Analytic Network Process for Developing Relative Weight of Wastewater Treatment Technology Selection

Selecting the best wastewater treatment (WWT) technology requires a thorough qualitative and quantitative evaluation of multi-dependence criteria. A network based method is one of the many possible techniques that able to handle multi-dependence criteria in the selection. This paper proposes relative importance weights of alternatives in selecting the WWT technology using the analytic network process (ANP) in Terengganu Malaysia. The ANP is applied to establish the relative weights of alternatives based on criteria and sub-criteria that available in the WWT technology selection. Two faculty members attached to a public university and an engineer in Malaysian government agency were interviewed to provide evaluation within the framework of ANP. Inner dependence and outer dependence analysis of ANP are fully utilised to establish relative importance weights of alternatives. The experiment result reveals that the relative importance weights of the three alternatives are 0.3074, 0.2795 and 0.2447. The alternative ‘Composting’ has decided as the most suitable technology in WWT which provides the highest relative importance weight among all the three alternatives. The results would be a great significance for the practical implementation of the WWT technology selection.


Background
Over the past century, there has been a dramatic increase in world population and economic growth.In the midst of these increasing trends, one of the basic infrastructures that really in a pressing need is treated water.Sustainable treated water infrastructure is essential so that the people will be able to consume clean and safe water.Treated water infrastructure may contribute in improvising the environmental, economic and social health of the nation's communities (Ross et al., 2012).In order to protect the environment from the negative impact of wastewater as well as to sustain a healthy life, it urgently important to treat wastewater in a good way with the use of effective technology.Wastewater treatment (WWT) technology is inevitable despite its highly operating cost and less effective results.Among the popular technologies in WWT are anaerobic digestion, phytoremediation, and composting (Bottero et al, 2011).Selecting the ideal technology is very tricky due many considerations need to be accounted concurrently, especially from technology specification perspective and also from multiple intangible criteria that characterised the selection.It is more difficult if locations or regions where the technology should be deployed are also considered.Therefore, selecting the ideal WWT technology is not a straight forward process.There are many criteria that need to be considered for selecting the ideal WWT technology.However the main three criteria that normally available in the literature are economical aspect, environmental aspect, and technological aspect (Bottero et al, 2011).In other words, WWT technology selection can be regarded as a multi-criteria or attributes decision making problem.The method used in solving the problem must be flexible enough as to allow several criteria being taken into account simultaneously in a complex situation.The method used in analyzing these criteria and alternatives must help decision-makers to express their different options, which reflect the opinions of the actor involved Figueira et al., (2005).

Motivation and Objective
In decision analysis, there are many decision problems that cannot be analyzed hierarchically due to their interaction and dependencies of higher-level elements in a hierarchy on lower-level elements.In order to overcome this issue, Saaty (1996) proposed the method of analytic network process (ANP) where dependencies and interactions among criteria are taken care of.Unlike many other decision making methods, the ANP is rather represented by a network.Furthermore, the ANP is constructed based on feedback in clusters (Saaty, 1996).Many researchers had shown their interest over the applications of ANP.The ANP has been widely applied in strategic policy planning (Ulutas, 2005), marketing and logistics (Agarwal, et al., 2006), economics and finance (Niemura and saaty, 2004), and civil engineering (Neaupane and Piantanakulchai, 2006).There was also research on territorial and environmental assessment (Promentilla, et al., 2006;Bottero, et al., 2008;Wolfslehner, and Vacik, 2008).In waste management, ANP was used to prioritize and select the suitable municipal solid waste disposal method (Khan and faisal, 2008).Banar et al., (2007), used ANP to choose one out of four alternatives regarding landfill sites in Turkey, while Tuzkaya et al., (2008) used ANP to locate the undesirable facilities.To the best of the author's knowledge, there were a limited number of applications of ANP to WWT technology selection.This paper aims to develop a decision for selecting the WWT technology based on relative importance weights that established from the ANP.In contrast to previous works, this model considers the inner dependence and outer dependence among the criteria that give an additional effect to the model.The rest of this paper is organized as follows.Section 2 provides reviews regarding the methods used for WWT technologies.Section 3 presents computational steps of ANP.Section 4 presents the implementation of ANP to a case of WWT technology selection.Section 5 concludes

