# W6_HWB_ Analytical Hierarchy Process (AHP)

1. Problem Definition

As planned in the previous blog, this time I will demonstrate solution in the case of W5 blog with AHP method. The problem is selecting the purchase of motorbike by overlook cost as attribute or criteria. But in the end it tries to put back the cost factor by benefit-cost ratio calculation.

2. Development of Feasible Alternatives

The Analytic Hierarchy Process (AHP) is a structured technique for dealing with complex decisions. Rather than prescribing a “correct” decision, the AHP helps decision makers find one that best suits their goal and their understanding of the problem—it is a process of organizing decisions that people are already dealing with, but trying to do in their heads. Based on mathematics and psychology, the AHP was developed by Thomas L. Saaty in the 1970s and has been extensively studied and refined since then.[1]

3. Development Outcomes for Alternative

The information from W5 blog arranged in a hierarchical tree as below:

4. Selection of Criteria

Using pairwise comparisons, the relative importance of one criterion over another can be expressed with scale 1=equal ; 3=moderate ; 5=strong ; 7=very strong ; 9= extreme, and 2,4,6,8 are in between, as matrix below:

Now turn the matrix above into a ranking of criteria or eigenvector by:[2]

• A short computational way to obtain this ranking is to raise the pairwise matrix to powers that are successively squared each time.
• The row sums are then calculated and normalized.
• The computer is instructed to stop when the difference between these sums in two consecutive calculations is smaller than a prescribed value.

Convert the fractions to decimals (to four decimal places) as below :

Squaring the matrix above, then compute first eigenvector by sum the row (i.e. 4.0000+3.1667+4.7500+6.5000 = 18.4167), and nolmalize by dividing the row-sum by the row-sum total (i.e. 18.4167 / 87.000 = 0.2117), the result as below :

This process must be iterated until the eigenvector solution does not change from the previous iteration (can be done by computer program: expert choice), in this case I stop iterating up to two times square matrix, as below:

So, the relative ranking of criteria :

• The most important criteria is performa (0.3540)
• The second most important criteria is fitur (0.2400)
• The third most important criteria is model (0.2151)
• The least important criteria is fuel (0.1908)

5. Analysis of the Alternatives

In the term of each criteria, using pairwise comparisons to determines the preference of each alternative over another, then we get :

Computing the eigenvector to determines the relative ranking of alternatives under each criterion, using the same calculation when compute the relative ranking of criteria before, then we get:

The rank calculation for fuel consumption criteria can be ranked by normalizing the value, so AHP can combine both qualitative and quantitative information. For each distance per fuel consumption are: 42.4 km./ltr, 28 km/ltr, 45.7 km/ltr, and 47.5 km/ltr.[3]

Below is the rank of fuel consumption:

Here is the tree with all the weights:

The solution is :

Although costs could have included, in many complex decisions, costs should be set aside until the benefits of the alternatives are evaluated. Discussing costs together with benefits can sometimes bring forth many political and emotional responses. [2]

In this case I am trying to calculate the benefit-cost ratio regarding to determine whether there are changes in decision if cost factors influence as criteria. The price data obtained from W5 blog. The result as below:

6. Selection of Preferred Alternative

The final choice would be Honda Vario CW because it has top-ranked benefit, but after calculate benefit-cost ratio, Suzuki Spin 125 SR is the “winner”.

7. Performance Monitoring & Post Evaluation of Results

The results obtained different with the results of the non-compensatory models in W5 blog. But the end result using AHP was more make sense in terms of all the criteria are accommodated by pairwise comparison using range of scale relatively larger than the other methods (1-9). The cost factor can be ignored if the price difference between alternative is felt no or little influence on decisions. To get more accurate results, pairwise comparison matrix can be done by surveying experts, end users, or anyone who is understand the problems faced.

References:

[1] Analytic Hierarchy Process – AHP (Decision makeing process) | Project Smart. (n.d.). Retrieved from  http://www.projectsmart.co.uk/forums/viewtopic.php?f=2&t=721

[3] W5_HWB_ Multiattributes Decision Non Compensatory Model – Selecting Motorbike | Simatupang AACE 2014. (n.d.). Retrieved from https://simatupangaace2014.wordpress.com/2013/09/19/w5_hwb_-multiattributes-decision-non-compensatory-model-selecting-motorbike/

Filed under Hari W, Week 06

### 3 responses to “W6_HWB_ Analytical Hierarchy Process (AHP)”

1. WOW!!! AWESOME posting, Pak Hari……. Very nicely done!!!

After using the non-compensatory, compensatory and AHP approaches, which one do you think is the “best” or “better” approach?

Maybe you can create another blog posting next week which compares the various methods and recommend with using one over the others? Which one is the easiest to use? Which one produces the “best” or “most reliable” results? Which one would you use to make a presentation to management?

Again, very interesting and appropriate topic and one I hope to see you actually using in your day to day working environment!!

Keep up the good work!!

BR,
Dr. PDG, Jakarta