W5_WW_ Analytical Hierarchy Process

1. Problem Definition

In this blog, I would like to analyze the same case study as in my previous blog, choosing a car, using Analytic Hierarchy Process, and comparing the result.

2. Identify the Feasible of Alternatives

Based on previous research, I found top four candidates that will be select using Analytic Hierarchy Process.

Information Summary for Choice of Cars

info summary

3. Development of the Outcome for Alternative
The information above is arranged in a hierarchical tree as below:

2. generate hierachy

In complex decision, costs (price) should be set aside until the benefits of the alternatives are evaluated.

4. Selection of Criteria

Perform pairwise comparison.

1. Fundamental scale of absolute numbers.png
The fundamental scale of absolute numbers

Pairwise comparison matrix

3. pairwise matrix.jpg

Normalized matrix of paired comparisons and calculation of priority weights (eigenvalue).

4. normalized pairwise matrix.jpg

The consistency ratio (C.R.) for the comparison above is calculated to determine the acceptance of the priority weighting.
Based on Saaty’s empirical suggestion that a C.R. = 0.10 is acceptable.
To do that, we need Principal Eigen value that obtained from the summation of products between each element of Eigen value and the sum of columns of the reciprocal matrix.
5. rumus

6. RI
7. rumus 2

5. Analysis and Comparison of the Alternatives

We do the same procedures for alternatives and the results are below:

8. ranking

The alternative ranking is the product between alternative ranking matrix and criteria ranking.

9. ranking2

Alternative that having highest weights will be selected. Car C is the highest ranked Car.
6. Selection of the Preferred Alternative

After alternative ranking has been defined, we have to compare between benefits and costs (price) using benefit – cost ratio.

10. cost

Benefit – Cost Analysis

11. cost2

Based on benefit – cost analysis, Car C has highest ratio.

7. Performance Monitoring and the Post Evaluation of Result

The result is same with the result of the non-compensatory models. In order to have more accurate result, pairwise comparison matrix can be done by surveying the experts or anyone who has good understanding of the problems.
1. Saaty, T. L. (2008). Decision making with the analytic hierarchy process. Int. J. Services Sciences.
2. Triantaphyllou, E., Mann, S. H. (1995). Using The Analytic Hierarchy Process for Decision Making in Engineering Applications: Some Challenges, International Journal of Industrial Engineering: Applications and Practice.
3. Haas, R. (2014). An Illustrated Guide to the Analytic Hierarchy Process. Retrieved from: https://mi.boku.ac.at/ahp/ahptutorial.pdf
4. Laksono, A. (2014). Vendor Evaluation. Retrieved from: https://kristalaace2014.wordpress.com/2014/05/14/w12_al_vendor-evaluation/
5. Auto Bild Magazine (2014). 289 edition, 44 – 49.
6. Wijanarka, W. (2015). W3_WW_ Choosing a Car Using Non-Compensatory Model | GARUDA AACE 2015. Retrieved from: https://garudaaace2015.wordpress.com/2015/03/19/w3_ww_-choosing-a-car-using-non-compensatory-model/

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4 Responses to W5_WW_ Analytical Hierarchy Process

  1. drpdg says:

    Great job, Pak Wahyu…… Still not clear why you didn’t use the compensatory approaches shown on pages 560 to 568 in Engineering Economy, but using AHP is a perfectly acceptable method as well, even though you cannot claim credit for one of your problems from Chapter 14.

    Keep up the good work and if you wish, you can use this same case study but for your W6 blog, try the two COMPENSATORY approaches and at the end, see which of the three methods you think is “best” or “better” Non-compensatory, AHP or Compensatory methods. Explain which one you prefer or recommend and WHY.

    Dr. PDG, Jakarta


  2. wahyuwija says:

    Dear Dr. PDG,

    I have analyzed using compensatory approaches on my W4 blog.
    In my opinion, AHP could give better result if we could make a survey from experts.
    Thanks for your rating and comment.

    Best Regards,


  3. Pingback: W23_HI_Analytic Hierarchy Process | GARUDA AACE 2015

  4. Pingback: W12_OAN_Car Selection using AHP – EMERALD AACE 2017 – WEEKLY BLOG

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