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Prioritization of biofuels production pathways under uncertainties
CHAPTER 12
Prioritization of biofuels production pathways under uncertainties Ruojue Lin, Yue Liu, Jingzheng Ren Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong SAR, China
Contents 1 Introduction 2 Interval multicriteria decision making method 2.1 Interval numbers 2.2 Interval AHP 2.3 Interval gray relational analysis 3 Case study 4 Discussion 5 Conclusion Acknowledgment References
337 340 340 343 345 348 352 353 354 354
1 Introduction Biofuel has been recognized as a promising solution to sustainable and lowcarbon transport, because it can be produced from various types of biomass to substitute the petroleum-derived fuel and reduce emissions from transport sector (Hao et al., 2018). Biofuel is one of the most promising renewable energy carriers, and it can be produced from various feedstocks such as biomass, algal, and some other nonstaple food crops (Liang et al., 2016). However, there are also some challenges for promoting the development of biofuels including the relatively higher production, the negative impacts on food security, and competition with some other renewable energy resources (Ren et al., 2015a). Meanwhile, there are also some emissions in the whole life cycle of biofuels, because there is also some consumption for cropping, transportation of biomass resources, biofuel production, transportation of biofuels, and so on (Ren et al., 2014). Therefore the Biofuels for a More Sustainable Future https://doi.org/10.1016/B978-0-12-815581-3.00012-9
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development of biofuel industry is still “in debate,” and people are usually puzzled with two questions: (i) Is biofuel really sustainable? (ii) Which is the most sustainable pathway for biofuel production? As for the question: is biofuel really sustainable? There are many studies for answering this question. The most typical is to use life cycle tools to analyze the sustainability of biofuel production pathways from cradle to grave. For instance, Ou et al. (2009) employed life cycle assessment (LCA) to investigate the energy consumption and GHG emissions of six biofuel pathways in China. Yang et al. (2011) used life cycle thinking to analyze the water footprint and nutrients balance of biodiesel from microalgae. Requena et al. (2011) employed LCA to study the environmental impacts of biofuels from sunflower oil, rapeseed oil, and soybean oil. However, all these studies can only answer the first question. As for the second question: which is the most sustainable pathway for biofuel production? It is usually different and even the stakeholders/decision-makers know the performances of different biofuel production pathways and there are two main reasons: (i) there are usually various conflict criteria for sustainability assessment of biofuel production pathways; (ii) there are various data uncertainties, and the data of the alternative biofuel production pathways with respect to the evaluation criteria usually varies. Therefore this study aims at developing an interval multicriteria decision making (MCDM) method for sustainability prioritization of biofuel production pathways under uncertainties. MCDM is a widely used decision-making tool that allows for scientific and comprehensive analysis based on multiple data and decision-maker’s preferences (Triantaphyllou, 2000). MCDM methods commonly used include Analytic Hierarchy Process (AHP) (Saaty, 1980), Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) (Hwang and Yoon, 1981), Gray Relational Analysis (GRA) (Deng, 1989), The Preference Ranking Organization Method for Enrichment of Evaluations (PROMETHEE) (Brans et al., 1986), and Elimination and Choice Expressing Reality (ELECTRE) (Benayoun et al., 1966). The decision-making method based on uncertain data is an extension of MCDM, which is used to analyze the ranking, selection, and classification of more than one evaluation criterion with uncertain or fuzzy information in the data (Ho et al., 2010). Due to the uncertainty of subjective judgment, the normal fluctuation caused by environmental factors, and the uncertainty caused by knowledge limitations, the application of MCDM under uncertainties plays a significant role in strategy establishment (Ren and Toniolo, 2018). MCDM dealing with uncertain data can be classified into interval MCDM, fuzzy
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MCDM, intuitional fuzzy MCDM, and stochastic MCDM. Interval MCDM takes the interval number as the input data in the decision process, so that the value of each criterion reflects its maximum and minimum values (Tsaur, 2011). For example, Giove (2002) and Jahanshahloo et al. (2006) have extended TOPSIS into interval TOPSIS. Fuzzy MCDM is the MCDM that bringing fuzzy number such as triangular fuzzy number and trapezoidal fuzzy number into consideration (Pohekar and Ramachandran, 2004; Kahraman, 2008). The fuzzy number consists more information than interval number to express the uncertainty (Pohekar and Ramachandran, 2004; Kahraman, 2008). For instance, Sevkli (2010) extended ELECTRE into fuzzy ELECTRE, Shemshadi et al. (2011) extended VIKOR into fuzzy VIKOR, and Liu and Wang (2007) developed a MCDM based on intuitionistic fuzzy. The fuzzy MCDM has been further extended into intuitional fuzzy MCDM which adds degree of nonmembership to better express the uncertainty (Liu and Wang, 2007). Different from fuzzy MCDM, stochastic MCDM uses randomness to reveal the uncertainty sets (Ramanathan, 1997). For example, Xiong and Qi (2010) have extended TOPSIS into stochastic multicriteria decision making method. Furthermore, many researchers have also tried to combine different MCDM methods under uncertainty to form hybrid MCDM. For example, B€ uy€ uk€ ozkan and C ¸ ifc¸i (2012) have proposed a hybrid MCDM approach combining fuzzy Decision making trial and evaluation laboratory (DEMATEL), fuzzy (Analytic Network Process) ANP, and fuzzy TOPSIS together. Some researchers have done studies to compare biofuel production processes sustainably (e.g., Ou et al., 2009; Yang et al., 2011; Larkum et al., 2012), but these researches cannot show the direct priority through the comparisons. Some people helped to make choices in this selection problem (e.g., Schaidle et al., 2011; Vlysidis et al., 2011; Sharma et al., 2011), but they did not consider uncertainties in the biofuel production processes. Furthermore, some scholars have studied energy selection problem but have not specifically scoped to biofuel such as Sadeghi et al. (2012) provided a fuzzy MCDM approach for renewable electricity production and Lee et al. (2009) have conducted a fuzzy AHP method for energy technology prioritization. Therefore we shall bring uncertainties into consideration and provide a scientific and comprehensive analysis for biofuel production pathways prioritization. Because the interval number represents the uncertainty of the data biofuel production process and leads to few obstacles in data collection, so the data type of interval MCDM is more in line with the operation of sustainable biofuel production selection. The interval AHP which allows the
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users to use interval numbers rather than the basketball numbers to establish the comparison matrix was employed for determining the weights of the criteria for sustainability assessment of biofuel production pathways, and the interval GRA method was employed to determine the sustainability sequence of alternative biofuel production pathways under uncertainties.
2 Interval multicriteria decision making method Interval multicriteria decision making method is a series of MCDM adapting interval numbers as criteria inputs and weights, which helps to deal with complex decision-making cases with vagueness of language and uncertainty of criteria values. The interval VIKOR raised by Sayadi et al. (2009) supports decision-makers to rank the alternatives with regards to its performances comparing to the best and the worst alternative. Giove (2002) and Jahanshahloo et al. (2006) have extended TOPSIS into interval TOPSIS, respectively. The interval TOPSIS considers the balance between needs fulfillment and lost compromise. Luo et al. (2015) developed an interval GRA method based on the grey theory invented by Deng (1989). Xu and Da (2003) have extended the AHP method into the interval analytic hierarchy process (IAHP), which assistant to quantify the criteria values and weights according to quality values. In addition, interval PROMETHEE (Le Teno and Mareschal, 1998) and interval Best Worst Method (BWM) (Rezaei, 2016) are methods for dealing qualified inputs as well. Among these, the IAHP is one of the most commonly used weighting methods in MCDM for its advantage of addressing the hesitations and ambiguity existing in human’s judgments. In this section, interval multicriteria decision making method for biofuel production pathways selection is described. Criteria system establishment, criteria weighting, and aggregating are three steps for MCDM method whose methods are designed as criteria system establishment, interval AHP, and interval GRA as shown in Fig. 12.1.
