1. Problem Definition
In previous blogs, I use Non Compensatory Model, Compensatory Model, and Full Analytical Criteria Method as decision making tools, to make decision on selecting a project to fix a network issue. In this blog I will use Analytic Hierarchy Process as decision making tool. I am also going to use the same problem as in blog Week 6[7].
Analytic Hierarchy Process is a tool which has been introduced by Thomas L. Saaty in the early 1980s[4]. It based on methodology where the problem is decomposed into hierarchy of criteria and alternatives (options). The information is then synthesized to determine relative ranking of alternatives/options. Both qualitative and quantitative information can be compared using informed judgements to derive weights and priorities
2. Development of Feasible Alternatives
As per previous blogs, the objectives in of this decision making are to select a project from several project options as a solution for a transmission networks issue. The project parameters are the criteria for the selection, which are: Development Cost, Maintenance Cost, Environmental Issue, Number of staging, and Finish Year. There are several project options, which listed below:
 Project A: Install 2 x 50MVA transformers at Blackberry Substation and 1 x 50MVA at iPhone Substation
 Project B: Build Docomo Substation with 1 x 50MVA Transformer and install 2x 50MVA Transformer at BlackBerry Substation and install 1x 50MVA Transformer at iPhone Substation
 Project C: Install 2x 100MVA transformers at BlackBerry Substation and 1x 50MVA transformers at iPhone Substation
 Project D: Build Docomo Substation with 2 x 100MVA Transformer and install 1x 50MVA Transformer at iPhone Substation
 Project E: Install 2x 100MVA transformers at BlackBerry Substation and relocate 1x 50MVA from BlackBerry Substation to iPhone Substation
Base on the information above, a problem hierarchy can be developed. The result is shown in Figure 1.
Figure 1. Problems Hierarchy
3. Alternatives Outcomes
Table 1 shows how each parameter impacting each project.
Develop. Cost 
Maint. Cost 
Environmental Issue 
# of Staging 
Finish Year 

A 
72.0 
5.55 
vegetation clearing 
3 
2033 
B 
87.2 
5.90 
vegetation clearing, possible native artefact 
3 
2033 
C 
71.6 
5.50 
vegetation clearing 
4 

D 
94.9 
6.50 
vegetation clearing, possible native artefact 
3 
2030 
E 
42.0 
5.50 
vegetation clearing 
4 
2032 
Table 1. Project to Parameter Matrix
4. Selection of Criteria
The above information is then synthesized to determine relative ranking of the criteria and options. Both qualitative and quantitative criteria can be compared based on informed judgement to determine its weight and priorities. The comparison is carried out based on pairwise importance between criteria, and between project alternatives for based on each criterion. The comparison value is represented by the following number:
1=equal ; 3=moderate ; 5=strong ; 7=very strong ; 9= extreme
5. Analysis of the Alternatives
Applying the comparison value to do pairwise comparison between each criterion to each other, the result is shown in Figure 2.
Figure 2. Pairwise comparison between criterion
From the table shows in Figure 2, a matrix can be developed, which is shows in Figure 3.
Figure 3. Matrix pairwise comparison of criteria
From the above matrix, an eigenvector is developed via the following methodology:
 Take successive squared powers of matrix
 Normalize the row sums
 Iterate the process until difference between successive row sums is less than a prespecified value
In this case the prespecified value is 0.0000.
The square power of the matrix in Figure 3 is shown in Figure 4.
Figure 4. Squared power of the matrix in Figure 3
The normalize row of sum is shown in Figure 4
Figure 5. Normalize row of sum of the matrix in Figure 3
Redo the process using the matrix in Figure 4, to get a normalized row of sum of the matrix in Figure 4. Checking the difference between these two normalize row of sum gives result as per Figure 6.
Figure 6. The difference between normalize row of sum of the matrix in Figure 3 and normalize row of sum of the matrix in Figure 4.
As the absolute value of the matrix in Figure 6 is bigger than 0.0000, the process is iterated until the absolute difference between two successive normalize row of sums is less than 0.0000. The eigenvector is the row of sum of the matrix. In this exercise, the result is shown in Figure 7.
Figure 7. Eigenvector of criterion pairwise comparison.
