0.0645 42.86
A6 0.0019 0.0675 0.0071 0.0850 56.46
A7 0.0035 0.0913 0.0298 0.0955 63.42
A8 0.0186 0.0475 0.0172 0.0547 36.32
A9 0.0186 0.0475 0.0154 0.0555 36.88
A10 0.0186 0.0475 0.0154 0.0555 36.88
A11 0.0186 0.0475 0.0125 0.0573 38.08
A12 0.0356 0.1384 0.0102 0.1505 100.00
A13 0.0434 0.0698 0.0116 0.0804 53.40
Rank
A1 12
A2 6
A3 2
A4 13
A5 7
A6 4
A7 3
A8 11
A9 9
A10 9
A11 8
A12 1
A13 5
Table 6. Rankings obtained by using various methods
Alternative Method
TOPSIS VIKOR SAW
Value Rank Value Rank Value Rank
A1 0.074 12 0.951 13 0.328 12
A2 0.147 6 0.798 6 0.393 7
A3 0.772 2 0.262 2 0.660 2
A4 0.043 13 0.929 9 0.295 13
A5 0.134 7 0.775 5 0.413 6
A6 0.302 4 0.688 4 0.514 3
A7 0.439 3 0.666 3 0.503 4
A8 0.086 11 0.946 12 0.356 11
A9 0.087 9 0.935 10 0.357 9
A10 0.087 9 0.935 10 0.357 9
A11 0.090 8 0.917 8 0.361 8
A12 0.841 1 0.000 1 0.774 1
A13 0.272 5 0.823 7 0.457 5
Alternative Final
MOORA ARAS Proposed model rank
(AHP-COPRAS)
Value Rank Value Rank Value Rank
A1 0.084 12 0.051 12 35.20 12 12.2
A2 0.127 6 0.067 6 46.14 6 6.8
A3 0.307 2 0.135 2 91.43 2 2.0
A4 0.059 13 0.040 13 27.25 13 12.3
A5 0.112 7 0.067 7 42.86 7 7.2
A6 0.164 4 0.091 4 56.46 4 4.0
A7 0.158 5 0.095 3 63.42 3 3.5
A8 0.088 11 0.055 11 36.32 11 10.3
A9 0.094 9 0.055 9 36.88 9 8.8
A10 0.094 9 0.055 9 36.88 9 8.8
A11 0.102 8 0.056 8 38.08 8 8.2
A12 0.344 1 0.151 1 100.00 1 1.0
A13 0.167 3 0.079 5 53.40 5 4.8
Table 7. Normalized decision matrix
P IR IP OH UL O&M tC[O.sub.2]/y
A1 0.022 0.046 0.057 0.038 0.077 0.037 0.052
A2 0.044 0.046 0.057 0.038 0.077 0.037 0.087
A3 0.110 0.046 0.057 0.038 0.077 0.038 0.260
A4 0.022 0.074 0.086 0.051 0.096 0.037 0.013
A5 0.088 0.035 0.114 0.033 0.096 0.018 0.007
A6 0.154 0.030 0.143 0.033 0.096 0.015 0.007
A7 0.219 0.248 0.114 0.042 0.096 0.107 0.013
A8 0.022 0.089 0.057 0.122 0.058 0.181 0.068
A9 0.022 0.089 0.057 0.122 0.058 0.138 0.068
A10 0.022 0.089 0.057 0.122 0.058 0.138 0.068
A11 0.022 0.089 0.057 0.122 0.058 0.072 0.068
A12 0.246 0.042 0.057 0.122 0.077 0.116 0.130
A13 0.009 0.074 0.086 0.114 0.077 0.064 0.159
Table 8. The utility degree and ranking results of thirteen
alternatives
P IR IP OH UL O&M
Max Min Min Max Max Min
A1 0.0060 0.0036 0.0013 0.0038 0.0089 0.0020
A2 0.0121 0.0036 0.0013 0.0038 0.0089 0.0020
A3 0.0302 0.0036 0.0013 0.0038 0.0089 0.0021
A4 0.0060 0.0058 0.0020 0.0051 0.0111 0.0020
A5 0.0242 0.0027 0.0026 0.0033 0.0111 0.0010
A6 0.0423 0.0023 0.0033 0.0033 0.0111 0.0008
A7 0.0604 0.0192 0.0026 0.0042 0.0111 0.0058
A8 0.0060 0.0069 0.0013 0.0122 0.0067 0.0099
A9 0.0060 0.0069 0.0013 0.0122 0.0067 0.0076