Literature Review
The literature review has been carried out by referring to leading journal databases.The literature has been reviewed from the perspective of various methods used for WWT techniques or selections.There are a handful of research that specifically conducted on the WWT technology selections.The various methods used for WWT selections are summarized in Table 1.Plakas et al., (2016) The participatory method called simple multi-attribute rating technique exploiting ranks has been employed for assigning weights to selected sustainability indicators.The multi-criteria analysis gives the opportunity to researchers, designers and decision-makers to examine decision options in a multi-dimensional fashion.Four tertiary WWT technologies were assessed regarding their sustainability performance in producing recycled wastewater.Kalbar et al., (2012) The multiple-attribute decision making methodology TOPSIS has been developed and applied to the selection of wastewater treatment alternatives.The four most commonly used WWT technologies for treatment of municipal wastewater in India are ranked in various scenarios.The articulated scenarios depict the most commonly encountered decision-making situations in addressing technology selection for wastewater treatment in India.A widely used compensatory technique, TOPSIS, has been selected to rank the WWT alternatives.Abdullah, L. (2015) Fuzzy simple additive weighting has been used to identify the most suitable WWT technology.Three decision makers were appointed to evaluate and provide information regarding the WWT technologies and its affiliated criteria.Ilangkumaran et al., (2014) The application of hybrid multi-criteria decision-making technique for the selection of WWT technology for treating wastewater.The proposed approach is based on fuzzy analytical hierarchy process and hierarchy grey relation analysis technique.The fuzzy analytical hierarchy process is used to determine the weights of criteria and then ranking of the WWT technology alternatives is determined by grey relation analysis technique.Ilangkumaran et al., (2013) The methods of Analytical Hierarchy Process under fuzzy environment, Preference Ranking Organization Method for Enrichment Evaluation and hierarchy Grey Relation Analysis techniques have been used for selection of WWT technology for treating wastewater.Molinos-Senante et al., (2014) The analytical hierarchical process has been used to assign weights of indicators of global sustainability of the WWT technologies.The proposed approach contributes to ease of interpretation of a complex problem such as the selection of the most sustainable WWT alternative.

Contributions
It is noticed that most of the methods are not considered the dependencies among criteria and sub-criteria of WWT.The following section provides a computational procedure of ANP where dependencies among criteria and sub-criteria are purposely managed in the computation.

