Fuzzy AHP approach to selection problems in process engineering ...

Process Safety and Environmental Protection 9 2 ( 2 0 1 4 ) 467–475

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Fuzzy AHP approach to selection problems in process engineering involving quantitative and qualitative aspects R.R. Tan ∗ , K.B. Aviso, A.P. Huelgas, M.A.B. Promentilla Chemical Engineering Department, De La Salle University, 2401 Taft Avenue, 1004 Manila, Philippines

a b s t r a c t Selection problems are common in process engineering. In most cases, it is necessary to rank alternatives based on multiple criteria (e.g., cost, safety, environmental impact), which are often conflicting. In addition, some criteria may be fundamentally difficult to quantify due to data scarcity, in which case subjective assessments need to be used as a proxy. Decision analysis tools such as the analytic hierarchy process (AHP) are useful to ensure decision-making is done rationally. In this work, we propose a fuzzy AHP variant, wherein pairwise comparison of decision elements by domain experts is expressed with triangular fuzzy numbers. This approach allows the degree of confidence of the expert to be quantified explicitly; it also allows inconsistencies in judgment to be reconciled within the bounds of the fuzzy numbers to generate reasonable values for the weighting factors. We demonstrate the methodology on three case studies, involving the comparison of different types of chlor-alkali electrolytic cells, CO2 capture techniques in cement plants and wastewater treatment options for municipal wastewater. © 2013 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. Keywords: Decision analysis; Fuzzy AHP; Process safety; Electrolysis; CO2 capture; Wastewater treatment

1.

Introduction

Many process engineering problems involve the selection from a predefined set of alternatives, often using multiple, potentially conflicting criteria. Such cases require the systematic use of multiple attribute decision making (MADM) techniques to provide a rigorous and rational approach to problem-solving. In addition, industrial applications also tend to require the integration of viewpoints from multiple decision makers, such as personnel involved in different aspects of process engineering (e.g., design, operation maintenance). Thus, decision-making tends to become a complex task that requires the development of appropriate process systems engineering (PSE) tools. In particular, MADM techniques have been shown to be effective for various problems, such as reactor selection (Hanratty and Joseph, 1992), process diagnostics (Mahdipoor, 2006) and ranking of sustainable process options (Sikdar, 2003, 2009; Qian et al., 2007; Othman et al., 2010), among others. Many MADM approaches entail the use of an aggregation

∗

function to derive a single composite score for each option being evaluated; various techniques make use of different aggregation philosophies, often with the integration of subjective inputs from decision-makers. The analytic hierarchy process (AHP), originally developed by Saaty (1977, 1980), is a theory of relative measurement that provides the analytical tool to model the complexity of the problem and process the subjective and personal judgment of individuals or a group in decision making. The underlying philosophy of AHP is to integrate subjectivity within a rigorous mathematical framework, rather than to try to eliminate it entirely from the decision-making process. In practice, the AHP framework provides a means of problem decomposition and structuring, so as to maximize coherence of the subjective judgments (which are usually elicited from domain experts). AHP has been widely used as an MADM tool or weight estimation technique in many areas of application (Vaidya and Kumar, 2006; Sipahi and Timor, 2010), such as energy planning (Pohekar et al., 2004) and process safety assessment

Corresponding author. Tel.: +63 2 536 0260; fax: +63 2 524 0563. E-mail addresses: [email protected], [email protected] (R.R. Tan), [email protected] (K.B. Aviso), [email protected] (A.P. Huelgas), [email protected] (M.A.B. Promentilla). Received 25 September 2013; Received in revised form 10 November 2013; Accepted 20 November 2013 Available online 28 November 2013 0957-5820/$ – see front matter © 2013 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.psep.2013.11.005

