Analytic hierarchy process
Analytical hierarchy process is a decision making tool developed by Thomas L. Saaty of the University of Pittsburg (Saaty 1977). AHP is used when has various measures are available for comparison (Yu 2017).
Development of a hierarchy model
In this step, a three-level hierarchy model was developed as shown in Fig. 6 to select the suitable leaching method using AHP. Criteria and sub-criteria are discussed in detail.
Fig. 6 Three-level hierarchy model for selection of feasible leaching method
Selection of criteria
Several leaching methods used for the recovery of metals from e-waste. The main criteria that will assist in deciding the suitable process for heavy metal recovery are represented here, i.e., economic feasibility, environmental impact, and reagent reuse.
Economic feasibility (EF)
Economic feasibility is the economic analysis of the process, which include all expenditure or investment during the process. If all the expenditure are in low cost, then the process is called as an economically feasible process.
Environmental impact (EI)
Environmental impact refers to the impact on the ecosystem. A suitable method should not impact or harm the environment.
Reagent reuse (RR)
In leaching process reagent is the heart of the process, therefore, it should be reused again and again. Regeneration of reagent is a good characteristic of economic and eco-friendly process.
Selection of sub-criteria
On the basis of criteria, six sub-criteria such as leaching rate, reagent cost, toxicity, safety, corrosiveness, and reagent regeneration were selected for all the four methods.
Leaching Rate (LR)
Leaching rate is related to the kinetics of a process i.e., how much heavy metal is recovered in a particular time. A suitable method should have high leaching rate.
Reagent Cost (RC)
Reagent cost is the cost of reagent used for recovery of 1g of e-waste. A suitable method should have low reagent cost.
Toxicity (TO)
Toxicity is the degree at which the reagent can harm the environment (organism) and human beings. A suitable method should be less toxic to flora and fauna.
Safety (SF)
Safety includes the condition of being protected from unlikely caused danger, risk, or injury. A suitable method should be safe.
Corrosiveness (CO)
Corrosiveness means the ability of a reagent to cause corrosion. A suitable method should be non-toxic and non-corrosive in nature.
Regeneration (RG)
After the completion of one cycle of recovery, the reagent can be recovered and used again for subsequent cycles. If regenerated reagent recovers in good amount, then the process is considered as suitable method.
Alternative
Comparison was made between thiosulfate (M1), iodide (M2) aqua-regia (M3) and thiourea (M4) for recovery of heavy metals.
Pairwise comparison matrix
In AHP, pairwise comparisons are made to get exact ratio scale priorities. A pairwise comparison matrix is constructed for each level (criteria, sub-criteria and alternatives) and generate a matrix of relative rankings. For example, comparing LR to all six sub-criteria, i.e., LR, RC, TO, SF, CO, and RG.
Judgment for pairwise comparison
In this step, judgments are made on the basis of decision makers experience and knowledge (literature survey). Pairwise comparison has been done as per Table 1. After that all values were normalized in the matrix by summing each column and then dividing each element of the matrix by the sum of its respective column to obtain the normalized pair-wise matrix which is called as priority vector (PV).
Table 1 Scale for pair-wise comparisons Saaty (1977)
Value
|
Definition
|
Explanation
|
1
|
Identical value
|
Two requirements are of equal value
|
3
|
Slightly more value
|
Experience slightly favours one requirement over another
|
5
|
Strong value
|
Experience strongly favours one requirement over another
|
7
|
Very strong value
|
Experience very strongly favours one requirement over another
|
9
|
Extreme value
|
Experience Extreme value favours one requirement over another
|
2,4,6,8
|
Intermediate values
|
When compromise is needed
|
Reciprocals
|
|
Reciprocals for inverse comparison
|
Consistency verification
i. For consistency verification, we multiply the value of criteria weights by each column of the pair-wise comparison matrix. Then we have to calculate the value of the weighted sum by summing the elements in each row and named as New Vector (NV).
ii. Maximum eigen value (ℷmax) was calculated by averaging the value of NV/PV.
iii. Consistency index (CI) was calculated using equation (1);
CI = (ℷmax – n)/ (n – 1) (1)
where n is the number of elements.
iv. Consistency ratio (CR) was calculated using equation (2);
CR = CI/RI (2)
where RI = Random Index (see Table 2). The value of CR < 0.10, only then the matrix is reasonably correct to make the decisions based on the AHP.
v. Finally, the criteria weights are used to decide the priority of each criterion and tells its percentage weightage when multiplied by 100.
Table 2 Random index value
n
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
RI
|
0.00
|
0.00
|
0.58
|
0.90
|
1.12
|
1.24
|
1.32
|
1.41
|
1.45
|
1.49
|