Analytic Hierarchy Process

Australian Journal of Engineering Research

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Australian Society for Commerce Industry & Engineering

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Analytic Hierarchy Process

Hadia Rafi

Abstract

To make any decision in any work/task/project it involves many factors that needed to be looked. The

analytic Hierarchy process (AHP) is based on the judgments of experts to derive the required results this

technique measures the intangibles and then by the help of judgment and software analysis the comparisons

are made which shows how much a certain element/unit leads another.

AHP includes how an inconsistent judgment should be made consistent and how the judgment should be

improved when possible. The Priority scales are obtained by multiplying them with the priority of their

parent node and after that they are added.

The Ahp Method

AHP is a decision making technique. It is specially used in those cases where there are more than one

options in making a certain decision. In this method the complex problems are structured in the form of

hierarchy. Hierarchy includes three levels which are: the goal, the criteria and the alternatives.

Building A Hierarchy

The first step is to decompose the problem from top to bottom in a tree-like diagram. The diagram will

include from top to bottom: the goal (or objective), the criteria and finally the alternatives. Fig. 1 illustrates

a two levels hierarchy with three criteria and four alternatives from which the solution will be defined. A

hierarchic structure can have an unlimited number of levels. [3] In practice, it is preferable not to exceed

three or four levels, the last level always consisting in the alternatives.

Evaluate the Hierarchy

When the hierarchy is constructed the one analysis it by number of comparisons. Which leads to

Measurement of nodes numerically? The goals and criteria are compared with each other. Then for the

preference the alternatives are compared with criteria.

In this way the comparisons are compiled and priorities are gained for each node.

Each of the criteria and then alternatives will then compared with each other and find out the best way like

what would be the reason for generator failure and what should be adopt to make it correct for future

purpose.

Establish Priorities

In case of each pair of criteria the decision maker has to answer some of the questions like ―how important

is criterion X then criterion Y?‖ Rating of criteria is done by giving a weight between 1 and 9 to important

criterion then the reciprocal of this velour is given to other criterion in the pair. Like this the average weight

for each criterion is founded by taking the average of the weightings.

Synthesizing Results

In the last step the option scores are merged with the criterion weights to get an overall result.

Finally, after the judgment have been made and the priorities have been compiled for hierarchy the less

important elements may be dropped as they have a very less impact on the overall hierarchy.

The priorities then can be recompiled.

1 Analytic hierarchy process with an Example of Choosing a Leader:

This will include AHP in selecting a leader for a certain company whose current leader will be retiring from

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the job soon. By the help of AHP technique the board can choose the most suitable person in a very

transparent way, without any kind of favors. The following diagram shows how AHP is helpful in choosing

the most suitable leader.

There are four criteria which are used in choosing the right person which are Education, Age, Experience

and Charisma, as the person has to lead the whole company it is important for him to have a complete

knowledge of what and how he has to lead the whole company forward therefore education is very

important. Age is also very important as her or she will want to have a good career path ahead.

[1]As the new leader should keep his workers active and relax during the difficult times so it is important to

prefer someone who is active and charismatic. As the job requires knowledge, it is important for the new

leader to be experienced.

Deciding A Hierarchy

The AHP hierarchy for "choosing a leader "decision is given in the following diagram.

As the decision makers will go on with AHP. The priorities will be made With respect to decision criteria

for each candidate. And then the priorities will also be made of each criterion according to their importance

in achieving a goal.

[1]The priorities will be combined in order to generate the result of overall priority of each candidate.

The most suitable option will be the one with the highest priority.

[1]The priorities will be derived from the pair wise comparison including all the nodes. The result of these

comparisons will be entered into the form of the matrix which will give the result of priorities for each

node.

[1] The comparison will be made between criteria and their importance in reaching the required goal.

According to the criterion the board will examine that which candidate is strong and which is weaker.

According to this they will give the weight to the candidates.

EXPERIENCE

The board will evaluate the candidate’s experience. They have the complete information about the

candidate’s history but using AHP technique they will create a scale which will measure the candidate’s

strengths in accordance with experience.