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Fig. 1 – Generic decision hierarchy. and design (Arslan, 2009; Perez-Vega et al., 2011), among others. Aside from its use as a stand-alone decision tool, AHP has also been effectively combined with other tools such as multi-objective mathematical programming (Ho, 2008). In general, AHP structures the decision problem in a hierarchy as shown in Fig. 1. The approach is based on the systematic decomposition of complex decision problems into a set of simple, individual pairwise comparisons of elements, and then subsequently unifying such local decisions into a coherent outcome. Aggregation in AHP to compute the global or overall priorities involves additive weighting of the local priorities of the elements in (e.g., alternatives) the lower level with respect to each local priority (e.g., criteria) in the higher level. Using the principal eigenvalue method (Aw = max w), the priorities of these n elements are derived from the eigenvector (w) of the pairwise comparison judgment matrix A of order n where aij is the judgment obtained from the comparison between element i and element j. If the cardinal transitivity in judgments holds true such that aij = aik akj for all comparisons, then it is a perfectly consistent matrix A with its principal eigenvalue max equal to n. As cardinal consistency in subjective judgments are rarely observed in practice, Saaty (1980) proposed a consistency index defined as CI = (max − n)/(n − 1) to measure the degree of inconsistency, i.e., the deviation of A from a perfectly consistent matrix. The said matrix A also requires exact judgments using Saaty’s fundamental 9-point scale to compare in pairwise the elements in the lower level with respect to each element in the higher level. The 9-point scale has been calibrated based on typical subjective or linguistic equivalents, as shown in Table 1 (Saaty, 1980). The psychological basis for the scale is described in Saaty’s seminal paper (Saaty, 1977), although alternative scales have also been proposed that are summarized in a recent review (Ishizaka and Labib, 2011). However, it is often more natural to provide fuzzy judgments in

pairwise comparisons because of the complexity and uncertainty involved in decision making, especially since AHP results are highly dependent on expert inputs (Promentilla et al., 2008). Fuzzy set theory was first proposed as a means of representing ambiguity by Zadeh (1965), and was subsequently extended for general decision-making applications by Bellman and Zadeh (1970). In particular, fuzzy set theory has been used to enhance various MADM techniques to incorporate uncertainties inherent in subjectivity. Many such extensions are described in Chen et al. (1992). In particular, fuzzy AHP (FAHP) was first proposed by van Laarhoven and Pedrycz (1983), who proposed to replace precise pairwise comparisons with triangular fuzzy numbers (TFNs) and applied the fuzzy version of the logarithmic least squares method (LLSM). Boender et al. (1989) modified their methodology using a more robust approach to the normalization of priorities whereas Wang et al. (2006) proposed a modified fuzzy LLSM based on a constrained nonlinear optimization model. On the other hand, Buckley (1985) determined the priorities from judgments whose membership functions were trapezoidal through fuzzification of the geometric mean method, and then later proposed an evolutionary algorithm by directly computing the fuzzy eigenvalue and eigenvectors (Buckley et al., 2001). To reduce the computational requirement, Chang (1996) proposed the extent analysis to derive the crisp weights from TFNs and this has been applied to numerous real-life problems such as in implementing cleaner production in a manufacturing firm (Tseng et al., 2009) and prioritizing environmental issues in off-shore oil and gas operations (Yang et al., 2011). Some drawbacks in using existing FAHP were also pointed out by Wang et al. (2008) and Promentilla et al. (2008). Mikhailov (2003) argued that these FAHP variants require an additional defuzzification procedure to convert fuzzy weights to crisp weights and he proposed fuzzy preference programming

Table 1 – Conventional AHP numerical scale for subjective judgments (Saaty, 1980). Numerical value 1 3 5 7 9

Linguistic equivalent for comparison of criteria Equally important Moderately more important Strongly more important Very strongly more important Extremely more important

Linguistic equivalent for comparison of preferences Equally preferred Moderately preferred Strongly preferred Very strongly preferred Extremely preferred

