1. IME634: Management Decision Analysis
Raghu Nandan Sengupta
Industrial & Management Department
Indian Institute of Technology Kanpur
IME634
RNSengupta,IME Dept.,IIT Kanpur,INDIA

2. Analytic Hierarchy Process (AHP)
The Analytic Hierarchy Process (AHP) is a structured technique for organizing and analyzing complex decisions
It was developed by Thomas L. Saaty in the 1970s
Application in group decision making.
IME634
RNSengupta,IME Dept.,IIT Kanpur,INDIA

3. RNSengupta,IME Dept.,IIT Kanpur,INDIA
AHP (contd..)
Decision analysis problems involving finite number of alternatives arise frequently in practical situations
One must remember that the type of data available for analysis, based on which one has to draw some conclusions can be deterministic, probabilistic or uncertain
When the data is uncertain, then one of the many tools used for analysis is Analytical Hierarchy Process (AHP)
IME634
RNSengupta,IME Dept.,IIT Kanpur,INDIA

4. RNSengupta,IME Dept.,IIT Kanpur,INDIA
AHP (contd..)
In AHP, subjective judgement is quantified in logical manner and then utilized to reach some meaningful conclusions
One must remember that the decision makers assessment towards risk and his/her attitude towards return or average benefit reflects the decision makers overall outlook about any decision process
IME634
RNSengupta,IME Dept.,IIT Kanpur,INDIA

5. RNSengupta,IME Dept.,IIT Kanpur,INDIA
AHP (contd..)
Consider Ram has received the final calls from IIMA, IIMB and IIMC. His main criterion based on which he will take the decision is
1. Academic reputation
2. Placement potential
For his academic reputation is two (2) more important than placement potential. Thus placement potential is 1/3, while academic reputation is 2/3
IME634
RNSengupta,IME Dept.,IIT Kanpur,INDIA

6. Percent weight estimates
AHP (contd..)
Thus Ram ranks this as
IIMA: (0.30*1/3+0.40*2/3)
IIMB: (0.40*1/3+0.25*2/3)
IIMC: (0.30*1/3+0.35*2/3)
Criterion
Percent weight estimates
IIMA
IIMB
IIMC
Academic reputation
0.40
0.25
0.35
Placement potential
0.30
IME634
RNSengupta,IME Dept.,IIT Kanpur,INDIA

7. RNSengupta,IME Dept.,IIT Kanpur,INDIA
AHP (contd..)
Now consider Rams brother Shyam, also has got calls from the same three institutes and both want to be in the same place, so that their parents can reduce their overall cost of expenditure
Decision: Select IIM
Hierarchy # 1: Placement potential Academic Reputation
¼ ¾
Placement potential
Alternatives: IIMA IIMB IIMC
Academic Reputation
IME634
RNSengupta,IME Dept.,IIT Kanpur,INDIA

8. RNSengupta,IME Dept.,IIT Kanpur,INDIA
AHP (contd..)
IIMA: (0.25*1/4+0.35*3/4)
IIMB: (0.25*1/4+0.35*3/4)
IIMC: (0.50*1/4+0.30*3/4)
IME634
RNSengupta,IME Dept.,IIT Kanpur,INDIA

9. RNSengupta,IME Dept.,IIT Kanpur,INDIA
AHP (contd..)
So Rams and Shyams collective hierarchy is as given
Decision Select IIM
Hierarchy # 1 Ram Shyam
0.5 (p) 0.5 (q)
Hierarchy # 2: PP AR PP AR
1/3 2/3 ¼ ¾
(p1) (p2) (q1) (q2)
IME634
RNSengupta,IME Dept.,IIT Kanpur,INDIA

10. RNSengupta,IME Dept.,IIT Kanpur,INDIA
AHP (contd..)
Alternatives: IIMA IIMB IIMC
(p11) (p12) (p13)
(p21) (p22) (p23)
Alternatives: IIMA IIMB IIMC
(q11) (q12) (q13)
Alternatives: IIMA IIMB IIMC
(q21) (q22) (q23)
IME634
RNSengupta,IME Dept.,IIT Kanpur,INDIA