2.1 Interval numbers The basic information of interval numbers was presented in this section based on the work of He et al. (2017), Zhang et al. (2005), Bohlender and Kulisch (2011), Moore (1966), Dymova et al. (2013), and Xu and Da (2003). Let x ¼ ½x , x + ¼ fxjx x x + , x x + ,x , x + 2 R g. Here + x ¼ ½x , x is called an interval number and is a positive interval number
Prioritization of biofuels production pathways under uncertainties
Criteria system establishment
Topic information collection
All criteria summarization
Criteria selection and criteria system building
Criteria weighting—interval AHP
30% 20% 5% ... Criteria information and prioritization opinions collection
Criteria pairwise comparison Criteria weighting based on information and through calculation expert judgements
Alternative ranking—interval GRA
A1
A2
A3
...
C1 C2 C3 ...
Best alternative selection through calculation
Alternative information collection and make decision matrix 30% 20% 5%
...
Use alternative data and criteria weights as input
Fig. 12.1 Methodology of biofuel production pathways selection.
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if 0 x x + [see the work of Zhang et al. (2005)]. It is apparent that an interval number can take an arbitrary value between its lower bound and upper bound. Definition 1 Distance between two interval numbers (Yue, 2011) If x ¼ ½x , x + and y ¼[ y, y+] are two arbitrary interval numbers, the distance from x ¼ ½x , x + to y ¼[ y, y+] can be determined by qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (12.1) jx yj ¼ ðx y Þ2 + ðx + y + Þ2 Definition 2 Number product between a positive real number and an interval number (Zhang et al., 2005) The number product of a positive real number λ and an interval number x ¼ ½x , x + is defined as λ x ¼ λ½x , x + ¼ ½λx , λ x +
(12.2)
Note that a crisp number λ could also be transformed into an interval number λ ¼ λ, λ]. Definition 3 Addition (Bohlender and Kulisch, 2011) If x ¼ ½x , x + and y ¼[ y, y+] are two arbitrary interval numbers, the sum of the two interval numbers can be obtained by x + y ¼ ½x , x + + ½y , y + ¼ ½x + y , x + + y +
(12.3)
Definition 4 Subtraction (Moore, 1966; Dymova et al., 2013) If x ¼ ½x , x + and y ¼[ y, y+] are two arbitrary interval numbers, the subtraction between two interval numbers can be determined by x y ¼ ½x , x + ½y , y + ¼ ½x y + ; x + y
(12.4)
Definition 5 Multiplication (Zhang et al., 2005) If x ¼ ½x , x + and y ¼[ y, y+] are two arbitrary interval numbers, the interval product can be obtained according to the following two cases: (1) when y+ > 0, the interval product can be determined by x y ¼ ½x , x + ½y , y ¼ ½x y , x + y +
(12.5)
(2) when y+ < 0, the interval product can be determined by x x ¼ ½x , x + ½y , y + ¼ ½x + y , x y +
(12.6)
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Definition 6 The possibility of an interval being greater than another For two arbitrary interval numbers x ¼ ½x , x + and y ¼[ y, y+], the possibilities that x y and that b a are defined in the following two equations, respectively (Xu and Da, 2003): y + x + + ,0 pxy ¼ pð½x , x ½y , y Þ ¼ max 1 max + y y + x + x (12.7)
2.2 Interval AHP The interval analytic hierarchy process (IAHP) developed by Xu and Da (2003) has been widely used in various fields for its advantage of address ambiguity and hesitation existing in human judgments. Ren (2018) summarized the IAHP method developed by Xu and Da (2003) in the following three steps: Step 1: Establishing the interval pair-wise comparison matrix. Assuming that there are n criteria (C1, C2, … , Cn) which need the stakeholders/decision-makers to determine the relative importance (weights), the stakeholders/decision-makers were asked to use the Saaty’s nine-scale system (Saaty, 2008) to establish the pair-wise comparison matrix (see Table 12.1). However, it is different from the traditional AHP method which relies on employing the numbers(from 1 to 9) and their corresponding reciprocals to establish the pair-wise comparison matrix, the users of the interval numbers rather than the single numbers which sometime cannot Table 12.1 Saaty scales for establishing the pair-wise comparison matrix (Saaty, 2008) Scales
Definition
Explanation
1
Equal importance Moderate importance Essential importance Very strong importance Absolute importance Intermediate value
Two elements perform equally
3 5 7 9 2,4,6,8
Experience and judgment slightly favor one element over another Experience and judgment strongly favor one element over another An element is favored very strongly over another; its dominance demonstrated in practice The evidence favoring one element over another is of the highest possible order of affirmation Intermediate value
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depict the relative importance/preference of one criterion over another accurately. For instance, it is difficult or even impossible to depict the relative weight/priority of a criterion over another when the stakeholders/ decision-makers think that the relative importance of a criterion over another is between “moderate importance” (corresponding to number 3) and “essential importance” (corresponding to number 5). Accordingly, the interval number [3 5] should be used to depict this judgment. In a similar way, the interval comparison matrix for determining the relative importance (weights) of the n metrics can be established: C1 C2 C1 1 mL12 , mU 12 1 M ¼ C2 mL21 , mU 21 ⋮ ⋮ ⋮ Cn mLn1 , mU mLn2 , mU n1 n2
⋯ Cn ⋯ mL1n , mU 1n ⋯ mL2n , mU 2n ⋱ ⋮ ⋯ 1
(12.8)
where M represents the interval pair-wise matrix for determining the relative weights of the n criteria, [mLij , mU ij ] which is an interval number represents the relative preference of the ith criterion over the jth criterion, and mLij L U and mU ij are the lower and upper boundary of the interval number [qij , qij ]. The relative preference of the jth criterion over ith metric can be determined by Eq. (12.9). " # h i 1 1 1 h i ¼ U , L , i, j ¼ 1,2,…,n (12.9) mLji , mU ji ¼ mij mij mL , mU ij
ij
Step 2: Decomposing the interval pair-wise comparison matrix into two crisp nonnegative matrices. The interval pair-wise comparison matrix in Eq. (12.8) can be decomposed into two crisp nonnegative matrices, as presented in Eqs. (12.10), (12.11), respectively. 1 mL12 ⋯ mL1n 1=mU 1 ⋯ mL2n 21 ML ¼ (12.10) ⋮ ⋱ ⋮ ⋮ 1=mU 1=mU ⋯ 1 n1 n2 U 1 m12 ⋯ mU 1n U 1=mL 1 ⋯ m2n 21 (12.11) MU ¼ ⋮ ⋮ ⋱ ⋮ 1=mL 1=mL ⋯ 1 n1 n2
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The geometric mean method (Ren, 2018) can be used to determine the weights according to the matrices presented in Eqs. (12.10), (12.11), and the weight vectors determined by these two matrices are presented in Eqs. (12.12), (12.13), respectively. (12.12) WL ¼ ωL1 ωL2 ⋯ ωLn U U WU ¼ ω1 ω2 ⋯ ωU (12.13) n where WL and WU represent the weight vectors determined by the matrices presented in Eqs. (12.10), (12.11), respectively. ωLj and ωU j are the weights of the jth metric in WL and WU, respectively. Step 3: Determining the interval weights. The interval weights of each metric can be determined by Eqs. (12.14)–(12.16). vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uX u n 1 k¼u (12.14) n u X t j¼1 + qij i¼1
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uX u n 1 m¼u n u X t j¼1 q ij
(12.15)
i¼1
It is worth pointing out that if k and m satisfy 0 < k 1 m, then the users can use Eq. (12.16) to determine the interval weight of the jth metric, or the users should modify the interval pair-wise comparison matrix to make k and m satisfy this condition. h i ω ω (12.16) ¼ kωLj mωU ¼ ω j j j , L , U j where ω j represents the interval weight of the jth criterion and ωj, L and ωj, U are the lower and upper bounds of ωj , respectively.