Process Safety and Environmental Protection 9 2 ( 2 0 1 4 ) 467–475

technique to derive the crisp weights from fuzzy the fuzzy pairwise comparison judgment matrix. In this work, we propose a fuzzy AHP methodology for process engineering decision-making problems that involve multiple options and criteria. It is assumed that criteria weights are established primarily through pairwise comparisons by domain experts, where subjective judgments are used to establish weight ratios. The latter are expressed as TFNs whose spread signify ambiguity, or lack of confidence, of a given judgment. In effect, the methodology places more credence in judgments which are made with a higher degree of confidence by the domain expert. An approach analogous to fuzzy regression (Tanaka et al., 1982) or fuzzy data reconciliation (Tan et al., 2007) is used to account for variations in degrees of confidence; such nuances cannot be accounted for in conventional AHP. On the other hand, criterion-wise scores of the alternatives are either quantitative or qualitative. For the latter case, subjective judgments of experts are used in a similar manner as with the weights, in order to establish normalized scores for aspects that are inherently difficult to quantify (e.g., process safety). Inputs from the domain experts are then reconciled within the methodology to derive a set of weights and scores, which are consistent to the fuzzy degree, , where  = 1 denotes perfect consistency and  = 0 denotes complete inconsistency. The reconciled weights can then be used to determine the ranks of the alternatives, which finally allows for the selection of the most preferred option. The rest of this paper is organized as follows. A formal problem statement is given in the next section. The methodology for deriving weights from subjective pairwise comparisons is then described. This step entails solving a fuzzy mathematical program based on the symmetric formulation first proposed by Zimmermann (1978). The methodology is then demonstrated using three examples. The first case study involves ranking of different types of electrolytic cells for the chloralkali process. Next, a case study involving comparison of CO2 capture options in cement plants is solved. The third case study involves the selection of a treatment process for industrial effluent treatment. Finally, conclusions and prospects for future work are given at the end of the paper.

2.

Problem statement

The problem considered in this work may be formally stated as follows:

• We consider a set of alternatives I (i = 1, 2, . . ., M) to be assessed based on a set of criteria J (j = 1, 2, . . ., N). • An expert provides a set of fuzzy pairwise comparisons for the criteria set J. The fuzzy judgments incorporate both degrees of preference as well as degree of confidence for each pairwise comparison. Note that the latter aspect of quantifying the degree of doubt is the main departure from conventional AHP. • Criterion weights wj must then be derived from all available pairwise comparisons. The consistency of these weights may be quantified on the fuzzy scale  ∈ [0,1], where 0 denotes complete inconsistency and 1 denotes perfect consistency. The weights are determined so as to maximize consistency. Note that the resultant weights are not fuzzy, thus eliminating the need to defuzzify the final results. • If necessary, the expert also provides a set of fuzzy pairwise comparisons for the alternatives set I, based on the

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subset of criteria J for which no quantitative performance data is available. The subjective judgments are then quantified in the same manner as weights, as described in the previous step. Again, the resultant scores from this step are non-fuzzy. • The aggregate score of each alternative i is then determined as the weighted average of its criterion scores. • The alternatives are ranked, and the most desirable option is selected from the result of the ranking.

3.

Methodology

Nomenclature Sets I J

set of alternatives {i|i = 1, 2, . . ., M} set of criteria {j|j = 1, 2, . . ., N}

Variables fuzzy consistency  wj weight of criterion j ratio between the weight of criterion j and criterion ajj j Parameters aU upper limit of the triangular fuzzy pairwise comparjj ison ratio aM fuzzy mode or core of triangular fuzzy pairwise comjj parison ratio aLjj lower limit of the triangular fuzzy pairwise comparison ratio The over-all objective is to maximize the consistency index, , of the judgments provided by the experts as given in Eq. (1). max 

(1)

This consistency index ranges from 0 to 1 where 0 denotes complete inconsistency and 1 denotes complete consistency as shown in Eq. (2). 0≤≤1

(2)

