A multi-criteria decision support framework for municipal solid waste landfill siting: a case study of New South Wales (Australia)

Abstract

Sanitary waste disposal and site selection for establishing landfills are challenging problems for environmental planners. This paper aims to take environmental, socio-economic, geological, geomorphological, hydrological and ecological factors into consideration to provide a decision support framework for landfill siting. Analytical hierarchy process (AHP) and Decision Making Trial and Evaluation Laboratory (DEMATEL) are coupled to develop an efficient multi-criteria decision-making method to be utilized in a Geographic Information System (GIS) environment for evaluating the suitability for landfill siting. As the first attempt to employ DEMATEL effectively in a landfill site selection problem, the proposed method is tested with landfill siting scenarios in New South Wales (NSW), Australia. Regional analysis is also performed to identify the potentially most suitable statistical divisions for landfill siting in NSW. The top two ranked zones covering 0.7% and 22% of the study area, respectively, are considered as the optimal areas for establishing landfills, while the bottom two ranked zones are not recommended for further consideration. Further detailed analysis is also conducted on the existing landfills, which shows that 1.0% and 37.0% of them are ranks 1 and 2, respectively. The scenario-based analysis implies that, among the contributing factors; geological and economic factors are highly important.

Appendix 1. The framework of the proposed AHP-DEMATEL

Phase 1: Developing the hierarchical structure

The hierarchical structure is a graphic presentation of a complex problem where the top involves the overall goal and the other levels and sub-levels include criteria, sub-criteria and alternatives (Saaty 1980; Dyer and Forman 1991; Çimren et al. 2007).

Phase 2: Evaluating the factors and allocating the weights

To provide analysis of the identified factors and address the interrelations among them, DEMATEL is implemented by the following steps based on Tzeng et al. (2007) and Wu (2008):

• Step 1: Gathering experts’ opinions and computing the average matrix Z Each expert was asked to evaluate the degree of direct influence between any two factors by an integer score ranging from 0 (no influence), 1 (low influence), 2 (medium influence) and 3 (high influence). The level of influence to which the respondent believes factor i affects factor j is denoted as x_ij. The diagonal elements (i = j) are set to zero. For each respondent, a n × n non-negative matrix is constructed as $X^{k}=[x_{ij}^{k}]$, where k is the number of respondents participated in the evaluation process (1 ≪ k ≪ H) and n denotes the number of factors. Accordingly, $X^{1},X^{2},\dots ,X^{H}$ are matrices gathered from H respondents. To aggregate and conclude all opinions from H respondents, first it is assumed in this study that if more than a half of respondents allocate zero to one relation, the independency of the relation is proven. Then, for the rest of relations the average matrix Z = [z_ij] is established by using Eq. A1.1 as below:

  $$ \begin{array}{@{}rcl@{}} z_{ij} =\frac{{\sum}_{k=1}^{H} x_{ij}^{k}}{H} \end{array} $$

  (A1.1)

• Step 2: Computing the normalized initial direct-relation matrix D The normalized initial direct-relation matrix D = [d_ij] where 0 ≪ d_ij ≪ 1 is calculated by Eq. A1.2 as below :

  $$ \begin{array}{@{}rcl@{}} D=Z \times S \end{array} $$

  (A1.2)

  where S value can be obtained from Eq. A1.3 as below:

  $$ \begin{array}{@{}rcl@{}} S = \frac{1}{{{\text{Max}}_{1\ll i \ll n} \sum\limits_{j=1}^{n} z_{i}}} \end{array} $$

  (A1.3)

• Step 3: Deriving the total relation matrix T

  The total relation (influence) matrix T = [t_ij] is obtained as T = D(I − D)^− 1 where I is a n × n identity matrix. Let r and c be n × 1 and 1 × n vectors representing the sum of rows and sum of columns of matrix T respectively. Let r_i denotes the sum of i th row in matrix T, then r_i summarizes both direct and indirect effects given by factor i to the other factors. Suppose that c_j is the sum of j th column in matrix T, then c_j represents both direct and indirect affects by factor j. If j = i, the sum (r_i + c_i) shows the total effects given and received by factor i. Therefore, (r_i + c_i) is a representing measure for the degree of importance that factor i plays in the entire system. In contrast, the value of (r_i − c_i) indicates the net effect that factor i contribute to the system. In addition, when (r_i − c_i) is positive, factor i is a net cause, and factor i is a net receiver if (r_i − c_i) is negative (Liou et al. 2007; Yang et al. 2008).