2.3 Interval gray relational analysis The interval gray relational analysis (GRA) method was presented in the following six steps based on the work of Zhang (2005), Wang et al. (2017), and Manzardo et al. (2012). Step 1: Establishing the interval decision-making matrix. This step is to determine the weights of the decision criteria by using the IAHP method and to collect the data of the alternatives with respect to the decision criteria.
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Assuming that there are a total of n decision attributes C1, C2, … , Cn to assess the n alternatives, namely, A1, A2, … , Am, then, the interval decisionmaking matrix can be determined, as presented in Eq. (12.17). C1 C2 ⋯ Cn A1 x x ⋯ x 11 12 1n x ⋮ x ¼ A2 x X ¼ xij (12.17) 21 22 2n mn ⋮ ⋮ ⋯ ⋱ ⋮ Am x x ⋯ x m1 m2 mn h i x+ represents the value of the ith alternative with respect ¼ x where x ij ij ij to the jth attribute. Step 2: Normalizing the decision-making matrix. In order to avoid the effects caused by the unit gaps existing in the data of the interval decisionmaking matrix, all the data determined by step 1 can be normalized according to Eqs. (12.18), (12.19). As for the benefit-type criteria, 8 x ij > > s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi > m > X > 1 > + > x 2 > < n j¼1 ij h i > rij ¼ rij rij+ ¼ (12.18) xij+ > > > sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi > m > X > 1 > + > xij 2 > : n j¼1 As for the cost-type criteria,
h i rij ¼ rij rij+ ¼
8 1=xij+ > > s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi > > m > X 1 2 > > > 1=xij > < n j¼1 1=x > ij > > sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi > > m
2 X > 1 > > 1=x > ij : n
(12.19)
j¼1
Step 3: Determining the weighted normalized decision-making matrix. After determining the normalized decision-making matrix, the weighted normalized decision-making matrix, Eq. (12.20), can be obtained by incorporating the criterion weights.
Prioritization of biofuels production pathways under uncertainties
C2 C1 ω 2 r12 A1 ω1 r11 V ¼ vij ¼ A2 ω1 r21 ω2 r22 mn ⋮ ⋮ ⋯ A m ω r ω r 1 m1 2 m2
⋯ Cn ⋯ ω n r1n ⋮ ωn r2n ⋱ ⋮ ⋯ ωn rmn
347
(12.20)
where ω 1 represents the interval weight of the jth criterion determined by the interval AHP method. Step 4: Determining the reference series. The reference series (RS) h i vjRS ¼ vjRS vjRS + , j ¼ 1 , 2,…,n can be determined by Eqs. (12.21)–(12.23).
RS ¼ v1RS , v2RS , …, vnRS
(12.21)
vjRS + ¼
max v + , j ¼ 1,2,…,n i¼1, 2, …, m ij
(12.22)
vjRS ¼
max v , j ¼ 1,2,…, n i¼1, 2, …, m ij
(12.23)
Step 5: Calculating the correlation coefficients of the series of each alternative to the reference series with respect to each criterion. ρ takes the value of 0.5 in this study.
min min d vij , vjRS + ρ max max d vij , vjRS i j j i
ξi ð j Þ ¼ (12.24) d vij , vjRS + ρmax max d vij , vjRS i
j
RS RS ) represents the distance between v , and it can be d(v ij , vj ij and vj determined according to the work of Wang et al. (2017). Step 6: Determining the correlation degree of the series of each alternative to the reference series.
ri ¼
n X
ξij ,i ¼ 1,2,…, m
(12.25)
j¼1
After determining the correlation degree of the series of each alternative to the reference series, the priority sequence of the alternatives can be determined according to the rule that the greater the value of ri, the more superior the alternative will be. Accordingly, the greater the value of ri, the more sustainable the corresponding pathway for biofuel production will be.
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3 Case study In order to illustrate the developed interval multicriteria decision making method for sustainability prioritization of biofuel production pathways under uncertainties, three alternative bioethanol production pathways including wheat-, corn-, and cassava-based technologies for bioethanol production were studied by the developed method. Eight criteria including life cycle cost (LCC) in economic aspect, climate change (CC), terrestrial acidification (TA), human toxicity (H.Tox), particulate matter formation (PMF) in environmental aspect, and social benefits (SB), contribution to economic development (CED), and food security (FS) in social-political aspect were used for sustainability assessment of these three bioethanol production pathways, and the data were modified from the work of Ren et al. (2015b), as presented in Table 12.2. The interval decision-making matrix can be determined by changing the data with 10% positive/negative derivations, and the results are presented in Table 12.3. Table 12.2 The data of the alternative bioethanol production pathways with respect to the eight criteria (Ren et al., 2015b) Criteria
Unit
Wheat-based
Corn-based
Cassava-based
CC TA H.Tox PMF LCC SB CED FS
kg CO2eq kg SO2eq kg1,4-dB eq Kg PM10 eq RMB Yuan – – –
5.746 2.806 1.619 0.342 5220 8.75 7 0.25
0.461 0.166 0.096 0.017 4937 8.75 8.75 1.25
1.662 0.834 0.481 0.105 4259 9.75 9.75 9.75
Table 12.3 The interval multicriteria decision making matrix for ranking the three alternative bioethanol production pathways Criteria
Unit
Wheat-based
Corn-based
Cassava-based
CC TA H.Tox PMF LCC SB CED FS
kg CO2eq kg SO2eq kg1,4-dB eq Kg PM10 eq RMB Yuan – – –
[5.171 6.321] [2.525 3.087] [1.457 1.781] [0.308 0.376] [4698 5742] [7.875 9.625] [6.3 7.7] [0.225 0.275]
[0.415 0.507] [0.149 0.183] [0.086 0.106] [0.015 0.019] [4443.3 5430.7] [7.875 9.625] [7.875 9.625] [1.125 1.375]
[1.496 1.828] [0.751 0.917] [0.433 0.529] [0.095 0.116] [3833.1 4684.9] [8.775 10.725] [8.775 10.725] [8.775 10.725]
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The interval AHP was then employed to determine the interval weights of the three dimensions (environmental, economic, and social aspects) and the local interval weights of the criteria in each dimension. Taking the weights of the three dimensions as an example, the interval comparison matrix was first determined, as presented in Eq. (12.26). Environmental Economic Social
Environmental Economic Social ½3 5 ½2 4 1 1 1 1 ½1 2 5 3 1 1 1 1 1 4 2 2
(12.26)
The interval pair-wise comparison matrix (presented in Eq. 12.26) into two crisp nonnegative matrices, as presented in Eqs. (12.27), (12.28), respectively. Environmental Economic Social 1 3 2 1 (12.27) 1 1 5 1 1 1 Social 4 2 Environmental Economic Social Environmental 1 5 4 1 (12.28) 1 2 Economic 3 1 1 1 Social 2 According to the geometric mean method, WL and WU can be determined, and the results are presented in Eqs. (12.29), (12.30), respectively. Environmental Economic
WL ¼ ½ 0:6262 0:2015 0:1723
(12.29)
WU ¼ ½ 0:6195 0:1994 0:1811
(12.30)
According to Eqs. (12.14), (12.15), the values of m and k can be determined, and m ¼ 1.0779, and k ¼ 0.9117. It can satisfy 0 < k 1 m, thus, the interval weights of the three dimensions can be determined by Eq.(12.16), and the results are presented in Eq. (12.31). W ¼ ½½ 0:5709 0:6678 , ½ 0:1837 0:2149 , ½ 0:1571 0:1953
(12.31)
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Table 12.4 The local weights of the four criteria in environmental aspect and the three criteria in social-political aspect
CC TA H.Tox PMF
SB CED FS Local weights
CC
TA
H.Tox
PMF
1 [1/3 1] [1/5 1/3] [1/5 1/3] [0.4051 0.5414]
[1 3] 1 [1/3 1/2] [1/3 1/2] [0.2513 0.3187]
[3 5] [2 3] 1 [1/2 1] [0.1188 0.1398]
[3 5] [2 3] [1 2] 1 [0.0999 0.1176]
SB
CED
FS
1 [1/2 1] [1 3] [0.2315 0.3190]
[1 2] 1 [3 5] [0.1550 0.1756]
[1/3 1] [1/5 1/3] 1 [0.4816 0.6244]
Table 12.5 The global weights of the criteria for sustainability assessment of bioethanol production pathways Dimension
Weights
Criteria
Local weights
Global weights
Environmental
[0.5709 0.6678]
Economic Social
[0.1837 0.2149] [0.1571 0.1953]
CC TA H.Tox PMF LCC SB CED FS
[0.4051 [0.2513 [0.1188 [0.0999 1 [0.2315 [0.1550 [0.4816
[0.2313 [0.1435 [0.0678 [0.0570 [0.1837 [0.0364 [0.0244 [0.0757
0.5414] 0.3187] 0.1398] 0.1176] 0.3190] 0.1756] 0.6244]
0.3615] 0.2128] 0.0934] 0.0785] 0.2149] 0.0623] 0.0343] 0.1219]
In a similar way, the local weights of the four criteria in environmental aspect and the three criteria in social-political aspect can also be determined, and the results are presented in Table 12.4. After this, the global weights of the eights criteria for sustainability assessment of bioethanol production pathways can be determined, and the global weight of each criterion ¼ the local weights of the each criterion the weight of the corresponding dimension to which it belongs to. It is worth pointing out that there is only one criterion (LCC) in economic aspect, and the local weight of LCC is 1. The global weights of these eight criteria are presented in Table 12.5.