The  can also be interpreted as the highest degree of membership in a membership function of triangular fuzzy numbers that indicates the degree of satisfaction of all computed pairwise comparison ratios to satisfy the initial fuzzy judgments. A  value of 1 means that the ratios are within the fuzzy bounds and coincide with the modal value of the fuzzy judgments whereas a  value of 0 means that the fuzzy judgments are satisfied at their boundaries only. Furthermore,  is influenced by the expert’s pairwise comparison ratio (ajj ) of criterion j with criterion j which in turn must be approximately equal , aU ), as to the fuzzy value elicited from the expert, (aLjj , aM jj jj shown in Eqs. (3) and (4). The central value of the fuzzy ratio is still based on the AHP scale shown in Table 1. The spread between the lower limit, aLjj , and the upper limit, aU , jj varies depending on the expert’s degree of confidence on his given pairwise judgment such that the spread shortens with increasing degree of confidence, as shown in Fig. 2. These TFNs are also based on prior values proposed in literature (e.g., van Laarhoven and Pedrycz, 1983; Promentilla et al., 2008; Tseng et al., 2009) with the added provision of variable widths to reflect precision of judgment. Note for example that, in Fig. 2a,

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Fig. 2 – Fuzzy AHP linguistic scale for (a) low, (b) moderate and (c) high degrees of confidence.

there is an overlap between adjacent linguistic judgments of Saaty’s 9-point scale when the expert’s confidence level is = 3) could low. For example, “moderately more important” (aM jj



aU − ajj jj aU − aM jj jj

 ≥ ∀j < j ∈ J

(4)

also plausibly be “equally important” (aLjj = 1) on one hand,

and “strongly more important” (aU = 5) on the other extreme, jj due to doubts regarding the judgment. This overlap becomes smaller at higher levels of confidence. The parameter aM corjj responds to the comparison ratio that is judged to be the most plausible value. Thus, the actual ratio, ajj , is said to be approx, aU ); this equivalence imately equal to the fuzzy ratio (aLjj , aM jj jj can be expressed as:



ajj − aLjj aM − aLjj jj

Note that, in order to increase the value of , Eqs. (3) and (4) will tend to push ajj , toward the most plausible value aM . The jj pairwise comparison ratio, ajj , is equivalent to the ratio of the weights of criterion j and criterion j :

 ≥ ∀j < j ∈ J

(3)

wj wj

= ajj

∀j < j ∈ J

(5)

Process Safety and Environmental Protection 9 2 ( 2 0 1 4 ) 467–475

Furthermore, the sum of the weights of all considered criteria, wj , is equal to 1: N 

wj = 1

(6)

j=1

The significance of the optimization model is that the weights determined through this procedure have ratios that agree with the fuzzy judgments of the experts by at least a degree given by the optimal numerical value of . This  is analogous to the consistency index proposed by Mikhailov (2003), i.e., the highest degree of membership from membership functions that represents the decision maker’s satisfaction on the computed pairwise comparison ratios in relation to their initial judgments. Thus, by maximizing the objective function, the model seeks out the most consistent set of weights (i.e., based on the principle of transitivity) within the fuzzy bounds elicited from the domain expert. However, no strict correlation has been established between  and the consistency index (CI) used in conventional AHP (Saaty, 1980). Furthermore, it is theoretically possible for completely inconsistent pairwise comparisons to be encountered. In such cases, no solution will exist for the model described here. Note that this model is a non-linear program (NLP) due to the fractional form of Eq. (5). In this work, the methodology is implemented using LINGO 13.0, which has a global optimization feature based on branch-and-bound algorithm (Gau and Schrage, 2004). In the case studies that follow, the solutions were determined using a laptop with 8.00 GB RAM, i7-3540M CPU and a 64-bit operating system running on Windows 8 Pro. Solutions for all case studies here were found with negligible computing time.

4.

Case studies

4.1.

Case study 1 – Chlor-Alkali Process

This case study considers the evaluation of different technologies for the chlor-alkali industry. The chlor-alkali industry refers to the simultaneous production of chlorine gas, Cl2 , and an alkali which can either be caustic soda (NaOH) or potassium hydroxide (KOH). The process is done through the electrolysis of salt (NaCl or KCl) in the presence of water. Hydrogen gas is also produced as a by-product of the reaction. The technologies for chlor-alkali production differ based on the technology for separating the chlorine gas from the alkali and the generated hydrogen. The three main processes utilized are the mercury cell, the diaphragm cell and the membrane cell (European Commission, 2001; Eurochlor, 2012). In this case study, the technologies are evaluated based on four criteria: energy intensity, material intensity, potential chemical risk index and the environmental impact index. Since the chlor-alkali industry is based on an electrolytic process, it requires large amounts of electricity ranging from 2500 to 3600 kWh/ton of chlorine (European Commission, 2001; Sikdar, 2009), making energy intensity a significant factor. Material intensity, on the other hand, is associated with the required amount of raw material necessary to produce a kg of Cl2 . Stoichiometrically, the balance requires 1.6 kg of NaCl per kg of Cl2 . However, due to system inefficiencies the actual ratio is somewhat more than this. The potential chemical risk index refers to hazards which impact human health, while the environmental impact index pertains to the effect on

