1. MULTI CRITERIA DECISION MAKING - APPLICATIONS IN PROJECT MANAGEMENT
AN INTRODUCTION TO THE ANALYTIC HIERARCHY PROCESS-AHP
Vassilis C. Gerogiannis, PhD
Assistant Professor, Department of Project Management
Technological Education Institute of Larissa

2. DO YOUR DECISION CONFERENCES TURN OUT LIKE THIS ?
TOO BAD!
WE WANT PROJECT B !!
WE WANT PROJECT A !!
COME ON IN
THE WATER IS FINE!
SEA OF INDECISION
OR DOES THIS HAPPEN?

3. DO YOUR RECOMMENDATIONS TURN OUT LIKE THIS?
BUT BOSS...
THAT WAS MY BEST GUESS!
GUESS AGAIN
MAYBE YOU NEED A
NEW APPROACH

4. Decision Making
To make an effective decision making, one has to consider
Details about problem for which the decision is required
The people or stakeholders involved
Their objectives and policies
The influences affecting outcomes
The time horizons, scenarios, and constraints

5. Analytic Hierarchy Process - AHP
Introduced by Thomas Saaty in late 70’s.
AHP, McGraw-Hill, 1980.
A Multi Criteria Decision Making (MCDM) Technique.
It structures any complex, multi-criterion, multi-person problem hierarchically.
Identifies the strength with which one alternative dominates another with respect to a given criteria.

6. Advantages of AHP Multi-criterion, Multi-person.
Can handle qualitative input.
Decision making in presence of environmental, social and other influences.
Can handle subjective judgements of individuals.

7. I THINK I ‘LL TRY THE ANALYTIC HIERARCHY PROCESS (AHP) !!!

8. AHP - Steps Define the problem and specify the objective.
Structure the hierarchy from overall managerial perspective.
Construct a pairwise comparison matrix of the relative contribution on each criteria.
Obtain overall ranking of each decision alternative.
Evaluation of consistency.

9. AHP - Inputs Relative importance of criteria.
Preference on each criterion for each decision alternative.
Construction of pairwise comparison matrix using the above two inputs.

10. AHP Output
Prioritised ranking indicating the overall preference for each decision alternative.

11. AHP - Measurement Methodology
Objective of measurement methodology is to establish priorities among alternatives within each stratum of hierarchy.
This is accomplished through by asking participating stakeholders (e.g., managers) to evaluate each set of elements in a pairwise.
This data constitutes the core element of AHP.

12. Pairwise Comparison Matrix
A pairwise comparison matrix is constructed for each criteria based on the data collected.
Pairwise comparison matrix for a criteria with 4 decision alternatives is given by:

13. 9-Point Scale for Construction of Pairwise Comparison Matrix
Intensity of Importance
Definition 1
Equal importance 3
Weak importance of one over other 5
Strong Importance 7
Demonstrated Importance 9
Absolute Importance
2,4,6,8
Intermediate Values
Reciprocals of the above
If activity i has one of the above numbers assigned to it when compared with activity j, then j has the reciprocal value when compared with i.
1.1 – 1.9
When elements are close and nearly indistinguishable

14. Calculating Priorities
Sum the values in each column of the pairwise comparison matrix.
Divide each element in the pairwise comparison matrix by its column sum; the resulting matrix is called normalized pairwise comparison matrix.
Compute the average of the elements in each row of the normalized matrix. This averages provide relative importance of each alternative.

15. Calculating Priorities
Divide entry by column sum
Column Sum
Relative Priority

16. OKAY, HERE’S AN EXAMPLE OF A DECISION PROBLEM
THIS AHP STUFF SOUNDS INTERESTING. HOW ABOUT AN EXAMPLE OF HOW IT WORKS IN PRACTICE.
OKAY, HERE’S AN EXAMPLE OF A DECISION PROBLEM

17. I SEE A NEW CAR IN YOUR FUTURE

18. Car Selection Problem
XYZ corporation is planning to buy a new car for its transport section. The following four criteria has been identified for the selection of the car:
Price
Mileage per litre (MPL)
Comfort
Style
Use AHP to select the best of three cars named A, B and C from the market.

19. The Problem “Hierarchy”

20. Pairwise Comparison Matrix for Comfort

21. Priorities of cars with respect to Comfort
Pairwise Comparison Matrix
Normalized Matrix
Relative Priority

22. Pairwise Comparison for Other Criteria

23. Priority Vectors for Price, MPG and Style

24. Pairwise Comparison Matrix for the Criteria

25. Priorities for Four Criteria
Price  
MPG
Comfort
Style

26. Using AHP to Develop an Overall Priority Ranking
The procedure used to compute the overall priorities for each decision alternative by using the priority for each criterion as a weight that reflects its importance.
The overall priority for each decision alternative is obtained by summing the products of the criterion priority times the priority of its decision alternative.
For example overall car A priority = .398 (.123) (.087) (.593) (.265)

27. Overall Priority Matrix for Car
Alternative Priority
Car A
Car B
Car C

28. Estimating the Consistency
Step – 1. Multiply each value in the first column of the pairwise comparison matrix by corresponding relative priority matrix.
Step – 2. Repeat Step – 1 for remaining columns.
Step – 3. Add the vectors resulted from step-1 and 2.
Step – 4. Divide each elements of the vector of weighed sums obtained in step 1-3 by the corresponding priority value.
Step – 5. Compute the average of the values found in step –4. Let  be the average.
Step – 6. Compute the consistency index (CI), which is defined as ( - n) / (n-1).