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Then, the presented interval GRA method can be used to rank these three alternative bioethanol production pathways. According to Eqs. (12.18), (12.19), the data presented in Table 12.3 can be normalized. It is worth pointing out that the first five criteria including CC, TA, H. Tox, OMF, and LCC are cost-type criteria, thus, the data of the three biofuel production pathways with respect to these five criteria can be normalized by Eq. (12.19), and the other three criteria including SB, CEM, and FS are benefit-type criteria, thus, the data of the three biofuel production pathways with respect to these three criteria can be normalized by Eq. (12.18). The normalized decision-making matrix is presented in Table 12.6. According to Eq. (12.20), the weighted normalized decision-making matrix can be obtained. Taking the data of wheat-based pathway for bioethanol production with respect to CC can be obtained by Eq. (12.32). ½0:1092 0:1335 ½0:2313 0:3615 ¼ ½0:0253 0:0483
(12.32)
In a similar way, all the data in the weighted normalized decision-making matrix can be obtained, and the results are presented in Table 12.7. Table 12.6 The normalized decision-making matrix Criteria
Wheat-based
Corn-based
Cassava-based
CC TA H.Tox PMF LCC SB CED FS
[0.1092 [0.0821 [0.0823 [0.0695 [0.7448 [0.7871 [0.6679 [0.0360
[1.3615 [1.3875 [1.3874 [1.3972 [0.7875 [0.7871 [0.8348 [0.1802
[0.3777 [0.2762 [0.2769 [0.2262 [0.9129 [0.8771 [0.9302 [1.4052
0.1335] 0.1003] 0.1005] 0.0849] 0.9103] 0.9620] 0.8163] 0.0440]
1.6641] 1.6959] 1.6957] 1.7077] 0.9625] 0.9620] 1.0203] 0.2202]
0.4616] 0.3375] 0.3384] 0.2765] 1.1157] 1.0720] 1.1369] 1.7174]
Table 12.7 The weighted normalized decision-making matrix Criteria
Wheat-based
Corn-based
Cassava-based
CC TA H.Tox PMF LCC SB CED FS
[0.0253 [0.0118 [0.0056 [0.0040 [0.1368 [0.0287 [0.0163 [0.0027
[0.3149 [0.1991 [0.0941 [0.0796 [0.1447 [0.0287 [0.0204 [0.0136
[0.0874 [0.0396 [0.0188 [0.0129 [0.1677 [0.0319 [0.0227 [0.1064
0.0483] 0.0213] 0.0094] 0.0067] 0.1956] 0.0599] 0.0280] 0.0054]
0.6016] 0.3609] 0.1584] 0.1341] 0.2068] 0.0599] 0.0350] 0.0268]
0.1669] 0.0718] 0.0316] 0.0217] 0.2398] 0.0668] 0.0390] 0.2094]
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Table 12.8 The reference series Criteria
Reference series
CC TA H.Tox PMF LCC SB CED FS
[0.3149 [0.1991 [0.0941 [0.0796 [0.1677 [0.0319 [0.0227 [0.1064
0.6016] 0.3609] 0.1584] 0.1341] 0.2398] 0.0668] 0.0390] 0.2094]
Table 12.9 The correlation degree of the series of each alternative to the reference series
Correlation degree Ranking
Wheat-based
Corn-based
Cassava-based
5.4678 3
7.4517 1
6.2592 2
According to Eqs. (12.21)–(12.23), the reference series can be obtained, and the results are presented in Table 12.8. Finally, the correlation degree of the series of each alternative to the reference series can be determined by Eqs. (12.24)–(12.25), and the results are presented in Table 12.9. Therefore the corn-based pathway for bioethanol production was recognized as the most sustainable, followed by cassava- and wheat-based pathways in the descending order.
4 Discussion In order to investigate the effects of the weights of the criteria on the sustainability ranking of the three pathways for biofuel production, sensitivity analysis was carried out by changing the weights of the criteria for sustainability assessment of biofuel production pathways, and the following nine cases have been studied: Case 0: Equal weights—an equal weight (0.1250) was assigned to the eight criteria for sustainability assessment of biofuel production pathways. Case 1–8: A dominant weight (0.4400) was assigned to each of the eight criteria in each case and all the other nine criteria were assigned an equal weight (0.0800).
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8 7.5 7 6.5 6
Wheat-based Corn-based Cassava-based
5.5 5 4.5 4 3.5 3 Case 0 Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7 Case 8
Fig. 12.2 The results of sensitivity analysis.
The results of sensitivity analysis are presented in Fig. 12.2. It is apparent that the results are robust; the sustainability sequence from the most sustainable to the least is corn-, cassava-, and wheat-based pathways for bioethanol production in all the nine cases.
5 Conclusion This study developed an interval multicriteria decision making method for sustainability ranking of alternative biofuel production pathways, the interval AHP was employed to determine the weights (relative importance) of the criteria for sustainability assessment of biofuel production pathways, and the interval GRA method was employed to determine the sustainability sequence of the alternative biofuel production pathways. The developed interval multicriteria decision making method for sustainability ranking of alternative biofuel production pathways has the following two advantages: (1) The use of interval AHP method can effectively address the ambiguity, hesitation, and vagueness existing in human’s judgments when comparing the relative preference of a criterion over another. (2) The use of interval GRA can achieve multicriteria decision making under uncertainties, because the data in the decision-making matrix are interval numbers rather than the traditional crisp numbers.
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Acknowledgment This method used in this study was based on Wang, Z., Xu, G., Ren, J., Li, Z., Zhang, B., Ren, X., 2017. Polygeneration system and sustainability: multi-attribute decision-support framework for comprehensive assessment under uncertainties. J. Clean. Prod. 167, 1122–1137.