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the surrounding environment; both are expressed in terms of dimensionless numerical scores (Sikdar, 2009). In general, hazards are encountered in the storage, distribution and handling of chlorine as well as in the utilization and disposal of the electrolytic cells. However, additional risks are taken into consideration depending on which technology is used. For example, there has been great interest in quantifying the mercury contamination in the surrounding environment of chlor-alkali plants (Grönlund et al., 2005; Sensen and Richardson, 2002) and in identifying the impacts of human ˇ et al., exposure to mercury (Wängberg et al., 2005; Gibicar 2009). There are also some risk issues associated with asbestos components typically used in diaphragm cells (Kazan-Allen, 2006; Giannasi, 2007). In this case study, the performance levels of three chlor-alkali technologies in the four criteria are adapted from Sikdar (2009). Scores are summarized in Table 2. Table 3 on the other hand shows the fuzzy pairwise comparison of the four criteria while Table 4 shows the fuzzy pairwise comparison of the technologies based on subjective chemical risk. These comparisons were elicited from a domain expert with a postgraduate chemical engineering background working for an environmental consultancy firm. The entries in Tables 3 and 4 reflect the relative importance of one criterion over another together with the lower and upper limit of the comparison. These limits indicate the degree of confidence of the expert. For example, in the second row and third column of Table 3, the entry of (0.4, 1, 2.5) indicates that energy intensity (j = 1) and material intensity (j = 2) are deemed to be equally important (as indicated by the central value of aM 12 = 1) with a moderate level of confidence (as indicated by the limits of aL12 = 0.4 and aU 12 = 2.5). Geometrically, this expert judgment corresponds to the leftmost TFN in Fig. 2b. A similar approach is used to convert subjective inputs into the corresponding TFN values. By maximizing the objective function given by Eq. (1), subject to constraints as defined by Eqs. (2)–(6), the most consistent set of weights can be determined. The solution results in  = 0.22, with the weights of 0.089 for energy intensity, 0.083 for material intensity, 0.313 for potential chemical risk and 0.515 for environmental impact. In addition, the original chemical risk scores are replaced here with the subjective assessments from Table 4, from which a similar computational procedure results in dimensionless scores of 0.094, 0.173 and 0.732 for mercury, diaphragm and membrane cells, respectively, at  = 0.23. Based on these, the aggregate scores can be determined using weighted arithmetic means of scores relative to each of the four criteria. For example, the mercury cell aggregate score is found to be 0.257 = (0.089 × 0.344) + (0.083 × 0.333) + (0.313 × 0.094) + (0.515 × 0.329). Repeating these calculations for the other two alternative technologies then shows that the membrane cell is the most preferred technology, followed by the diaphragm cell and lastly the mercury cell, as shown in Table 5.

4.2.

Case study 2 – CO2 Capture

This case study considers the selection of post-combustion CO2 capture options for cement plants. Cement plants contribute roughly 6% of global carbon emissions, with an intensity rate of approximately 1 kg CO2 per kg cement produced (Benhelal et al., 2013). Thus, there is significant interest in developing measures to reduce emissions from the cement industries. One particular option is carbon capture and storage (CCS), which involves removal of CO2 from combustion products for subsequent storage in offsite geological

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Table 2 – Alternatives and criteria for case study 1. Alternative

Energy intensity (MJ/kg Cl2 )

Mercury cell Diaphragm cell Membrane cell

Material intensity (kg/kg Cl2 )

10.80 10.98 11.70

Potential chemical risk index

2.15 2.15 2.15

Environmental impact index

202,114 202,116 200,104

116,102 116,103 112,002

Adapted from Sikdar (2009).