Computational Procedure
The ANP can be represented by super-matrix by evaluating the elements in the network on other elements in the network.It consists of two-dimensional element-by-element matrix that may change the relative importance weight to build a new overall super-matrix which consists of eigen-vector of the changed relative importance weights.The ANP can be divided into four main steps namely model construction and problem structuring, pair-wise comparison matrices and its priority vectors construction, super-matrix formation, and selection of the best alternatives (Yuksel and Dagdeviren, 2007;Saaty, 1996).The main steps are described as follows.
Step 1: Model construction and problem structuring.
Identify the sub-criteria for each criterion and determine the alternative strategies according to sub-criteria.
Step 2: Determine degree of importance and normalized weight.
Assume that there is no dependent among the criteria.Then, determine the importance degrees of the criteria with a 1-9 scale by constructing pair-wise comparison matrix (see Table 2).Here, w 1 is calculated where w 1 is the normalized weight of the pair-wise comparison matrix of criteria with respect to goal.To compute the eigen-vector (normalized weight), the row sum for each row, sum of column of each row, and sum of the matrix must be computed beforehand.Divide each row sum by the sum of the matrix.Eigenvector, x (normalised weights) is computed using the equation ( 1). ( where i w is the sum of row for pair-wise comparison and n is the size of matrix.
Step 3: Determine the inner dependence matrix of each criterion with respect to the other criteria by constructing the pair-wise comparison matrix of inner dependence among the criteria.
Here, 2 w is calculated where 2 w is the normalized weight obtained from each inner dependence matrix of each criterion with respect to the other criteria.
Step 4: Determine the inner dependence weights of the criteria.
Here, w criteria is calculated such that w criteria = 1 2 w × w which are obtained from Step 2 and Step 3.
Step 5: Determine the local importance degrees of the sub-criterion by constructing the pair-wise comparison matrix of sub-criteria with respect to each criterion.
Here, w sub-criteria(local) is calculated.It is obtained from the normalized weight of pair-wise comparison matrix of sub-criteria with respect to each criterion.
Step 6: The global importance degree of the sub-criteria is determined.
( Step 2: Determine degree of importance and normalized weight.
The importance of criteria was determined using 1-9 scale.Here, w 1 is obtained.The pair-wise comparison of the criteria with respect to goal was constructed.The weights of criteria are shown in Table 3. = C2 = 0.10314 C3 0.29148 Step 3: The inner dependence matrix among criteria is determined by analyzing the effect of each criterion to other criteria using pair-wise comparison matrix.Their normalized weights are summarized as w 2 . .Table 4, Table 5 and Table 6 show the inner dependence matrix of criteria with respect to other criteria.So, the weight for inner dependence for criteria C1, C2 and C3 are summarized as; C1 C2 C3 C1 0.0000 0.8750 0.9000 w 2 = C2 0.8333 0.0000 0.1000 C3 0.1667 0.1250 0.0000 Step 4: The interdependence weight of the criteria is computed.The w criteria is computed as follows; w criteria = w 2 * w 1 0.0000 0.8750 0.9000 0.60538 0.35258 = 0.8333 0.0000 0.1000 * 0.10314 = 0.53363 0.1667 0.1250 0.0000 0.29148 0.11379 So, the weights of criteria are changed from 0.60538 to 0.3526, 0.10314 to 0.5336, and 0.29148 to 0.1138 for the weight values of criteria C1, C2 and C3 respectively.
Step 5: The local weights of the sub-criteria are determined using pair-wise comparison matrix.The three sub-criteria comparisons with respect to criteria C1, C2, and C3 are shown in Table 7, Table 8 and Table 9 respectively.The weighted sub-criteria and overall weighted sub-criteria are shown in Table 10.Based on the overall relative weights, it is shown that the best WWT technology is composting followed by phytoremediation and anaerobic digestion.

Conclusions
The aim of this paper was to propose a prioritization in real case experiment for solving the wastewater treatment technology decision problem.Selecting the wastewater technology is a complicated issue which multi dependence criteria must be considered concurrently.Thus, the analytic network process with the capability of unifying inner dependence and outer dependence among criteria was applied to explore the decision process and suggesting the relative weights of the technology alternatives.The analytic network process has included the weights of sub-criteria and criteria in proposing the final overall relative weights of alternatives.The multiplications of criteria weights and sub-criteria weights was utilized to obtain the final overall relative weights of alternatives.The technology of composting with the overall relative weight of 0.3074 was the most prioritized choice among all the three alternatives.The second prioritized choice in wastewater technology selection was Phytoremediation with the overall relative weight 0. 2795 followed by anaerobic digestion with the overall relative weight 0. 2447.The analytic network process was successfully identified 'composting' as the ideal technology in wastewater treatment in Terengganu Malaysia.The paper has highlighted a new insight into a decision making method that based on a network to propose weights and prioritization for WWT technology alternatives.However, this proposed preference method warrants further investigations, especially in the aspects of validity and reliability of the experiment.Further research with some other real case experiments would further enhance the robustness of the analytic network process.Comparative study and sensitivity analysis are some of the possible validation tools that can be explored in future research direction.

Table 2 .
The pair-wise comparison scale

Table 3 .
Pair-wise comparison of alternatives with respect to goal

Table 4 .
Inner dependence matrix of criteria with respect to C1

Table 10 .
Overall weights of sub-criteria The weight of alternatives with respect to each sub-criterion is computed.The w 4 is computed and results are shown in Table11.