  In this study, the normalized values of (r_i + c_i) are utilized to represent the weights of the factors in Eq. A1.4 as below:

  $$ \begin{array}{@{}rcl@{}} W_{i}=\frac{(r_{i}+c_{i})}{{\sum}_{i=1}^{n} (r_{i}+c_{i})} \end{array} $$

  (A1.4)

  where W_i represents the weight of i th factor, n is the total number of the factors.

• Step 4: Setting a threshold value (α) The threshold value (α) in this study is computed by the average of elements in matrix T. This value aimed to filter out some negligible effects (Yang et al. 2008).

• Step 5: Depicting causal diagram

  The causal diagraph is acquired by mapping the dataset of (r + c,r − c) to visualize interrelationships among the factors and provide information to judge which factors are the most influential (important) and how influence affected the factors (Shieh et al. 2010; Sumrit and Anuntavoranich 2013).

Phase 3: Prioritizing and scoring the alternative ranks

In the present study, five alternative levels are considered for each factor which represents the suitability from the highest level (rank 1) to the lowest level (rank 5). Scoring the alternatives (factor levels) is performed via the AHP framework. Here, pairwise comparisons were performed based on the most relevant studies (Kontos et al. 2003; Yalcin 2008; Wang et al. 2009) and considering the characteristics of the study area for all factor levels to identify the relative importance and score of the factor levels.

To compute the weights of the alternatives, each element in pairwise comparison matrix (a_ij) is divided by summation of its corresponding column to generate the normalized matrix (Eq. A1.5). Then, the arithmetic mean of elements of each row (w_i) of the normalized matrix is calculated as the weight of each alternative (Eq. A1.6).

$$ \begin{array}{@{}rcl@{}} r_{ij} = \frac{a_{ij}}{{\sum}_{i=1}^{m} a_{ij}} \end{array} $$

(A1.5)

$$ \begin{array}{@{}rcl@{}} w_{i} = \frac{{\sum}_{i=1}^{n} r_{ij}}{n} \end{array} $$

(A1.6)

where m and n denote the number of columns and rows in the pairwise comparison matrix; a_ij and r_ij show the elements in pairwise comparison and normalized matrices respectively and w_i denotes the importance weight of the i th alternative (factor level).

Phase 4: Evaluating validity of pairwise comparisons

To evaluate the goodness of performed judgments in pairwise comparisons, the incompatibility degree is calculated and assessed. To compute the Incompatibility Index (I.I), first the pairwise comparison matrix (A) is multiplied by the Weight vector (w) to establish an applicable approximation of $\lambda _{\max \limits }$ where $\lambda _{\max \limits }$ denotes the biggest eigenvalue which can be obtained once we have its associated eigenvector. Then, incompatibility index is calculated by Eq. A1.7 where n is the number of columns of matrix A.

$$ \begin{array}{@{}rcl@{}} I.R = \frac{\lambda_{\max}-n}{n-1} \end{array} $$

(A1.7)

Further, Incompatibility Ratio (I.R) is calculated using Eq. A1.8 as follows:

$$ \begin{array}{@{}rcl@{}} I.R = \frac{I.I}{I.I.R} \end{array} $$

(A1.8)

where I.I.R is the random index extracted from Saaty (1980). The incompatibility ratio for values lower than 0.10 (I.R < 0.10) indicates a reasonable level of consistency for pairwise comparisons. Greater values for this ratio (I.R ≥ 0.10) represent inconsistent judgements implying that the decision-maker should reconsider judgements in pairwise comparisons (Boroushaki and Malczewski 2008).

Phase 5: Final ranking the alternatives

The final scores of the alternatives are determined at this step by incorporation of the interrelated factors (Eq. A1.9).

$$ \begin{array}{@{}rcl@{}} S_{j}=\sum\limits_{i=1}^{n}W_{i}\times w_{ij} \end{array} $$

(A1.9)

where S_j is the final score of j th alternative, W_i is the weight of i th factor and w_ij is the weight of j th alternative for i th factor.