Table 3 – Pairwise comparison of criteria for case study 1. Energy intensity

Material intensity

Potential chemical risk index

Environmental impact index

1

(0.4, 1.0, 2.5) 1

(0.22, 0.33, 0.67) (0.25, 0.33, 0.50) 1

(0.17, 0.20, 0.25) (0.13, 0.14, 0.17) (0.5, 1, 2.0) 1

Energy intensity Material intensity Potential chemical risk index Environmental impact index

reservoirs. Removal of CO2 thus results in drastic reductions in greenhouse gas releases, but at the expense of additional capital costs and energy consumption. This incremental fuel consumption arises from the parasitic energy demand for the physical and chemical processes needed to isolate CO2 . In addition to the obvious effect on operating costs for fuel purchases, it has been estimated that such added fuel consumption results in an increase in system-wide fatalities, primarily from deaths occurring throughout the fuel supply chain (Minh and Loisel, 2011). In addition, there are also risks that arise from CO2 capture (e.g., fugitive emissions of capture solvents and degradation products), transport and storage (e.g., catastrophic release of CO2 ); however, lack of extensive field data and experience with full CCS chains makes assessment inherently difficult (Koornneef et al., 2012). In this case study, data for the options are based on the summary given in Kuramochi et al. (2012). Post-combustion capture options are considered due to their suitability for retrofit of existing plants. The four options involve different solvents (i.e., monoethanolamine or MEA, and the proprietary amine-based KS-1) and different options to provide the incremental heat and power requirements for solvent regeneration (i.e., steam and power import, or on-site cogeneration), these are shown in Table 6. In the case of on-site generation, it is assumed that the additional CO2 from the CHP plant is also captured. Power and heat are converted into primary energy equivalent, based on typical thermal efficiencies of conversion processes, to give the first criterion. Capture rate and incremental capital cost of retrofit are the second and third criteria, respectively.

Next, Table 7 shows the fuzzy pairwise comparisons of the three criteria, as elicited from a domain expert. The respondent in this case is a university-based researcher currently doing work on optimization of CCS systems. Solving the optimization model gives normalized weights of 0.636, 0.253 and 0.111 for incremental primary energy, capture rate and incremental capital cost, respectively. The fuzzy degree of consistency is determined to be  = 0.51. Given these weights, further analysis is straightforward. The scores for each criterion must first be normalized, following standard procedure in AHP, as shown in the second, third and fourth columns of Table 8. The aggregate scores are then computed, as shown in the final column of Table 8, which clearly indicates that the second alternative (Use of MEA with on-site NG CHP and CO2 capture) is the preferred option.

4.3.

Case study 3 – Wastewater Treatment

The third case study considers the evaluation of different technologies for the treatment of municipal wastewater. This type of wastewater typically includes discharges from residential, commercial and institutional establishments within a catchment area. Industrial wastewater maybe included after pre-treatment. Treatment of municipal wastewater requires at least secondary or biological treatment to achieve regulatory standards on effluent characteristics. Main components of a secondary treatment facility include an aeration tank and appurtenances for removal of solids. An aeration tank or reactor holds the microorganisms responsible for treatment of wastewater. These microorganisms metabolize the organic

Table 4 – Pairwise comparison of alternatives based on subjective chemical risk for case study 1. Mercury cell Mercury cell Diaphragm cell Membrane cell

1

Diaphragm cell

Membrane cell

(0.22, 0.33, 0.67) 1

(0.13, 0.14, 0.17) (0.17, 0.20, 0.25) 1

Table 5 – Normalized alternatives and criteria for case study 1. Alternative

Mercury cell Diaphragm cell Membrane cell

Normalized energy (w1 = 0.089) 0.344 0.338 0.318

Normalized material intensity (w2 = 0.083) 0.333 0.333 0.333

Normalized potential chemical risk (w3 = 0.313) 0.094 0.173 0.732

Normalized environmental impact (w4 = 0.515)