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Prioritization of biofuels production pathways under uncertainties Ruojue Lin, Yue Liu, Jingzheng Ren Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong SAR, China
Contents 1 Introduction 2 Interval multicriteria decision making method 2.1 Interval numbers 2.2 Interval AHP 2.3 Interval gray relational analysis 3 Case study 4 Discussion 5 Conclusion Acknowledgment References
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1 Introduction Biofuel has been recognized as a promising solution to sustainable and lowcarbon transport, because it can be produced from various types of biomass to substitute the petroleum-derived fuel and reduce emissions from transport sector (Hao et al., 2018). Biofuel is one of the most promising renewable energy carriers, and it can be produced from various feedstocks such as biomass, algal, and some other nonstaple food crops (Liang et al., 2016). However, there are also some challenges for promoting the development of biofuels including the relatively higher production, the negative impacts on food security, and competition with some other renewable energy resources (Ren et al., 2015a). Meanwhile, there are also some emissions in the whole life cycle of biofuels, because there is also some consumption for cropping, transportation of biomass resources, biofuel production, transportation of biofuels, and so on (Ren et al., 2014). Therefore the Biofuels for a More Sustainable Future https://doi.org/10.1016/B978-0-12-815581-3.00012-9
© 2020 Elsevier Inc. All rights reserved.
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development of biofuel industry is still “in debate,” and people are usually puzzled with two questions: (i) Is biofuel really sustainable? (ii) Which is the most sustainable pathway for biofuel production? As for the question: is biofuel really sustainable? There are many studies for answering this question. The most typical is to use life cycle tools to analyze the sustainability of biofuel production pathways from cradle to grave. For instance, Ou et al. (2009) employed life cycle assessment (LCA) to investigate the energy consumption and GHG emissions of six biofuel pathways in China. Yang et al. (2011) used life cycle thinking to analyze the water footprint and nutrients balance of biodiesel from microalgae. Requena et al. (2011) employed LCA to study the environmental impacts of biofuels from sunflower oil, rapeseed oil, and soybean oil. However, all these studies can only answer the first question. As for the second question: which is the most sustainable pathway for biofuel production? It is usually different and even the stakeholders/decision-makers know the performances of different biofuel production pathways and there are two main reasons: (i) there are usually various conflict criteria for sustainability assessment of biofuel production pathways; (ii) there are various data uncertainties, and the data of the alternative biofuel production pathways with respect to the evaluation criteria usually varies. Therefore this study aims at developing an interval multicriteria decision making (MCDM) method for sustainability prioritization of biofuel production pathways under uncertainties. MCDM is a widely used decision-making tool that allows for scientific and comprehensive analysis based on multiple data and decision-maker’s preferences (Triantaphyllou, 2000). MCDM methods commonly used include Analytic Hierarchy Process (AHP) (Saaty, 1980), Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) (Hwang and Yoon, 1981), Gray Relational Analysis (GRA) (Deng, 1989), The Preference Ranking Organization Method for Enrichment of Evaluations (PROMETHEE) (Brans et al., 1986), and Elimination and Choice Expressing Reality (ELECTRE) (Benayoun et al., 1966). The decision-making method based on uncertain data is an extension of MCDM, which is used to analyze the ranking, selection, and classification of more than one evaluation criterion with uncertain or fuzzy information in the data (Ho et al., 2010). Due to the uncertainty of subjective judgment, the normal fluctuation caused by environmental factors, and the uncertainty caused by knowledge limitations, the application of MCDM under uncertainties plays a significant role in strategy establishment (Ren and Toniolo, 2018). MCDM dealing with uncertain data can be classified into interval MCDM, fuzzy
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MCDM, intuitional fuzzy MCDM, and stochastic MCDM. Interval MCDM takes the interval number as the input data in the decision process, so that the value of each criterion reflects its maximum and minimum values (Tsaur, 2011). For example, Giove (2002) and Jahanshahloo et al. (2006) have extended TOPSIS into interval TOPSIS. Fuzzy MCDM is the MCDM that bringing fuzzy number such as triangular fuzzy number and trapezoidal fuzzy number into consideration (Pohekar and Ramachandran, 2004; Kahraman, 2008). The fuzzy number consists more information than interval number to express the uncertainty (Pohekar and Ramachandran, 2004; Kahraman, 2008). For instance, Sevkli (2010) extended ELECTRE into fuzzy ELECTRE, Shemshadi et al. (2011) extended VIKOR into fuzzy VIKOR, and Liu and Wang (2007) developed a MCDM based on intuitionistic fuzzy. The fuzzy MCDM has been further extended into intuitional fuzzy MCDM which adds degree of nonmembership to better express the uncertainty (Liu and Wang, 2007). Different from fuzzy MCDM, stochastic MCDM uses randomness to reveal the uncertainty sets (Ramanathan, 1997). For example, Xiong and Qi (2010) have extended TOPSIS into stochastic multicriteria decision making method. Furthermore, many researchers have also tried to combine different MCDM methods under uncertainty to form hybrid MCDM. For example, B€ uy€ uk€ ozkan and C ¸ ifc¸i (2012) have proposed a hybrid MCDM approach combining fuzzy Decision making trial and evaluation laboratory (DEMATEL), fuzzy (Analytic Network Process) ANP, and fuzzy TOPSIS together. Some researchers have done studies to compare biofuel production processes sustainably (e.g., Ou et al., 2009; Yang et al., 2011; Larkum et al., 2012), but these researches cannot show the direct priority through the comparisons. Some people helped to make choices in this selection problem (e.g., Schaidle et al., 2011; Vlysidis et al., 2011; Sharma et al., 2011), but they did not consider uncertainties in the biofuel production processes. Furthermore, some scholars have studied energy selection problem but have not specifically scoped to biofuel such as Sadeghi et al. (2012) provided a fuzzy MCDM approach for renewable electricity production and Lee et al. (2009) have conducted a fuzzy AHP method for energy technology prioritization. Therefore we shall bring uncertainties into consideration and provide a scientific and comprehensive analysis for biofuel production pathways prioritization. Because the interval number represents the uncertainty of the data biofuel production process and leads to few obstacles in data collection, so the data type of interval MCDM is more in line with the operation of sustainable biofuel production selection. The interval AHP which allows the
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users to use interval numbers rather than the basketball numbers to establish the comparison matrix was employed for determining the weights of the criteria for sustainability assessment of biofuel production pathways, and the interval GRA method was employed to determine the sustainability sequence of alternative biofuel production pathways under uncertainties.
2 Interval multicriteria decision making method Interval multicriteria decision making method is a series of MCDM adapting interval numbers as criteria inputs and weights, which helps to deal with complex decision-making cases with vagueness of language and uncertainty of criteria values. The interval VIKOR raised by Sayadi et al. (2009) supports decision-makers to rank the alternatives with regards to its performances comparing to the best and the worst alternative. Giove (2002) and Jahanshahloo et al. (2006) have extended TOPSIS into interval TOPSIS, respectively. The interval TOPSIS considers the balance between needs fulfillment and lost compromise. Luo et al. (2015) developed an interval GRA method based on the grey theory invented by Deng (1989). Xu and Da (2003) have extended the AHP method into the interval analytic hierarchy process (IAHP), which assistant to quantify the criteria values and weights according to quality values. In addition, interval PROMETHEE (Le Teno and Mareschal, 1998) and interval Best Worst Method (BWM) (Rezaei, 2016) are methods for dealing qualified inputs as well. Among these, the IAHP is one of the most commonly used weighting methods in MCDM for its advantage of addressing the hesitations and ambiguity existing in human’s judgments. In this section, interval multicriteria decision making method for biofuel production pathways selection is described. Criteria system establishment, criteria weighting, and aggregating are three steps for MCDM method whose methods are designed as criteria system establishment, interval AHP, and interval GRA as shown in Fig. 12.1.
