Bab 4: Hasil dan Pembahasan
39 �
…
… ⋮ ⋮ ⋮ ⋮
… matrices e.g., Haas and Meixner, 2005; and Hamdeh, 2010. However, greater decimals
would provide more precise calculations for better results.
4.4.1. Pair-Wise Comparisons of the Evaluation-Criteria
The dimension of pair-wise comparisons is calculated by given
Equation 1
. The eigenvalue methods
Equation 2
and its reciprocal values are used to form the matrix
A
through comparing each element of evaluation-criteria Project Type, Project Phase, Project Monitoring, and Project Deliveries. Following the matrix formula
Equation 3
, it is deconstructed as the matrix algebra in Table 4-1.
Number of Comparisons � � =
× −
Equation 1 Eigenvalue method:
� − � �� × � = Equation 2
Matrix formula:
Equation 3
Where, Dimension of matrix A
� Pair-wise comparison matrix A
� � Principal eigenvalue of matrix A
� Relative weights eigenvectors of matrix A
, , ..., and
The weights of element 1, 2, ..., and n The
� � and eigenvalue are calculated using Equation 1 and 2 to decompose the matrix algebra A as explained in the example below:
Bab 4: Hasil dan Pembahasan
40 � � =
× −1
2
=
4 ×4 −1
2
= 6
= 725
778 = 0.931877
Where, � � = 6
The 6 sets of pair-wise comparisons are located on the top-right side of diagonal matrix A and its reciprocals placed on bottom-left side
= 725 The weight of element number 1 Project Type
= 778 The weight of element number 2 Project Phase
0.931877 The eigenvalue of Project Type relative to Project Phase, included in
the matrix algebra The eigenvalues e.g., 0.91877, 0.834292, etc. and their reciprocals 1.073103,
1.198621, etc. of each element relative to other elements are represented in Table 4-1.
Tabel 4-1: Matrix Algebra of the Evaluation-Criteria
4.4.2. Eigenvector Solution of the Evaluation-Criteria
The process of AHP techniques must be iterated properly in order to achieve the best result on the eigenvector solution. The following matrices in Table 4-2 and Table 4-3
are the last two squared and iterated matrices, and normalised eigenvectors are calculated by dividing each row sum with the total column sum.
Criteria Types
Phases Monitors
Deliveries Types
1 0.931877
0.834292 1.186579
Phases 1.073103
1 0.895282
1.273322
Monitors 1.198621
1.116967 1
1.422259
Deliveries 0.842759
0.785347 0.703107
1 Column Sum
4.114483 3.834190
3.432681 4.882160
Bab 4: Hasil dan Pembahasan
41
Tabel 4-2: The First Iteration of Squared Matrices of the Evaluation-Criteria
The normalised eigenvector summation, for example: all elements of Evaluation- criteria Project Type, Project Phase, Project Monitoring, and Project Delivery should
always be an absolute value of
‘one’
,
as shown in Table 4-2 and Table 4-3.
Tabel 4-3: The Second-Last Iteration of Squared Matrices of the Evaluation-criteria
There is not a different value between each normalised eigenvector in the first iteration matrix Table 4-2 and the second-last iteration Table 4-3. It means that the
latest iteration matrix Table 4-3 has provided the best result for the eigenvector solution.
4.4.3. Consistency Ratio of the Evaluation-Criteria