Overall score

0.329 0.329 0.341

0.257 0.282 0.461

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Table 6 – Alternatives and criteria for case study 2. Alternative 1 2 3 4

Solvent

System details

Incremental primary energy (GJ/t CO2 )

MEA MEA MEA KS-1

Steam import On-site NG CHP + CO2 capture On-site coal CHP + CO2 capture On-site coal CHP + CO2 capture

Capture rate (t CO2 /t clinker)

6.8 3.6 5.5 4.0

Incremental capital cost (D /(t CO2 /y))

0.77 0.77 1.2 1.0

110 160 310 260

Adapted from Kuramochi et al. (2012).

Table 7 – Pairwise comparison of criteria for case study 2. Incremental primary energy Incremental primary energy Capture rate Incremental capital cost

1

Capture rate

Incremental capital cost

(2, 3, 4) 1

wastes present in the wastewater. These organic wastes are partly synthesized into new cells and partly oxidized to carbon dioxide and water. The new cells formed in the reactor are removed by a liquid–solids separation unit, i.e. secondary sedimentation tank or secondary clarifier (Hammer and Hammer, 2005). The secondary treatment technologies that are evaluated in this study include conventional activated sludge (CAS), sequencing batch reactor (SBR) and membrane bioreactor (MBR). The CAS system involves a suspended growth activated sludge process that utilizes a separate unit for aeration and for settling. The SBR system utilizes a single reactor where all the processes in the CAS take place in sequential order. The MBR on the other hand utilizes a microporous membrane for solid–liquid separation in place of a secondary sedimentation tank. In this case study, the technologies are evaluated based on four criteria: technical aspect, environmental aspect, cost and ease-to-upgrade. Technical aspect considers both process robustness and ease-to-operate. Process robustness refers to the length of time that the particular process has been operated/proven (i.e. both worldwide and in the Philippines) while ease-to-operate refers to the requirement level of operator input and training. The environmental aspect considers final effluent quality from an ideally operated plant. It has been reported that CAS, SBR and MBR systems can achieve around 85–93% BOD5 removal (Von Sperling and de Lemos

(3.5, 5, 6.5) (1.5, 3, 4.5) 1

Chernicharo, 2005), 89–98% BOD5 removal (Mahvi, 2008) and >95% BOD5 removal (Cicek, 2003), respectively. Typically, cost of the system dictates the choice of technology. Relative costs for each of the technologies will be presented in terms of Net Present Value (NPV). In this study, the NPV analysis includes both Capital Expenditure (CAPEX) and Operating Expenditure (OPEX) for a 500 m3 /day plant considering 20 years of operation at 9% discount rate. Lastly, technologies may need to be upgraded in terms of compliance with stricter discharge criteria. In the Philippines for instance, the existing regulation (DENR Administrative Order No. 35 Series of 1990) requires carbonaceous matter removal only. However, there is a draft revision to the existing Philippine regulation that requires nutrient removal. Thus, a possible need to consider ease-toupgrade from carbonaceous matter to nutrient removal type of system should be considered in the assessment of wastewater treatment technology options. This criterion can alternatively be interpreted as a technical risk factor, taking into account the possibility of undesirable technological lock-in. The performance of three WWT technologies as elicited from a domain expert in the four criteria is summarized in Table 9. The preference weights (in column 1 and column 4 of Table 9) from the subjective evaluation of alternatives with respect to technical aspects and ease-to-upgrade are obtained from the fuzzy PCJM described in Tables 10 and 11, respectively. The fuzzy degree of consistency () for alternative weighting with respect to technical

Table 8 – Normalized alternatives and criteria for case study 2. Alternative

1 2 3 4

Normalized incremental primary energy (w1 = 0.636)

Normalized capture rate (w2 = 0.253)

Normalized incremental primary energy (w3 = 0.111)

Overall score

0.172 0.324 0.212 0.292

0.293 0.293 0.188 0.226

0.406 0.279 0.144 0.172

0.228 0.311 0.199 0.262

Table 9 – Alternatives and criteria for case study 3. Alternatives

Conventional activated sludge (CAS) Sequencing batch reactor (SBR) Membrane bioreactor (MBR) a

Technical aspecta 0.64 0.25 0.11

Environmental aspect (BOD) 89.0 93.5 97.0

Cost in NPV (CAPEX/OPEX), Php, in millions

Ease-to-upgradea

54.9 54.5 73.3

0.14 0.43 0.43

Using AHP to get the preference weight of each alternative according to wastewater consultant’s judgment.