2.1 Interval numbers The basic information of interval numbers was presented in this section based on the work of He et al. (2017), Zhang et al. (2005), Bohlender and Kulisch (2011), Moore (1966), Dymova et al. (2013), and Xu and Da (2003). Let x ¼ ½x , x + ¼ fxjx x x + , x x + ,x , x + 2 R g. Here + x ¼ ½x , x is called an interval number and is a positive interval number
Prioritization of biofuels production pathways under uncertainties
Criteria system establishment
Topic information collection
All criteria summarization
Criteria selection and criteria system building
Criteria weighting—interval AHP
30% 20% 5% ... Criteria information and prioritization opinions collection
Criteria pairwise comparison Criteria weighting based on information and through calculation expert judgements
Alternative ranking—interval GRA
A1
A2
A3
...
C1 C2 C3 ...
Best alternative selection through calculation
Alternative information collection and make decision matrix 30% 20% 5%
...
Use alternative data and criteria weights as input
Fig. 12.1 Methodology of biofuel production pathways selection.
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if 0 x x + [see the work of Zhang et al. (2005)]. It is apparent that an interval number can take an arbitrary value between its lower bound and upper bound. Definition 1 Distance between two interval numbers (Yue, 2011) If x ¼ ½x , x + and y ¼[ y, y+] are two arbitrary interval numbers, the distance from x ¼ ½x , x + to y ¼[ y, y+] can be determined by qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (12.1) jx yj ¼ ðx y Þ2 + ðx + y + Þ2 Definition 2 Number product between a positive real number and an interval number (Zhang et al., 2005) The number product of a positive real number λ and an interval number x ¼ ½x , x + is defined as λ x ¼ λ½x , x + ¼ ½λx , λ x +
(12.2)
Note that a crisp number λ could also be transformed into an interval number λ ¼ λ, λ]. Definition 3 Addition (Bohlender and Kulisch, 2011) If x ¼ ½x , x + and y ¼[ y, y+] are two arbitrary interval numbers, the sum of the two interval numbers can be obtained by x + y ¼ ½x , x + + ½y , y + ¼ ½x + y , x + + y +
(12.3)
Definition 4 Subtraction (Moore, 1966; Dymova et al., 2013) If x ¼ ½x , x + and y ¼[ y, y+] are two arbitrary interval numbers, the subtraction between two interval numbers can be determined by x y ¼ ½x , x + ½y , y + ¼ ½x y + ; x + y
(12.4)
Definition 5 Multiplication (Zhang et al., 2005) If x ¼ ½x , x + and y ¼[ y, y+] are two arbitrary interval numbers, the interval product can be obtained according to the following two cases: (1) when y+ > 0, the interval product can be determined by x y ¼ ½x , x + ½y , y ¼ ½x y , x + y +
(12.5)
(2) when y+ < 0, the interval product can be determined by x x ¼ ½x , x + ½y , y + ¼ ½x + y , x y +
(12.6)
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Definition 6 The possibility of an interval being greater than another For two arbitrary interval numbers x ¼ ½x , x + and y ¼[ y, y+], the possibilities that x y and that b a are defined in the following two equations, respectively (Xu and Da, 2003): y + x + + ,0 pxy ¼ pð½x , x ½y , y Þ ¼ max 1 max + y y + x + x (12.7)
2.2 Interval AHP The interval analytic hierarchy process (IAHP) developed by Xu and Da (2003) has been widely used in various fields for its advantage of address ambiguity and hesitation existing in human judgments. Ren (2018) summarized the IAHP method developed by Xu and Da (2003) in the following three steps: Step 1: Establishing the interval pair-wise comparison matrix. Assuming that there are n criteria (C1, C2, … , Cn) which need the stakeholders/decision-makers to determine the relative importance (weights), the stakeholders/decision-makers were asked to use the Saaty’s nine-scale system (Saaty, 2008) to establish the pair-wise comparison matrix (see Table 12.1). However, it is different from the traditional AHP method which relies on employing the numbers(from 1 to 9) and their corresponding reciprocals to establish the pair-wise comparison matrix, the users of the interval numbers rather than the single numbers which sometime cannot Table 12.1 Saaty scales for establishing the pair-wise comparison matrix (Saaty, 2008) Scales
Definition
Explanation
1
Equal importance Moderate importance Essential importance Very strong importance Absolute importance Intermediate value
Two elements perform equally
3 5 7 9 2,4,6,8
Experience and judgment slightly favor one element over another Experience and judgment strongly favor one element over another An element is favored very strongly over another; its dominance demonstrated in practice The evidence favoring one element over another is of the highest possible order of affirmation Intermediate value
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depict the relative importance/preference of one criterion over another accurately. For instance, it is difficult or even impossible to depict the relative weight/priority of a criterion over another when the stakeholders/ decision-makers think that the relative importance of a criterion over another is between “moderate importance” (corresponding to number 3) and “essential importance” (corresponding to number 5). Accordingly, the interval number [3 5] should be used to depict this judgment. In a similar way, the interval comparison matrix for determining the relative importance (weights) of the n metrics can be established: C1 C2 C1 1 mL12 , mU 12 1 M ¼ C2 mL21 , mU 21 ⋮ ⋮ ⋮ Cn mLn1 , mU mLn2 , mU n1 n2
⋯ Cn ⋯ mL1n , mU 1n ⋯ mL2n , mU 2n ⋱ ⋮ ⋯ 1
(12.8)
where M represents the interval pair-wise matrix for determining the relative weights of the n criteria, [mLij , mU ij ] which is an interval number represents the relative preference of the ith criterion over the jth criterion, and mLij L U and mU ij are the lower and upper boundary of the interval number [qij , qij ]. The relative preference of the jth criterion over ith metric can be determined by Eq. (12.9). " # h i 1 1 1 h i ¼ U , L , i, j ¼ 1,2,…,n (12.9) mLji , mU ji ¼ mij mij mL , mU ij
ij
Step 2: Decomposing the interval pair-wise comparison matrix into two crisp nonnegative matrices. The interval pair-wise comparison matrix in Eq. (12.8) can be decomposed into two crisp nonnegative matrices, as presented in Eqs. (12.10), (12.11), respectively. 1 mL12 ⋯ mL1n 1=mU 1 ⋯ mL2n 21 ML ¼ (12.10) ⋮ ⋱ ⋮ ⋮ 1=mU 1=mU ⋯ 1 n1 n2 U 1 m12 ⋯ mU 1n U 1=mL 1 ⋯ m2n 21 (12.11) MU ¼ ⋮ ⋮ ⋱ ⋮ 1=mL 1=mL ⋯ 1 n1 n2
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The geometric mean method (Ren, 2018) can be used to determine the weights according to the matrices presented in Eqs. (12.10), (12.11), and the weight vectors determined by these two matrices are presented in Eqs. (12.12), (12.13), respectively. (12.12) WL ¼ ωL1 ωL2 ⋯ ωLn U U WU ¼ ω1 ω2 ⋯ ωU (12.13) n where WL and WU represent the weight vectors determined by the matrices presented in Eqs. (12.10), (12.11), respectively. ωLj and ωU j are the weights of the jth metric in WL and WU, respectively. Step 3: Determining the interval weights. The interval weights of each metric can be determined by Eqs. (12.14)–(12.16). vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uX u n 1 k¼u (12.14) n u X t j¼1 + qij i¼1
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uX u n 1 m¼u n u X t j¼1 q ij
(12.15)
i¼1
It is worth pointing out that if k and m satisfy 0 < k 1 m, then the users can use Eq. (12.16) to determine the interval weight of the jth metric, or the users should modify the interval pair-wise comparison matrix to make k and m satisfy this condition. h i ω ω (12.16) ¼ kωLj mωU ¼ ω j j j , L , U j where ω j represents the interval weight of the jth criterion and ωj, L and ωj, U are the lower and upper bounds of ωj , respectively.
