Analisis Prioritas CSFs dengan Metoda AHP The Relative Importance of the CSF-Alternatives

Bab 4: Hasil dan Pembahasan 38 Sebanyak 40 CSFs telah teridentifikasi melalui kajian pustaka mereferensi pada Lampiran 1 . Selanjutnya didisain kuisioner dengan lima skala Likert menggunakan 40 variabel CSFs tersebut. Sebelum disebarkan kepada responden, kuisioner tersebut terlebih dahulu telah didiskusikan dengen 5 orang para pakar ahli dan profesional dibidang managemen biaya proyek konstruksi.

4.3. Analisis Prioritas CSFs dengan Metoda AHP

The most important CSFs are analysed using AHP techniques. The three main stages of AHP techniques are implemented during data analysis refer to Jaya and Pathirage, 2013. Firstly, calculating the relative importance between four evaluation-criteria i.e., Project Type, Project Phase, Project Monitoring, and Project Deliveries in respect of the decision-goal the most important CSFs; Second, calculating the relative importance between eight CSF-alternatives i.e., MARCON, DEVFOC, INVTEC, LOCRES, INTBEN, PROCOM, ROPRAC, and METOOL in respect of each element of the four different evaluation-criteria; Third, determining the relative importance ranking of eight CSF-alternatives under the four evaluation-criteria through establishing the AHP solution tree for the highest priority CSFs.

4.4. The Relative Importance of the Evaluation-Criteria

The judgements of five experts were considered to determine the relative importance of four evaluation-criteria using five Likert scales whilst scoring forty variable CSFs. The cumulative scores of every element of the four evaluation-criteria were used to develop pair-wise comparisons between them. The relative importance of each element of evaluation-criteria over another was analysed in respect of the decision-goal as structured on the top level of Figure 3-3. AHP can be expressed by examining pair-wise comparisons to develop matrix algebra, and squaring the matrix with multiple iterations until the last normalised eigenvector does not change too much to the preceding iteration. Prescribed measures are placed in four digit decimals of change values between consecutive iterated 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

The level of inconsistency must be checked to see if the result relating to the relative importance of evaluation-criteria was derived from acceptable consistent matrices. If the outcomes are considered to be valid, robust enough and makes sense, it should be obtained from consistent or near consistent matrices Ishizaka and Labib, 2009. The principal eigenvalue is necessary for examining the level of inconsistency of the matrix Saaty, 2008. Saaty 1977 has calculated the Consistency Index CI and Consistency Ratio CR using the given Equation 4 and Equation 5 below: �� = � �� − − Equation 4 Criteria Types Phases Monitors Deliveries Row Sum Eigenvector Types 4 3.727506 3.337169 4.746318 15.810993 0.243044 Phases 4.292414 4 3.581128 5.093290 16.966831 0.260811 Monitors 4.794483 4.467866 4 5.689034 18.951383 0.291317 Deliveries 3.371034 3.141388 2.812428 4 13.324851 0.204827 Column Sum 16.457931 15.336761 13.730725 19.528642 65.054059 1 Criteria Types Phases Monitors Deliveries Row Sum Eigenvector Changes Ranking Types 64 59.640103 53.394707 75.941080 252.975890 0.243044 0.00 3rd Phases 68.678621 64 57.298044 81.492635 271.469299 0.260811 0.00 2nd Monitors 76.711724 71.485861 64 91.024550 303.222135 0.291317 0.00 1st Deliveries 53.936552 50.262211 44.998849 64 213.197612 0.204827 0.00 4th Column Sum 263.326897 245.388175 219.691600 312.458265 1,040.864936 1 0.00 Bab 4: Hasil dan Pembahasan 42 �� = �� �� Equation 5 Where, �� 10 Consistency Ratio less than 10 an acceptable inconsistency of the matrices �� Random Index The average random index was randomly generated from reciprocals through analysing a sample size of 500 matrices Ishizaka and Labib, 2009, and this is provided in Table 4-4. Tabel 4-4: Random Inconsistency Index RI The consistency ratio has been calculated following this procedure with given n= 4 units and RI= 0.90 , resulting in CR~0.00 10. This indicates that the matrices examined are near perfectly consistent . Therefore, outcomes are considered valid.