A10 0.0060 0.0069 0.0013 0.0122 0.0067 0.0076
A11 0.0060 0.0069 0.0013 0.0122 0.0067 0.0039
A12 0.0677 0.0033 0.0013 0.0122 0.0089 0.0063
A13 0.0024 0.0058 0.0020 0.0114 0.0089 0.0035
tC[O.sub.2]/y [P.sub.i] [R.sub.i] [Q.sub.i] [N.sub.i]
Max
A1 0.0184 0.037 0.007 0.054 35.60
A2 0.0306 0.055 0.007 0.072 47.68
A3 0.0919 0.135 0.007 0.152 100.00
A4 0.0045 0.027 0.010 0.039 25.55
A5 0.0024 0.041 0.006 0.060 39.34
A6 0.0024 0.059 0.006 0.077 51.05
A7 0.0046 0.080 0.028 0.085 55.85
A8 0.0241 0.049 0.018 0.055 36.60
A9 0.0241 0.049 0.016 0.056 37.22
A10 0.0241 0.049 0.016 0.056 37.22
A11 0.0241 0.049 0.012 0.059 38.68
A12 0.0461 0.135 0.011 0.146 96.08
A13 0.0563 0.079 0.011 0.089 59.00
Rank
A1 12
A2 6
A3 1
A4 13
A5 7
A6 5
A7 4
A8 11
A9 9
A10 9
A11 8
A12 2
A13 3
Table 9. Rankings yielded by six methods
Alternative Method
TOPSIS VIKOR SAW
Value Rank Value Rank Value Rank
A1 0.068 12 0.834 11 0.314 12
A2 0.161 6 0.626 6 0.386 6
A3 0.870 1 0.053 1 0.695 2
A4 0.031 13 0.975 13 0.268 13
A5 0.083 11 0.926 12 0.375 7
A6 0.179 5 0.846 5 0.466 4
A7 0.273 4 0.829 4 0.443 5
A8 0.088 10 0.781 10 0.340 11
A9 0.089 8 0.765 8 0.341 9
A10 0.089 8 0.765 8 0.341 9
A11 0.093 7 0.741 7 0.347 8
A12 0.741 2 0.058 2 0.730 1
A13 0.391 3 0.578 3 0.471 3
Alternative Final
MOORA ARAS Proposed model rank
(AHP-COPRAS)
Value Rank Value Rank Value Rank
A1 0.087 12 0.052 12 35.60 12 11.8
A2 0.135 6 0.070 6 47.68 6 6.3
A3 0.345 1 0.149 1 100.00 1 1.3
A4 0.053 13 0.038 13 25.55 13 13.0
A5 0.098 8 0.062 7 39.34 7 9.3
A6 0.143 4 0.084 5 51.05 5 4.8
A7 0.135 5 0.085 4 55.85 4 4.3
A8 0.088 11 0.056 11 36.60 11 9.7
A9 0.095 9 0.056 9 37.22 9 8.3
A10 0.095 9 0.056 9 37.22 9 8.3
A11 0.106 7 0.058 8 38.68 8 7.8
A12 0.332 2 0.147 2 96.08 2 1.7
A13 0.191 3 0.088 3 59.00 3 3.2
Table 10. Ranking results of alternatives
P IR IP OH UL O&M
Max Min Min Max Max Min
A1 0.0073 0.0033 0.0012 0.0035 0.0082 0.0019
A2 0.0145 0.0033 0.0012 0.0035 0.0082 0.0019
A3 0.0363 0.0033 0.0012 0.0035 0.0082 0.0019
A4 0.0073 0.0053 0.0018 0.0047 0.0103 0.0019
A5 0.0290 0.0025 0.0024 0.0030 0.0103 0.0009
A6 0.0508 0.0021 0.0030 0.0030 0.0103 0.0008
A7 0.0726 0.0178 0.0024 0.0039 0.0103 0.0054
A8 0.0073 0.0064 0.0012 0.0113 0.0062 0.0091
A9 0.0073 0.0064 0.0012 0.0113 0.0062 0.0070
A10 0.0073 0.0064 0.0012 0.0113 0.0062 0.0070
A11 0.0073 0.0064 0.0012 0.0113 0.0062 0.0036
A12 0.0813 0.0030 0.0012 0.0113 0.0082 0.0059
A13 0.0029 0.0053 0.0018 0.0106 0.0082 0.0032
tC[O.sub.2]/y [P.sub.i] [R.sub.i] [Q.sub.i] [N.sub.i]
Max
A1 0.0170 0.0360 0.0064 0.052 33.61