2.3 Interval gray relational analysis The interval gray relational analysis (GRA) method was presented in the following six steps based on the work of Zhang (2005), Wang et al. (2017), and Manzardo et al. (2012). Step 1: Establishing the interval decision-making matrix. This step is to determine the weights of the decision criteria by using the IAHP method and to collect the data of the alternatives with respect to the decision criteria.
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Assuming that there are a total of n decision attributes C1, C2, … , Cn to assess the n alternatives, namely, A1, A2, … , Am, then, the interval decisionmaking matrix can be determined, as presented in Eq. (12.17). C1 C2 ⋯ Cn A1 x x ⋯ x 11 12 1n x ⋮ x ¼ A2 x X ¼ xij (12.17) 21 22 2n mn ⋮ ⋮ ⋯ ⋱ ⋮ Am x x ⋯ x m1 m2 mn h i x+ represents the value of the ith alternative with respect ¼ x where x ij ij ij to the jth attribute. Step 2: Normalizing the decision-making matrix. In order to avoid the effects caused by the unit gaps existing in the data of the interval decisionmaking matrix, all the data determined by step 1 can be normalized according to Eqs. (12.18), (12.19). As for the benefit-type criteria, 8 x ij > > s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi > m > X > 1 > + > x 2 > < n j¼1 ij h i > rij ¼ rij rij+ ¼ (12.18) xij+ > > > sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi > m > X > 1 > + > xij 2 > : n j¼1 As for the cost-type criteria,
h i rij ¼ rij rij+ ¼
8 1=xij+ > > s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi > > m > X 1 2 > > > 1=xij > < n j¼1 1=x > ij > > sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi > > m
2 X > 1 > > 1=x > ij : n
(12.19)
j¼1
Step 3: Determining the weighted normalized decision-making matrix. After determining the normalized decision-making matrix, the weighted normalized decision-making matrix, Eq. (12.20), can be obtained by incorporating the criterion weights.
Prioritization of biofuels production pathways under uncertainties
C2 C1 ω 2 r12 A1 ω1 r11 V ¼ vij ¼ A2 ω1 r21 ω2 r22 mn ⋮ ⋮ ⋯ A m ω r ω r 1 m1 2 m2
⋯ Cn ⋯ ω n r1n ⋮ ωn r2n ⋱ ⋮ ⋯ ωn rmn
347
(12.20)
where ω 1 represents the interval weight of the jth criterion determined by the interval AHP method. Step 4: Determining the reference series. The reference series (RS) h i vjRS ¼ vjRS vjRS + , j ¼ 1 , 2,…,n can be determined by Eqs. (12.21)–(12.23).
RS ¼ v1RS , v2RS , …, vnRS
(12.21)
vjRS + ¼
max v + , j ¼ 1,2,…,n i¼1, 2, …, m ij
(12.22)
vjRS ¼
max v , j ¼ 1,2,…, n i¼1, 2, …, m ij
(12.23)
Step 5: Calculating the correlation coefficients of the series of each alternative to the reference series with respect to each criterion. ρ takes the value of 0.5 in this study.
min min d vij , vjRS + ρ max max d vij , vjRS i j j i
ξi ð j Þ ¼ (12.24) d vij , vjRS + ρmax max d vij , vjRS i
j
RS RS ) represents the distance between v , and it can be d(v ij , vj ij and vj determined according to the work of Wang et al. (2017). Step 6: Determining the correlation degree of the series of each alternative to the reference series.
ri ¼
n X
ξij ,i ¼ 1,2,…, m
(12.25)
j¼1
After determining the correlation degree of the series of each alternative to the reference series, the priority sequence of the alternatives can be determined according to the rule that the greater the value of ri, the more superior the alternative will be. Accordingly, the greater the value of ri, the more sustainable the corresponding pathway for biofuel production will be.
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3 Case study In order to illustrate the developed interval multicriteria decision making method for sustainability prioritization of biofuel production pathways under uncertainties, three alternative bioethanol production pathways including wheat-, corn-, and cassava-based technologies for bioethanol production were studied by the developed method. Eight criteria including life cycle cost (LCC) in economic aspect, climate change (CC), terrestrial acidification (TA), human toxicity (H.Tox), particulate matter formation (PMF) in environmental aspect, and social benefits (SB), contribution to economic development (CED), and food security (FS) in social-political aspect were used for sustainability assessment of these three bioethanol production pathways, and the data were modified from the work of Ren et al. (2015b), as presented in Table 12.2. The interval decision-making matrix can be determined by changing the data with 10% positive/negative derivations, and the results are presented in Table 12.3. Table 12.2 The data of the alternative bioethanol production pathways with respect to the eight criteria (Ren et al., 2015b) Criteria
Unit
Wheat-based
Corn-based
Cassava-based
CC TA H.Tox PMF LCC SB CED FS
kg CO2eq kg SO2eq kg1,4-dB eq Kg PM10 eq RMB Yuan – – –
5.746 2.806 1.619 0.342 5220 8.75 7 0.25
0.461 0.166 0.096 0.017 4937 8.75 8.75 1.25
1.662 0.834 0.481 0.105 4259 9.75 9.75 9.75
Table 12.3 The interval multicriteria decision making matrix for ranking the three alternative bioethanol production pathways Criteria
Unit
Wheat-based
Corn-based
Cassava-based
CC TA H.Tox PMF LCC SB CED FS
kg CO2eq kg SO2eq kg1,4-dB eq Kg PM10 eq RMB Yuan – – –
[5.171 6.321] [2.525 3.087] [1.457 1.781] [0.308 0.376] [4698 5742] [7.875 9.625] [6.3 7.7] [0.225 0.275]
[0.415 0.507] [0.149 0.183] [0.086 0.106] [0.015 0.019] [4443.3 5430.7] [7.875 9.625] [7.875 9.625] [1.125 1.375]
[1.496 1.828] [0.751 0.917] [0.433 0.529] [0.095 0.116] [3833.1 4684.9] [8.775 10.725] [8.775 10.725] [8.775 10.725]
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349
The interval AHP was then employed to determine the interval weights of the three dimensions (environmental, economic, and social aspects) and the local interval weights of the criteria in each dimension. Taking the weights of the three dimensions as an example, the interval comparison matrix was first determined, as presented in Eq. (12.26). Environmental Economic Social
Environmental Economic Social ½3 5 ½2 4 1 1 1 1 ½1 2 5 3 1 1 1 1 1 4 2 2
(12.26)
The interval pair-wise comparison matrix (presented in Eq. 12.26) into two crisp nonnegative matrices, as presented in Eqs. (12.27), (12.28), respectively. Environmental Economic Social 1 3 2 1 (12.27) 1 1 5 1 1 1 Social 4 2 Environmental Economic Social Environmental 1 5 4 1 (12.28) 1 2 Economic 3 1 1 1 Social 2 According to the geometric mean method, WL and WU can be determined, and the results are presented in Eqs. (12.29), (12.30), respectively. Environmental Economic
WL ¼ ½ 0:6262 0:2015 0:1723
(12.29)
WU ¼ ½ 0:6195 0:1994 0:1811
(12.30)
According to Eqs. (12.14), (12.15), the values of m and k can be determined, and m ¼ 1.0779, and k ¼ 0.9117. It can satisfy 0 < k 1 m, thus, the interval weights of the three dimensions can be determined by Eq.(12.16), and the results are presented in Eq. (12.31). W ¼ ½½ 0:5709 0:6678 , ½ 0:1837 0:2149 , ½ 0:1571 0:1953
(12.31)
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Table 12.4 The local weights of the four criteria in environmental aspect and the three criteria in social-political aspect
CC TA H.Tox PMF
SB CED FS Local weights
CC
TA
H.Tox
PMF
1 [1/3 1] [1/5 1/3] [1/5 1/3] [0.4051 0.5414]
[1 3] 1 [1/3 1/2] [1/3 1/2] [0.2513 0.3187]
[3 5] [2 3] 1 [1/2 1] [0.1188 0.1398]
[3 5] [2 3] [1 2] 1 [0.0999 0.1176]
SB
CED
FS
1 [1/2 1] [1 3] [0.2315 0.3190]
[1 2] 1 [3 5] [0.1550 0.1756]
[1/3 1] [1/5 1/3] 1 [0.4816 0.6244]
Table 12.5 The global weights of the criteria for sustainability assessment of bioethanol production pathways Dimension
Weights
Criteria
Local weights
Global weights
Environmental
[0.5709 0.6678]
Economic Social
[0.1837 0.2149] [0.1571 0.1953]
CC TA H.Tox PMF LCC SB CED FS
[0.4051 [0.2513 [0.1188 [0.0999 1 [0.2315 [0.1550 [0.4816
[0.2313 [0.1435 [0.0678 [0.0570 [0.1837 [0.0364 [0.0244 [0.0757
0.5414] 0.3187] 0.1398] 0.1176] 0.3190] 0.1756] 0.6244]
0.3615] 0.2128] 0.0934] 0.0785] 0.2149] 0.0623] 0.0343] 0.1219]
In a similar way, the local weights of the four criteria in environmental aspect and the three criteria in social-political aspect can also be determined, and the results are presented in Table 12.4. After this, the global weights of the eights criteria for sustainability assessment of bioethanol production pathways can be determined, and the global weight of each criterion ¼ the local weights of the each criterion the weight of the corresponding dimension to which it belongs to. It is worth pointing out that there is only one criterion (LCC) in economic aspect, and the local weight of LCC is 1. The global weights of these eight criteria are presented in Table 12.5.