4.5. The Relative Importance of the CSF-Alternatives

The individual responses of 107 project professionals were provided using five Likert scales through scoring forty variable CSFs. Cumulative weights of every factor of eight CSFs are used to develop pair-wise comparisons. Following similar AHP procedures to that of Section 4.4 , the relative importance of the CSF-alternatives is analysed in respect of the four elements of the evaluation-criteria as shown in Figure 1 Project Type, Project Phase, Project Monitoring, and Project Deliveries. For a calculation example, the relative importance of CSF-alternatives under the Project Type can be expressed by examining pair-wise comparisons through matrix algebra as provided in Table 4-5. Bab 4: Hasil dan Pembahasan 43 Tabel 4-5: Matrix Algebra of CSF-alternatives under the Project Type A normalised eigenvector of the iteration matrices can be obtained through squaring the matrices that are calculated in Table 4-6 and Table 4-7. These matrices are measured in six digit decimals. Tabel 4-6: The Before-Last Iteration of Squared Matrices of CSF-alternatives under the Project Type Normalised eigenvectors between the last two squared and iterated matrices Table 4-6 and Table 4-7 have shown insignificant changes. The highest change is represented by PROCOM =0.0005297. Therefore, an attempt to iterate one more squared matrix would not have changed the ranking of normalised eigenvectors. This eigenvector may be called the best eigenvector solution refer to Table 4-7. Tabel 4-7: The Last Iteration of Squared Matrices of CSF-alternatives under the Project Type Alternatives MARCON DEVFOC INVTEC LOCRES INTBEN PROCOM ROPRAC METOOL Row Sum MARCON 1 1.213592 1.30813953 1.322751 1.470588 1.12069 1.227094 0.953895 9.61675 DEVFOC 0.824 1 1.07790698 1.089947 1.211765 0.923448 1.011126 0.78601 7.924202 INVTEC 0.764444 0.927724 1 1.01117 1.124183 0.856705 0.938045 0.7292 7.351471 LOCRES 0.756 0.917476 0.98895349 1 1.111765 0.847241 0.927683 0.721145 7.270263 INTBEN 0.68 0.825243 0.88953488 0.899471 1 0.762069 0.834424 0.648649 6.53939 PROCOM 0.892308 1.082898 1.16726297 1.180301 1.312217 1 1.094946 0.851168 8.5811 ROPRAC 0.814933 0.988997 1.06604651 1.077954 1.198431 0.913287 1 0.777361 7.83701 METOOL 1.048333 1.272249 1.37136628 1.386684 1.541667 1.174856 1.286404 1 10.08156 Column Sum 6.780019 8.228178 8.86921064 8.968279 9.970616 7.598297 8.319722 6.467427 65.20175 Alternatives MARCON DEVFOC INVTEC LOCRES INTBEN PROCOM ROPRAC METOOL Row Sum Eigenvector MARCON 8 9.708738 10.4651163 10.58201 11.76471 8.965517 9.816754 7.631161 76.934 0.14797563 DEVFOC 5.768 8 8.62325581 8.719577 9.694118 7.387586 8.089005 6.288076 62.56962 0.120347 INVTEC 6.115556 7.421791 8 8.089359 8.993464 6.85364 6.508201 5.833598 57.81561 0.111203 LOCRES 6.048 7.339806 7.91162791 8 8.894118 6.777931 7.421466 5.769157 58.16211 0.11186958 INTBEN 5.44 6.601942 7.11627907 7.195767 8 6.096552 6.675393 5.189189 52.31512 0.10062343 PROCOM 7.138462 8.663181 9.33810376 10.49996 10.49774 8 7.76858 6.809343 68.71537 0.13216782 ROPRAC 6.519467 7.911974 8.52837209 8.623633 9.587451 7.306299 8 6.268455 62.74565 0.12068561 METOOL 8.386667 10.17799 10.9709302 11.09347 12.33333 9.398851 10.29123 8 80.65248 0.15512778 Column Sum 53.41615 65.82543 70.9536852 72.80378 79.76493 60.78638 64.57063 51.78898 519.91 1 Alternatives MARCON DEVFOC INVTEC LOCRES INTBEN PROCOM ROPRAC METOOL Ror Sum Eigenvector Rank Changes MARCON 504 621.3592 669.767442 686.7302 752.9412 573.7931 608.9626 488.8809 4906.43 0.1481122 2nd -0.0001366 DEVFOC 408.704 504 543.265116 557.1461 610.7294 465.4179 493.6962 396.5498 3979.51 0.1201308 5th 0.0002163 INVTEC 378.7856 467.113 503.5044 516.3765 566.031 431.3547 457.5488 367.4779 3688.19 0.1113367 7th -0.0001336 LOCRES 381.024 469.7476 506.344186 519.168 569.2235 433.7876 460.3757 369.5939 3709.26 0.1119728 6th -0.0001032 INTBEN 342.72 422.5243 455.44186 466.9765 512 390.1793 414.0946 332.439 3336.38 0.1007163 8th -0.0000929 PROCOM 449.6584 554.3652 597.554099 612.6891 671.7602 511.9276 526.6293 436.1214 4360.71 0.1316381 3rd 0.0005297 ROPRAC 411.1421 506.8708 546.359623 560.1892 614.2082 468.069 496.774 398.8019 4002.41 0.1208222 4th -0.0001366 METOOL 528.36 651.3916 702.139535 719.9221 789.3333 601.5264 638.3958 512.5101 5143.58 0.1552709 1st -0.0001432 Column Sum 3404 4197.372 4524.37622 4639.198 5086.227 3876.056 4096.477 3302.375 33126.47 1 0.0000000 Bab 4: Hasil dan Pembahasan 44 A consistency ratio for this matrix has been checked following procedures as Equations 4 and Equation 5, given n= 8 units, with RI= 1.41 refer to Table 4-4. The result shows that CR = 0.019 10 . This indicated the valid outcomes that the matrices examined are nearly consistent. The relative importance of the CSF-alternatives and their consistency ratios under the other three evaluation-criteria i.e., Project Phase, Project Monitoring, and Project Deliveries have been analysed through the same procedures as applied for CSF- alternatives under the Project Type. Their valid outcomes are also presented in the left- hand side of Table 4-8. Tabel 4-8: AHP Solution Matrix of CSF-Alternatives under Evaluation-criteria The best eigenvector solution of evaluation-criteria is derived from Table 4-3 into the right-hand side of Table 4-8, and all of the best eigenvector solutions of CSF- alternatives are restructured to develop an AHP Solution Tree.

4.6. The Solution through AHP Tree