STEP 5 Pairwise comparison matrices for interdependencies.
In this step, pairwise comparisons are made to capture interdependencies among the enablers.
One such comparison is presented in Table 5.
It is presents the result of a CPT- LTR clusters with INF as the controlling attribute over other enablers.
In the formation of this table, the question asked to the decision-maker is: "when considering INF with regard to increasing compatibility, what is the relative impact of enabler A when compared to enabler B" ?
For example, "when considering INF, with regard to increasing compatibility, what is the relative impact of QM when compared to FBP"?
From table 5 it is observed that QM has the maximum impact on an LTR-CPT cluster with INF as the control enabler over others.
The e- vectors from these matrices are used in the formation of a super-matrix.
For example, the e-vectors from Table 5 have been used in the sixth column of the super-matrix in Table 7.
For each determinant, there will be 16 such matrices at this level of relationship.
As there are four determinants, 64 such matrices would be formed.
STEP 6 Evaluation of providers
The final set of pairwise comparisons is made for the relative impact of each of the outsourcing alternatives (D, B and C) on the enablers in influencing the determinants.
The number of such pairwise comparison matrices is dependent on the number of enablers that are included in each determinant.
In the present case, there are 16 enablers for each determinant, which leads to the formation of 64 such pairwise comparison matrix is shown in Table 6.
In this table, the impacts of tree alternatives are evaluated on the enabler WIL in influencing the determinant CPT.
The e-vectors from this matrix are used in the third row (corresponding to WIL) of columns 6, 7 and 8 of the compatibility desirability indices matrix in Table 9.
Step 7 super- matrix formation
The super- matrix allows for a resolution of interdependencies that existamong the elements of a system.
It is a partitioned matrix where each sub-matrix is composed of a set of relationship between and within the levels as represented by the decision-maker's model.
The super-matrix M, as shown in Table 7, present the results of the relative importance measures for each of the enablers for the compatibility determinant.
The elements of the super-matrix have been imported from the pairwise comparison matrices of interdependencies (Table 5).
As there are 16 such pairwise comparison matrices, one for each interdependent enabler is the compatibility determinant, there will be 16 non-zero columns in this super-matrix.
Each of the non-zero values in a column is the relative importance weight associated with the interdependent pairwise comparison matrices.
In the next stage, the super-matrix is made to convergeto obtain a long-term stable set of weights.
For convergence to occour, the super-matrix needs to be column stochastic.
In other words, the sum of each column of the super-matrix needs to be one.
Raising the super-matrix to the power 2k+1, where K is an arbitarily large number, allows convergence [38,39].
In this example convergence is reached at M129.
The converged super-matrix is shown in Table 8.