From the matrix in Figure 7, the criterion ranking is shown in Figure 8.
Figure 8. Criterion ranking
Doing the same with each project options for each criterion, the result are shown in Figure 9.
Figure 9. Matrix of normalized comparison (eigenvector based) of each project options.
Figure 10 shows the ranking tree which combine the problem hierarchy (Figure 1) and the eigenvector results.
Figure 10. Ranking tree
The project options ranking can be calculated by multiplying the criteria ranking (Figure 8) and the options rankings (Figure 9). The result is shown in Figure 11.
Figure 11. Multiplication of project parameter (criterion) matrix and project options.
6. Selection of Preferred Alternative
Based on total project scoring as shown in Figure 11, Project E is having the biggest score. It means Project E should be selected as preferred options.
7. Performance Monitoring & Post Evaluation of Results
The AHP result is similar to the previous comparison. This is understandable, because Project E in general is dominance compare to other projects. This exercise assures us that Project E is the best compare to other projects.
The AHP method is basically an improvement to the Full Analytical Criteria method. The biggest difference between these two method is the implementation of eigenvector method to normalized the pairwise comparison rank either between the parameter or between the project options. These method produces near consistent matrices. Near consistent matrices are essential because when dealing with intangibles, human judgment is of necessity inconsistent, and if with new information one is able to improve inconsistency to near consistency, then that could improve the validity of the priorities of a decision. In addition, judgment is much more sensitive and responsive to large rather than to small perturbations, and hence once near consistency is attained; it becomes uncertain which coefficients should be perturbed by small amounts to transform a near consistent matrix to a consistent one. If such perturbations were forced, they could be arbitrary and thus distort the validity of the derived priority vector in representing the underlying decision.[8]
Even the AHP methodology seems to be the best method compare to the previous methodologies, unfortunately it is quite cumbersome and difficult to perform when we have a lot of criteria, which may have sub criteria as well, and options. If this method is used quite often, automating the process may warrant an investment.
References
1. Wibisono, H. (Sept 19, 2013). W6_HWB_ Analytical Hierarchy Process (AHP). Retrieved from: https://simatupangaace2014.wordpress.com/2013/09/19/w6_hwb_analyticalhierarchyprocessahp/
2. Sullivan, W. G., Wicks, E. M., & Koelling, C. P. (2012). Engineering Economy (15th ed.) (pp.551569). Boston: Prentice Hall.
3. College of Business Administration, UIC. (n.d). Analytic Hierarchy Process [PowerPoint slides]. Retrieved from: http://www.uic.edu/classes/idsc/ids422/ahp.ppt
4. Haas, R., Meixner, O. (n.d.). An Illustrated Guide to the Analytic Hierarchy Process [PDF]. Retrieved from: http://alaskafisheries.noaa.gov/sustainablefisheries/sslmc/july06/ahptutorial.pdf
5. Satisfactionuk. (Feb 19, 2011). Analytic Hierarchy Process – AHP (Decision making process). Retrieved from http://www.projectsmart.co.uk/forums/viewtopic.php?f=2&t=721
6. McCaffrey, J. (n.d.). Test Run: The Analytic Hierarchy Process. Retrieved from: http://msdn.microsoft.com/enus/magazine/cc163785.aspx
7. Daroeso, S. S., (Oct 9, 2013). W6_SSD_Non Compensatory Decision Making – Selecting Transmission Projects. Retrieved from: https://simatupangaace2014.wordpress.com/2013/10/09/w6_ssd_noncompensatorydecisionmakingselectingtransmissionprojects/
8. Saaty, T. L. (Jan 2002). Decisionmaking with the AHP: Why is the principal eigenvector necessary. European Journal of Operational Research, 145, 85–91. Retrieved from: http://galton.uchicago.edu/~lekheng/meetings/mathofranking/ref/saaty1.pdf
AWESOME job, Pak Sadat!! EXCELLENT case study and you did a great job on your analysis……
Also happy to see that you have built in a safety buffer…… A contingency of a few weeks just in case you run into a problem…..
Just be sure to claim credit for this blog and 1 of your two questions from Chapter 14……. You are entitled to earned value and given the situation, you need to be showing as much earned value as possible….
BR,
Dr. PDG, Jakarta