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Table 10 – Pairwise comparison of alternatives based on subjective technical aspects for case study 3. CAS

SBR

MBR

1

(2.0, 3.0, 4.0) 1

(3.5, 5.0, 6.5) (1.5, 3.0, 4.5) 1

Conventional activated sludge (CAS) Sequencing batch reactor (SBR) Membrane bioreactor (MBR)

Table 11 – Pairwise comparison of alternatives based on subjective ease to upgrade for case study 3. CAS

SBR

1

(0.25, 0.33, 0.5) 1

Conventional activated sludge (CAS) Sequencing batch reactor (SBR) Membrane bioreactor (MBR)

MBR (0.25, 0.33, 0.5) (0.4, 1, 2.5) 1

Table 12 – Pairwise comparison of criteria for case study 3. Technical aspect Technical aspect Environmental aspect Cost in NPV Ease-to-upgrade

Environmental aspect

1

Cost in NPV

(1.5, 3.0, 4.5) 1

Ease-to-upgrade

(0.25, 0.33, 0.50) (0.17, 0.20, 0.25) 1

(2.0, 3.0, 4.0) (0.5, 1.0, 2.0) (4.0, 5.0, 6.0) 1

Table 13 – Normalized alternatives and criteriaa for case study 3. Alternative

Technical aspect (w1 = 0.240)

Environmental aspect (w2 = 0.100)

0.64 0.25 0.11

0.32 0.33 0.35

Conventional activated sludge (CAS) Sequencing batch reactor (SBR) Membrane bioreactor (MBR) a

0.36 0.37 0.27

Ease-to-upgrade (w4 = 0.100)

Overall score

0.14 0.43 0.43

0.403 0.341 0.256

Weighting from FAHP method ( = 0.41).

aspects and ease-to-upgrade are determined to be 0.52 and 1.0, respectively. Likewise, Table 12 shows the fuzzy pairwise comparisons of the four criteria. For example, solving the optimization model gives normalized weights of 0.240, 0.100, 0.560 and 0.100 for technical aspects, environmental aspect, economic aspect and ease-to-upgrade, respectively. Note that the fuzzy degree of consistency for criteria weighting is determined to be  = 0.41. Given these weights, further analysis is straightforward and similar to what have been done in Cases 1 and 2. The scores for each criterion must first be normalized as shown in Table 13 and the aggregate scores are then computed, as shown in the final column. This clearly indicates that the first alternative (CAS) is the most preferred option.

5.

Cost in NPV (w3 = 0.560)

Conclusion

A fuzzy AHP approach to decision-making for process engineering problems has been developed. This approach enables the selection of optimal alternatives based on multiple criteria which may be quantitative or qualitative in nature, based on the judgment of domain experts. In addition, the degree of confidence of the expert may be quantified through the spread of fuzzy numbers used for the pairwise comparison ratios in the AHP framework. The approach can also derive crisp weights from an incomplete fuzzy PCJM. The methodology then determines a set of crisp weights that maximizes the degree of consistency of all judgments taken together. Three case studies have been solved to illustrate the technique. Although, as with conventional AHP, the approach developed here is still dependent on the inputs of the domain expert, it provides a more nuanced elicitation of judgments, by allowing confidence levels to be reflected for each pairwise

comparison. Future work would account for inputs from multiple decision makers for group decision making incorporating also the degree of importance of each decision maker.

Acknowledgement We are grateful for the financial support of the Philippine Commission on Higher Education (CHED) via the PHERNet Sustainability Studies Program.

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