Prioritization of biofuels production pathways under uncertainties
351
Then, the presented interval GRA method can be used to rank these three alternative bioethanol production pathways. According to Eqs. (12.18), (12.19), the data presented in Table 12.3 can be normalized. It is worth pointing out that the first five criteria including CC, TA, H. Tox, OMF, and LCC are cost-type criteria, thus, the data of the three biofuel production pathways with respect to these five criteria can be normalized by Eq. (12.19), and the other three criteria including SB, CEM, and FS are benefit-type criteria, thus, the data of the three biofuel production pathways with respect to these three criteria can be normalized by Eq. (12.18). The normalized decision-making matrix is presented in Table 12.6. According to Eq. (12.20), the weighted normalized decision-making matrix can be obtained. Taking the data of wheat-based pathway for bioethanol production with respect to CC can be obtained by Eq. (12.32). ½0:1092 0:1335 ½0:2313 0:3615 ¼ ½0:0253 0:0483
(12.32)
In a similar way, all the data in the weighted normalized decision-making matrix can be obtained, and the results are presented in Table 12.7. Table 12.6 The normalized decision-making matrix Criteria
Wheat-based
Corn-based
Cassava-based
CC TA H.Tox PMF LCC SB CED FS
[0.1092 [0.0821 [0.0823 [0.0695 [0.7448 [0.7871 [0.6679 [0.0360
[1.3615 [1.3875 [1.3874 [1.3972 [0.7875 [0.7871 [0.8348 [0.1802
[0.3777 [0.2762 [0.2769 [0.2262 [0.9129 [0.8771 [0.9302 [1.4052
0.1335] 0.1003] 0.1005] 0.0849] 0.9103] 0.9620] 0.8163] 0.0440]
1.6641] 1.6959] 1.6957] 1.7077] 0.9625] 0.9620] 1.0203] 0.2202]
0.4616] 0.3375] 0.3384] 0.2765] 1.1157] 1.0720] 1.1369] 1.7174]
Table 12.7 The weighted normalized decision-making matrix Criteria
Wheat-based
Corn-based
Cassava-based
CC TA H.Tox PMF LCC SB CED FS
[0.0253 [0.0118 [0.0056 [0.0040 [0.1368 [0.0287 [0.0163 [0.0027
[0.3149 [0.1991 [0.0941 [0.0796 [0.1447 [0.0287 [0.0204 [0.0136
[0.0874 [0.0396 [0.0188 [0.0129 [0.1677 [0.0319 [0.0227 [0.1064
0.0483] 0.0213] 0.0094] 0.0067] 0.1956] 0.0599] 0.0280] 0.0054]
0.6016] 0.3609] 0.1584] 0.1341] 0.2068] 0.0599] 0.0350] 0.0268]
0.1669] 0.0718] 0.0316] 0.0217] 0.2398] 0.0668] 0.0390] 0.2094]
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Table 12.8 The reference series Criteria
Reference series
CC TA H.Tox PMF LCC SB CED FS
[0.3149 [0.1991 [0.0941 [0.0796 [0.1677 [0.0319 [0.0227 [0.1064
0.6016] 0.3609] 0.1584] 0.1341] 0.2398] 0.0668] 0.0390] 0.2094]
Table 12.9 The correlation degree of the series of each alternative to the reference series
Correlation degree Ranking
Wheat-based
Corn-based
Cassava-based
5.4678 3
7.4517 1
6.2592 2
According to Eqs. (12.21)–(12.23), the reference series can be obtained, and the results are presented in Table 12.8. Finally, the correlation degree of the series of each alternative to the reference series can be determined by Eqs. (12.24)–(12.25), and the results are presented in Table 12.9. Therefore the corn-based pathway for bioethanol production was recognized as the most sustainable, followed by cassava- and wheat-based pathways in the descending order.
4 Discussion In order to investigate the effects of the weights of the criteria on the sustainability ranking of the three pathways for biofuel production, sensitivity analysis was carried out by changing the weights of the criteria for sustainability assessment of biofuel production pathways, and the following nine cases have been studied: Case 0: Equal weights—an equal weight (0.1250) was assigned to the eight criteria for sustainability assessment of biofuel production pathways. Case 1–8: A dominant weight (0.4400) was assigned to each of the eight criteria in each case and all the other nine criteria were assigned an equal weight (0.0800).
Prioritization of biofuels production pathways under uncertainties
353
8 7.5 7 6.5 6
Wheat-based Corn-based Cassava-based
5.5 5 4.5 4 3.5 3 Case 0 Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7 Case 8
Fig. 12.2 The results of sensitivity analysis.
The results of sensitivity analysis are presented in Fig. 12.2. It is apparent that the results are robust; the sustainability sequence from the most sustainable to the least is corn-, cassava-, and wheat-based pathways for bioethanol production in all the nine cases.
5 Conclusion This study developed an interval multicriteria decision making method for sustainability ranking of alternative biofuel production pathways, the interval AHP was employed to determine the weights (relative importance) of the criteria for sustainability assessment of biofuel production pathways, and the interval GRA method was employed to determine the sustainability sequence of the alternative biofuel production pathways. The developed interval multicriteria decision making method for sustainability ranking of alternative biofuel production pathways has the following two advantages: (1) The use of interval AHP method can effectively address the ambiguity, hesitation, and vagueness existing in human’s judgments when comparing the relative preference of a criterion over another. (2) The use of interval GRA can achieve multicriteria decision making under uncertainties, because the data in the decision-making matrix are interval numbers rather than the traditional crisp numbers.
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Acknowledgment This method used in this study was based on Wang, Z., Xu, G., Ren, J., Li, Z., Zhang, B., Ren, X., 2017. Polygeneration system and sustainability: multi-attribute decision-support framework for comprehensive assessment under uncertainties. J. Clean. Prod. 167, 1122–1137.
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