1. Analytic Hierarchy Process Prepared by Lee Revere and John Large
Module 1
Analytic Hierarchy Process
Prepared by Lee Revere and John Large
To accompany Quantitative Analysis for Management, 9e
\by Render/Stair/Hanna
M1-1

2. Learning Objectives Students will be able to:
Use the multifactor evaluation process in making decisions that involve a number of factors, where importance weights can be assigned.
Understand the use of the analytic hierarchy process in decision making.
Contrast multifactor evaluation with the analytic hierarchy process.
To accompany Quantitative Analysis for Management, 9e
\by Render/Stair/Hanna
M1-2

3. Module Outline M1.1 Introduction M1.2 Multifactor Evaluation Process
M1.3 Analytic Hierarchy Process
M1.4 Comparison of MFEP and AHP
To accompany Quantitative Analysis for Management, 9e
\by Render/Stair/Hanna
M1-3

4. Introduction
Multifactor decision making involves individuals subjectively and intuitively considering various factors prior to making a decision.
Multifactor evaluation process (MFEP) is a quantitative approach that gives weights to each alternative.
Analytic hierarchy process (AHP) is an approach designed to quantify the preferences for various factors and alternatives.
To accompany Quantitative Analysis for Management, 9e
\by Render/Stair/Hanna
M1-4

5. Multifactor Evaluation Process
Steve Markel is considering employment with three companies. He has determined three factors that are important to him and assigned each factor a weight.
Factor
Importance
(weight)
AA Co.
EDS,
LTD.
PW,
Inc.
Salary
0.3
0.7
0.8
0.9
Career Advancement
0.6
Location
0.1
Weights should sum to 1
To accompany Quantitative Analysis for Management, 9e
\by Render/Stair/Hanna
M1-5

6. Evaluation of AA Co. Factor Factor Factor Weighted
Weight Evaluation Evaluation X =
Factor Factor Factor Weighted
Name Weight Evaluation Evaluation
Salary
Career
Location
Total
To accompany Quantitative Analysis for Management, 9e
\by Render/Stair/Hanna
M1-6

7. Comparison of Results Factor AA Co. EDS,LTD. PW,Inc. Salary 0.21 0.24
0.27
Career
0.54
0.42
0.36
Location
0.06
0.08
0.09
Weighted Evaluation
0.81
0.74
0.72
Decision is AA Co: Highest weighted evaluation
To accompany Quantitative Analysis for Management, 9e
\by Render/Stair/Hanna
M1-7

8. Analytic Hierarchy Process
Break decision into stages or levels.
Starting at the lowest level, for each level, make pairwise comparison of the factors.
9-step scale:
equally preferred
equally to moderately preferred
moderately preferred
moderately to strongly preferred
strongly preferred
strongly to very strongly preferred
very strongly preferred
very to extremely preferred
extremely preferred
To accompany Quantitative Analysis for Management, 9e
\by Render/Stair/Hanna
M1-8

9. Analytic Hierarchy Process
Develop the matrix representation:
Comparison matrix
Normalized matrix
Priority matrix
Develop  and the consistency ratio.
Determine factor weights.
Perform a multifactor evaluation.
To accompany Quantitative Analysis for Management, 9e
\by Render/Stair/Hanna
M1-9

10. Decision Hierarchy for Computer System Selection
Judy Grim is considering purchasing a new computer system. The most important factors are hardware, software, and support. She has identified three alternatives.
Select Computer System
Hardware Software Vendor
Support
System: System: System:
To accompany Quantitative Analysis for Management, 9e
\by Render/Stair/Hanna
M1-10

11. Beginning Comparison Matrix
Judy Grim has used the 9-point scale for pairwise comparison to evaluate each system on hardware capabilities
Hardware
System-1
System-3
System-2 3 9 6 1
To accompany Quantitative Analysis for Management, 9e
\by Render/Stair/Hanna
M1-11

12. Comparison Matrix (continued)
Hardware
System-1
System-3
System-2 3 9 6 1
1/3
1/9
1/6
To accompany Quantitative Analysis for Management, 9e
\by Render/Stair/Hanna
M1-12

13. Normalizing the Matrix
Hardware
System-1
System-3
System-2 3 9 6 1
1/3
1/9
1/6
1.444
4.167
16.0
Column
Totals
The totals are used to create a normalized matrix
To accompany Quantitative Analysis for Management, 9e
\by Render/Stair/Hanna
M1-13

14. Normalized Matrix Hardware System-1 System-3 System-2 0.6923 0.7200
0.2300
0.2400
0.3750
0.0769
0.0400
0.0625
0.5625
= 1/ = .333/ 1.444
To accompany Quantitative Analysis for Management, 9e
\by Render/Stair/Hanna
M1-14

15. Final Matrix for Hardware
Factor
System-1
System-2
System-3
Hardware
0.6583
0.2819
0.0598
To accompany Quantitative Analysis for Management, 9e
\by Render/Stair/Hanna
M1-15

16. The Weighted Sum Vector
F = [ ] 1
3 9
(0.6583)(1) + (0.2819)(3) +(0.0598)(9) =
0.6583)(0.33) + (0.2819)(1) + (0.0598)(6) =
(0.6583)(0.167) + (0.2819)(0.167) + (0.0598)(1) =
To accompany Quantitative Analysis for Management, 9e
\by Render/Stair/Hanna
M1-16

17. The Consistency Vector/
= =
0.1799/
To accompany Quantitative Analysis for Management, 9e
\by Render/Stair/Hanna
M1-17

18. Computing Lambda
Lambda is the average value of the consistency vectors. = =
To accompany Quantitative Analysis for Management, 9e
\by Render/Stair/Hanna
M1-18

19. The Consistency Index CI = 3.0541 – 3 = 0.0270 3 – 1
The consistency index is:
CI = – 3
3 – 1 =
To accompany Quantitative Analysis for Management, 9e
\by Render/Stair/Hanna
M1-19

20. Consistency Ratio CI CR = RI (random index) = 0.0270 0.58 = 0.0466
The consistency ratio (CR) tells how consistent the decision maker is with her answers. A higher number means less consistency. In general, a number of 0.10 or greater suggests the decision maker should reevaluate her responses during the pairwise comparison. CI
RI (random index)
CR =
This is a table value =
0.58 =
Is Judy consistent in her answers regarding hardware??
To accompany Quantitative Analysis for Management, 9e
\by Render/Stair/Hanna
M1-20

21. Achieving a Final Ranking
We must now perform a second pairwise comparison regarding the relative importance of each of the remaining two factors.
For simplicity, computation of the software and vendor support factor evaluations are left to you.
To accompany Quantitative Analysis for Management, 9e
\by Render/Stair/Hanna
M1-21

22. Achieving a Final Rank (continued)
Factor Evaluation
System 1
System 2
System 3
Hardware
Software
Vendor Support
Using pairwise comparison we can obtain factor weights:
Factor
Factor Weight
Hardware
0.0820
Software
0.6816
Vendor Support
0.2364
To accompany Quantitative Analysis for Management, 9e
\by Render/Stair/Hanna
M1-22

23. Judy Grim’s Final Decision
The factor weights are then multiplied by the factor evaluations to obtain a weighted evaluation.
System or Alternative
Total Weighted Evaluation
System-1
0.2310
System-2
0.2275
System-3
0.5416
Best Decision!!
To accompany Quantitative Analysis for Management, 9e
\by Render/Stair/Hanna
M1-23