1. Analytic Hierarchy Process (AHP)
By : BasmahAlQadheeb- FatimahAlOtaibi

2. Analytic Hierarchy Process (AHP)
 Is one of Multi Criteria decision making method that was originally
developed by Prof. Thomas L. Saaty.
 Is an excellent modeling structure for representing multicriteria (multiple goals, multiple objectives) problems—with sets of criteria and alternatives (choices)-commonly found in business environments.
 In short, it is a method to derive ratio scales from paired comparisons

3. Level 0
Level 1
Level2

4.  Level 0 is the goal of the analysis. Level 1 is multi criteria that
consist of several factors . Level 2 in is the alternative choices.
 The input of AHP can be obtained from actual measurement such as price, weight etc., or from subjective opinion such as satisfaction feelings and preference.
 AHP allow some small inconsistency in judgment because human is not always consistent.

5. Standard Preference Table
PREFERENCE LEVEL
NUMERICAL VALUE
Equally preferred
Equally to moderately preferred Moderately preferred Moderately to strongly preferred Strongly preferred
Strongly to very strongly preferred Very strongly preferred
Very strongly to extremely preferred Extremely preferred 1 2 3 4 5 6 7 8 9

6. Analytic Hierarchy Process
 Step 1: Structure a hierarchy. Define the problem, determine the criteria and identify the alternatives.
 For example:
 Suppose that John has three fruits Apple ,banana and Cherry . We wanted to ask him, Which fruit you like better than the others, and how much you like it in comparison with the others

7.  Step 2: Make pairwise comparisons. Rate the relative importance
between each pair of decision alternatives and criteria.

8.  You may observe that the number of comparisons is a combination of the number of things to be compared. Since we have 3 objects (Apple, Banana and Cheery), we have 3 comparisons.
 Table below shows the number of comparisons:

9. Making Comparison Matrix
 We have 3 by 3 matrix
 The diagonal elements of the matrix are always 1 and we only need
to fill up the upper triangular matrix.
 How to fill up the upper triangular matrix is using the following rules:
 If the judgment value is on the left side of 1, we put the actual
judgment value.
 If the judgment value is on the right side of 1, we put the reciprocal
value .

10.  John made subjective judgment on which fruit he likes best, like the
following

11.  Comparing apple and banana, John slightly favor banana, thus we
put 1/3 in the row 1 column 2 of the matrix.
 Comparing Apple and Cherry, John stronglylikes apple, thus we put actual judgment 5 on the first row, last column of the matrix.
 Comparing banana and cherry, banana is dominant. Thus we put his actual judgment on the second row, last column of the matrix. Then based on his preference values above, we have a reciprocal matrix like this:

12.  Suppose we have 3 by 3 reciprocal matrix from paired comparison

13.  We sum each column of the reciprocal matrix to get

14.  Then we divide each element of the matrix with the sum of its column, we have normalized relative weight. The sum of each column is 1.

15. ► Step 3: Synthesize the results to determine the best alternative.
Obtain the final results.

16.  The normalized principal Eigen vector can be obtained by averaging
across the rows
 The normalized principal Eigen vector is also called priority vector

17.  In our example above,
 Apple is 28.28%, Banana is 64.34% and Cherry is 7.38%.
 John most preferable fruit is Banana, followed by Apple and Cheery

18. Our sample problem
 Jilley Bean Co. is selecting a new location to expand its operations.
The company want to use AHP to help it decide which location to build its new plant. Jilley Bean Co. has four criteria they will base their decision on these are the following: property price, distance from suppliers, the quality of the labor pool, and the cost of labor. They have three locations to decide from.

20. Matrices given criteria and preferencesB
PRICE
DISTANCE A B C 1 3 2 6
1/3
1/5
1/6
1/9
1/2 5 9
LABOR
WAGES 7 4
1/7
1/4 A C B C

21. How it is done ~ STEP ONE & TWO
PRICE A B C 1 3 2
1- First sum (add up) all the values in each column.
1/3
1/5 5
SUM
11/6 9
16/5
2- Next the values in each column are divided by the corresponding column sums
6/11
3/9
5/8
2/11
1/9
1/16
3/11
5/9
5/16
NOTICE: the values in each column sum to 1.

22. STEP THREE
PRICE A B C R
w Average =
1/3 *
6/11 +
3/9 +
5/8
0.0512
2/11 +
1/9 +
1/16
0.1185
3/11 +
5/9 +
5/16
0.3803
SUM 1 o
Next convert fractions to decimals and find the average of each row.

23. STEP FOUR
 Find the average for all the criterion by doing steps 1-3 on all the
criteria. Arriving at the following
Price
Distance
Labor
Wages A
0.0512
0.2819
0.1790
0.1561 B
0.1185
0.0598
0.6850
0.6196 C
0.3803
0.6583
0.1360
0.2243

24. STEP FIVE
 Rank the criteria in order of importance ~use the same method used
in ranking each criterion.
Price
Distance
Labor
Wages 1
1/5 3 4 5 9 7
1/3
1/9 2
1/7
1/2
SUM
6.583
1.454
13.5 14

25. STEP 6-9
 Repeat steps 1-4 with the new matrices. You should arrive at the
following :
Price
Distance
Labor
Wages
0.1519
0.1376
0.2222
0.7595
0.6878
0.6667
0.5
0.0506
0.0764
0.0741
0.0380
0.0983
0.0370
SUM 1

26. = ¼ * Row Average Price Distance Labor Wages 0.1519 0.1376+ + 0.2222+ +
0.2857
0.1994 =
Distance
¼ *
0.6535 =
Labor
0.1429
0.086
Wages
0.0714
0.0612
SUM 1

27. Take the criteria matrix and multiple it by the preference vector
Price
Distance
Labor
Wages
0.1994 A
0.0512
0.2819
0.1790
0.1561 X
0.6535 B
0.1185
0.0598
0.6850
0.6196
0.086 C
0.3803
0.6583
0.1360
0.2243
0.0612
Location A score =0.1994(0.0512) (0.2819)+0.086(0.1790) (0.1561)= Location B score =0.1994(0.1185) (0.2819)+0.086(0.1790) (0.1561)= Location C score =0.1994(0.3803) (0.2819)+0.086(0.1790) (0.1561)=0.5314

28.  In our example above,
 A is 30.91%, B is 15.95% and C is 53.14%.
 Location C should be chosen for Jilley Bean Co. to built a plant.