11. RNSengupta,IME Dept.,IIT Kanpur,INDIA
AHP (contd..) So
IIMA: p*p1*p11 + p*p2*p21+q*q1*q11+q*q2*q21
IIMB: p*p1*p12 + p*p2*p22+q*q1*q12+q*q2*q22
IIMC: p*p1*p13 + p*p2*p23+q*q1*q13+q*q2*q23
IME634
RNSengupta,IME Dept.,IIT Kanpur,INDIA

12. RNSengupta,IME Dept.,IIT Kanpur,INDIA
AHP (contd..)
Wide range of applications exists:
Selecting a car for purchasing
Deciding upon a place to visit for vacation
Deciding upon an MBA program after graduation
IME634
RNSengupta,IME Dept.,IIT Kanpur,INDIA

13. RNSengupta,IME Dept.,IIT Kanpur,INDIA
AHP (contd..)
AHP algorithm is basically composed of two steps:
Determine the relative weights of the decision criteria
Determine the relative rankings (priorities) of alternatives
Both qualitative and quantitative information can be compared by using informed judgments to derive weights and priorities.
IME634
RNSengupta,IME Dept.,IIT Kanpur,INDIA

14. RNSengupta,IME Dept.,IIT Kanpur,INDIA
AHP (contd..)
Objective: Selecting a car
Criteria: Style, Cost, Fuel-economy
Alternatives: Civic , i20 , Escort, Alto
IME634
RNSengupta,IME Dept.,IIT Kanpur,INDIA

15. AHP (contd..) Hierarchy tree
Civic i20 Escort Alto
Alternative courses of action
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RNSengupta,IME Dept.,IIT Kanpur,INDIA 3

16. AHP (contd..) Ranking Scale for Criteria & Alternatives
IME634
RNSengupta,IME Dept.,IIT Kanpur,INDIA

17. AHP (contd..) Ranking of Criteria
Style
Cost
Fuel Economy
1 1/2 3
1/3 1/4 1
IME634
RNSengupta,IME Dept.,IIT Kanpur,INDIA

18. AHP (contd..) Ranking of Priorities
Row
averages
Normalized
Column Sums
0.32
0.56
0.12 A= X=
Priority vector
Column sums
IME634
RNSengupta,IME Dept.,IIT Kanpur,INDIA 5

19. AHP (contd..) Criteria Weights
Style
Cost
Fuel Economy
Selecting a New Car
1.00
Style
0.32
Cost
0.56
Fuel Economy
0.12
IME634
RNSengupta,IME Dept.,IIT Kanpur,INDIA 7

20. AHP (contd..) Checking for consistency
The next stage is to calculate a Consistency Ratio (CR) to measure how consistent the judgments have been relative to large samples of purely random judgments.
AHP evaluations are based on the assumption that the decision maker is rational, i.e., if A is preferred to B and B is preferred to C, then A is preferred to C.
If the CR is greater than 0.1 the judgments are untrustworthy because they are too close for comfort to randomness and the exercise is valueless or must be repeated.
IME634
RNSengupta,IME Dept.,IIT Kanpur,INDIA

21. AHP (contd..) Calculation of consistency ratio
The next stage is to calculate max so as to lead to the Consistency Index (CI) and the Consistency Ratio.
Consider [Ax = max x] where x is the Eigenvector.
A x Ax x
0.98
1.68
0.36
0.32
0.56
0.12
0.32
0.56
0.12 =
= max
λmax= average{0.98/0.32, 1.68/0.56, 0.36/0.12}=3.04
CI = (λmax-n)/(n-1)=(3.04-3)/(3-1)= 0.02
IME634
RNSengupta,IME Dept.,IIT Kanpur,INDIA

22. RNSengupta,IME Dept.,IIT Kanpur,INDIA
AHP (contd..)
CR = CI/RI where RI is the random index n
R.I
C.I. = 0.02
n = 3
RI = 0.50 (from table)
Hence: CR = (CI/RI) = 0.02/0.52 = 0.04
CR ≤ 0.1 indicates sufficient consistency for decision.
IME634
RNSengupta,IME Dept.,IIT Kanpur,INDIA