The next step will be that the members of board will compare the pairs of candidates according to the

experience. Then they will give then weight using AHP Fundamental Scale. The weaker person will be

given the weight of 1.

Alternatives compared with respect to their Experience

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After processing the matrix mathematically the AHP will derive the properties for the candidates according

to their experience.

Alternatives compared with respect to their Education Our 2nd most important criteria for a team leader selection is education. Along with experience, education

is also an important need for a company to know about the person’s background reality and his ability to

work under stress and making a good judgment. So pair wise comparison of three possible alternatives is as

follow:

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The priorities are the measurement of their strength. They are the result of the judgment derived from

decision makers. In mathematical terms they are the values which can be calculated in using a spreadsheet

program, by hand or by using AHP software.

Ahp Analysis Through Software

By using AHP software named makeitrational.com, the following results were made i.e.

Evaluation in context of: Goal Age & Education 40

Experience 60

Criterion Weight

Experience

40

Age & Education 60

Evaluation in context of: Experience

B 20

A 15

C 10

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Criterion Weight

A 33.33

B 44.44

C 22.22

Evaluation in context of: A

A 1

C 4

B 0.25

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Alternative A

A 19.05

B 4.76

C 76.19

Evaluation in context of: B

A 4

C 9

B 1

Alternative B

A 28.57

B 7.14

C 64.29

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Evaluation in context of: C

A 0.25

C 1

B 0.11

Alternatives C

A 18.37

B 8.16

C 73.47

Evaluation in context of: age & education

Criterion Weight

A 21.74

B 34.78

C 43.48

Evaluation in context of: A

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A 1

C 0.2

B 3

Alternatives A

A 23.81

B 71.43

C 4.76

Evaluation in context of: B

A 0.33

C 0.14

B 1

Alternatives B

A 22.56

B 67.76

C 9.68

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Evaluation in context of: C

A 5

C 1

B 7

Alternatives C

A 38.46

B 53.85

C 7.69

Overall ranking for all of three person's

Alternatives Experience Age & Education Total

A 13.88 11.9 25.78

B 3.95 25 28.95

C 42.18 3.1 45.28

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Making the decision

By the judgment of all the candidates with respect to their respective criteria’s, candidate c is the most

suitable with the priority 0.452. B with priority 0.2895 is second and A with 0.25 is third. Because of AHP

it will be easy for them to make the best decision. If they are not satisfied with the result they can re visit

the process and can make changes if necessary.

Conclusion

AHP is indeed the best method which interconnects the beginning and final steps as we have seen above

with a simple example of choosing a leader. AHP is the kind of multi-attribute decision making technique.

This guides the users through the steps of developing the criteria to make a proper decision.

Acknowledgment

I would like to thank to all those who helped me during this thesis especially Sir Murad Habib, my

supervisor for his suggestions and encouragement on this research report.

References

[1]http://www.google.com.pk/url?sa=t&rct=j&q=analytical%20hierarchy%20process's%20steps&source=

web&cd=5&cad=rja&ved=0CD0QFjAE&url=http%3A%2F%2Fbrd4.braude.ac.il%2F~bashkansky%2Fatq

e%2Flectures%2FAHP%2FAHP-

Saaty%2Fahp.ppt&ei=77JgUKS7MofvsgbF4YG4Cg&usg=AFQjCNEuuP3mr2KIurUCtj3XIbExHioQ0g

[2] Mr. P. P. Kulkarni, Mr.A.P.Khot, ―Supply Chain Performance Measurement‖ MPGI National Multi

Conference 2012 (MPGINMC 2012)

http://en.wikipedia.org/wiki/Analytic_hierarchy_process

[3] http://css.engineering.uiowa.edu/~coneng/lectures/AHP.pdf

[4] http://www.johnsaunders.com/papers/ahpexpo.pdf

[5]http://www.ijest.info/docs/IJEST12-04-02-024.pdf

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Analytic Hierarchy Process