A2 0.0283 0.0546 0.0064 0.070 45.73
A3 0.0849 0.1330 0.0065 0.148 96.80
A4 0.0042 0.0264 0.0090 0.037 24.43
A5 0.0022 0.0446 0.0058 0.062 40.30
A6 0.0022 0.0664 0.0059 0.083 54.28
A7 0.0042 0.0910 0.0256 0.095 61.94
A8 0.0222 0.0470 0.0167 0.053 34.52
A9 0.0222 0.0470 0.0146 0.054 35.09
A10 0.0222 0.0470 0.0146 0.054 35.09
A11 0.0222 0.0470 0.0112 0.056 36.42
A12 0.0426 0.1434 0.0101 0.153 100.00
A13 0.0520 0.0737 0.0104 0.083 54.32
Rank
A1 12
A2 6
A3 2
A4 13
A5 7
A6 5
A7 3
A8 11
A9 9
A10 9
A11 8
A12 1
A13 4
Table 11. Rankings resulted by different methods
Alternative Method
TOPSIS VIKOR SAW
Value Rank Value Rank Value Rank
A1 0.056 12 0.939 11 0.297 12
A2 0.135 6 0.768 3 0.370 7
A3 0.811 1 0.160 2 0.676 2
A4 0.026 13 0.960 13 0.254 13
A5 0.097 7 0.902 7 0.374 6
A6 0.240 5 0.811 5 0.478 3
A7 0.385 3 0.769 4 0.477 4
A8 0.070 11 0.944 12 0.321 11
A9 0.071 9 0.930 9 0.322 9
A10 0.071 9 0.930 9 0.322 9
A11 0.074 8 0.909 8 0.327 8
A12 0.803 2 0.000 1 0.751 1
Alternative
MOORA ARAS Proposed model Final
(AHP-COPRAS) rank
Value Rank Value Rank Value Rank
A1 0.085 12 0.049 12 33.61 12 11.8
A2 0.133 6 0.068 6 45.73 6 6.2
A3 0.340 2 0.146 2 96.80 2 1.8
A4 0.053 13 0.037 13 24.43 13 13.0
A5 0.107 7 0.064 7 40.30 7 7.5
A6 0.162 5 0.089 4 54.28 5 4.7
A7 0.167 4 0.095 3 61.94 3 3.5
A8 0.085 11 0.053 11 34.52 11 10.3
A9 0.092 9 0.054 9 35.09 9 8.7
A10 0.092 9 0.054 9 35.09 9 8.7
A11 0.102 8 0.055 8 36.42 8 8.3
A12 0.354 1 0.154 1 100.00 1 1.2
Table 12. Ranking of the alternatives in three different cases
Alternative Method
TOPSIS VIKOR SAW
C1 * C2 * C3 * C1 C2 C3 C1 C2 C3
A1 12 12 12 13 11 11 12 12 12
A2 6 6 6 6 6 3 7 6 7
A3 2 1 1 2 1 2 2 2 2
A4 13 13 13 9 13 13 13 13 13
A5 7 11 7 5 12 7 6 7 6
A6 4 5 5 4 5 5 3 4 3
A7 3 4 3 3 4 4 4 5 4
A8 11 10 11 12 10 12 11 11 11
A9 9 8 9 10 8 9 9 9 9
A10 9 8 9 10 8 9 9 9 9
A11 8 7 8 8 7 8 8 8 8
A12 1 2 2 1 2 1 1 1 1
A13 5 3 4 7 3 6 5 3 5
Alternative
MOORA ARAS Proposed model
(AHPCOPRAS)
C1 C2 C3 C1 C2 C3 C1 C2 C3
A1 12 12 12 12 12 12 12 12 12
A2 6 6 6 6 6 6 6 6 6
A3 2 1 2 2 1 2 2 1 2
A4 13 13 13 13 13 13 13 13 13
A5 7 8 7 7 7 7 7 7 7
A6 4 4 5 4 5 4 4 5 5
A7 5 5 4 3 4 3 3 4 3
A8 11 11 11 11 11 11 11 11 11
A9 9 9 9 9 9 9 9 9 9
A10 9 9 9 9 9 9 9 9 9
A11 8 7 8 8 8 8 8 8 8
A12 1 2 1 1 2 1 1 2 1
A13 3 3 3 5 3 5 5 3 4
Alternative Final rank
C1 C2 C3
A1 12.2 11.8 11.8
A2 6.8 6.3 6.2
A3 2.0 1.3 1.8
A4 12.3 13.0 13.0
A5 7.2 9.3 7.5
A6 4.0 4.8 4.7
A7 3.5 4.3 3.5
A8 10.3 9.7 10.3
A9 8.8 8.3 8.7
A10 8.8 8.3 8.7
A11 8.2 7.8 8.3
A12 1.0 1.7 1.2
A13 4.8 3.2 4.3
* C1: Case 1, C2: Case 2 and C3: Case 3.