23. AHP (contd..) Ranking alternatives
Priority vector
Style
Civic
i20
Escort
Alto
Civic
/ /6
0.13
0.24
0.07
0.56
i20 /4
Escort
1/ / /5
Alto
Cost
Civic
i20
Escort
Alto
Civic
0.38
0.29
0.07
0.26
i20 1/
Escort
1/ / /4
Alto /
IME634
RNSengupta,IME Dept.,IIT Kanpur,INDIA 8

24. AHP (contd..) Ranking alternatives
Kilometer/litre
Priority Vector
Civic 34
0.30
Fuel Economy
i20 27
0.24
Escort 24
0.21
Alto 28
113
0.25
1.0
Since fuel economy is a quantitative measure, fuel consumption ratios can be used to determine the relative ranking of alternatives.
IME634
RNSengupta,IME Dept.,IIT Kanpur,INDIA 9

25. AHP (contd..) Ranking alternatives
Selecting a New Car
1.00
Style
0.32
Cost
0.56
Fuel Economy
0.12
Civic i
Escort
Alto
Civic i
Escort
Alto
Civic i
Escort
Alto
IME634
RNSengupta,IME Dept.,IIT Kanpur,INDIA 10

26. AHP (contd..) Ranking alternatives
Style
Economy
Cost
Fuel
Civic
Escort
Alto
i20 x
0.32
0.56
0.12 =
0.28
0.25
0.07
0.34
Priority matrix
Criteria Weights
IME634
RNSengupta,IME Dept.,IIT Kanpur,INDIA 11

27. AHP (contd..) Including Cost as a Decision Criteria
Adding “cost” as a a new criterion is very difficult in AHP
A new column and a new row will be added in the evaluation matrix
However, whole evaluation should be repeated since addition of a new criterion might affect the relative importance of other criteria as well!
Instead one may think of normalizing the costs directly and calculate the cost/benefit ratio for comparing alternatives!
Normalized
Cost
Cost/Benefits
Ratio
Cost
Benefits
Civic i Escort Alto
IME634
RNSengupta,IME Dept.,IIT Kanpur,INDIA 13

28. RNSengupta,IME Dept.,IIT Kanpur,INDIA
AHP (contd..)
Escort is the winner with the highest benefit to Cost Ratio, hence it is 1st
2nd position is that of i20
At 3rd is Alto
While 4th position goes to Civic
IME634
RNSengupta,IME Dept.,IIT Kanpur,INDIA

29. RNSengupta,IME Dept.,IIT Kanpur,INDIA
AHP (contd..)
Pros
It allows multi criteria decision making.
It is applicable when it is difficult to formulate criteria evaluations, i.e., it allows qualitative evaluation as well as quantitative evaluation.
It is applicable for group decision making environments
IME634
RNSengupta,IME Dept.,IIT Kanpur,INDIA

30. RNSengupta,IME Dept.,IIT Kanpur,INDIA
AHP (contd..)
Cons
There are hidden assumptions like consistency.
Repeating evaluations is cumbersome
It is difficult to use when the number of criteria or alternatives is high, i.e., more than 7
It is difficult to add a new criterion or alternative
It is difficult to take out an existing criterion or alternative, since the best alternative might differ if the worst one is excluded
IME634
RNSengupta,IME Dept.,IIT Kanpur,INDIA

31. RNSengupta,IME Dept.,IIT Kanpur,INDIA
AHP (contd..)
IME634
RNSengupta,IME Dept.,IIT Kanpur,INDIA

32. RNSengupta,IME Dept.,IIT Kanpur,INDIA
AHP (contd..)
Now if the matrix is consistent, then its form will be
Such that we have:
IME634
RNSengupta,IME Dept.,IIT Kanpur,INDIA

33. RNSengupta,IME Dept.,IIT Kanpur,INDIA
AHP (contd..)
and:
IME634
RNSengupta,IME Dept.,IIT Kanpur,INDIA

34. RNSengupta,IME Dept.,IIT Kanpur,INDIA
AHP (contd..)
Thus we have:
Hence: A(nXn)w(nX1) = nw(nX1) iff A is consistent and in case of inconsistency we try to find
IME634
RNSengupta,IME Dept.,IIT Kanpur,INDIA