29. Estimating Consistency
Compute the random index, RI, using ratio:
RI = 1.98 (n-2)/n
Accept the matrix if consistency ratio, CR, is less than 0.10, where CR is
CR = CI / RI

30. Consistency of Comfort Matrix

31. Applications of AHP Marketing Make Versus Buy Decision
Resource Allocation
New Product Development
Consumer Behaviour
Project Management (Project Selection, Contractor Prequalification)

32. APPICATIONS OF AHP IN PROJECT MANAGEMENT

33. Project Selection Problem
Screening models help managers pick winners from a pool of projects. Screening models are numeric or nonnumeric and should have:
Realism
Capability
Flexibility
Ease of use
Cost effectiveness
Comparability

34. Screening & Selection Issues
Risk – unpredictability to the firm
Commercial – market potential
Internal operating – changes in firm operations
Additional – image, patent, fit, etc.
All models only partially reflect reality and have both objective and subjective factors imbedded

35. Approaches to Project Screening
Checklist model
Simplified scoring models
Analytic hierarchy process
Profile models
Financial models

36. Checklist Model
A checklist is a list of criteria applied to possible projects.
Requires agreement on criteria
Assumes all criteria are equally important
Checklists are valuable for recording opinions and encouraging discussion

37. Simplified Scoring Models
Each project receives a score that is the weighted sum of its grade on a list of criteria. Scoring models require:
agreement on criteria
agreement on weights for criteria
a score assigned for each criteria
Relative scores can be misleading!

38. Analytic Hierarchy Process
A four step process:
Construct a hierarchy of criteria and subcriteria
Allocate weights to criteria
Assign numerical values to evaluation dimensions
Scores determined by summing the products of numeric evaluations and weights
Unlike the simple scoring model, these scores can be compared!

39. Step 1& 2

40. Step 3 & 4

41. Contractor (Pre-)Qualification in a Project Bid Process Example taken from the article: “Application of the AHP in project management “ by Kamal M. Al-Subhi Al-Harbi, International Journal of Project Management Volume 19, Issue 1, January 2001, Pages 19-27

43. The Problem Hierarchy

44. 15 QUESTIONS - PAIRWISE COMPARISONS

45. 15 QUESTIONS - PAIRWISE COMPARISONS
EXAMPLE ANSWERS

46. FINANCIAL STABILITY (FS) 0,293 QUALITY PERFORMANCE (QP) 0,156
EXPERIENCE (EXP)
FINANCIAL STABILITY (FS)
QUALITY PERFORMANCE (QP)
MANPOWER RESOURCES (MPR)
EQUIPMENT RESOURCES (ER)
CURRENT WORKLOAD (CWL)
1,00
2,00
3,00
6,00
5,00
0,50
0,33
4,00
0,17
0,25
0,20
Priority Vector
EXPERIENCE (EXP)
0,372
FINANCIAL STABILITY (FS)
0,293
QUALITY PERFORMANCE (QP)
0,156
MANPOWER RESOURCES (MPR)
0,053
EQUIPMENT RESOURCES (ER)
0,039
CURRENT WORKLOAD (CWL)
0,087

47. 10 QUESTIONS - PAIRWISE COMPARISONS PER EACH CRITERION

48. 10 QUESTIONS - PAIRWISE COMPARISONS PER EACH CRITERION
EXAMPLE ANSWERS

49. Pairwise Comparisons for ExperienceB C D E
1,00
0,33
0,50
0,17
2,00
3,00
4,00
6,00
7,00
0,25
0,14

50. 15 + 10x6 = 75 pair wise comparisons
In total:
x6 = 75 pair wise comparisons
are required

51. Contractors are ranked according to their priorities as follows:
Finally:
EXPERIENCE (EXP)
FINANCIAL STABILITY (FS)
QUALITY PERFORMANCE (QP)
MANPOWER RESOURCES (MPR)
EQUIPMENT RESOURCES (ER)
CURRENT WORKLOAD (CWL) A
0,086
0,425
0,269
0,151
0,084
0,144 B
0,249
0,089
0,074
0,273
0,264
0,537 C
0,152
0,178
0,462
0,449
0,556
0,173 D
0,457
0,268
0,164
0,081
0,057 E
0,055
0,040
0,032
0,045
0,038
0,062 x
Priority Vector
EXPERIENCE (EXP)
0,372
FINANCIAL STABILITY (FS)
0,293
QUALITY PERFORMANCE (QP)
0,156
MANPOWER RESOURCES (MPR)
0,053
EQUIPMENT RESOURCES (ER)
0,039
CURRENT WORKLOAD (CWL)
0,087 =
Contractors are ranked according to their priorities as follows:
D, C, A, B and E
Overall Priority Vector A 0, B 0, C 0, D 0, E 0,

52. IF YOU’RE HOOKED HERE’S SOME BOOKS FOR FURTHER READING I LIKE AHP
Y Wind and T L Saaty, ‘Marketing Applications of Analytic Hierarchy Process,’ Management Science, Vol. 26, No. 7, July 1980.
T L. Saaty, ‘How to make Decision: The Analytic Hierarchy Process, Interfaces, Vol. 24, No. 6, pp , 1994.
Some recent personal research:
V. C. Gerogiannis, P. Fitsilis, D. Voulgaridou, K.A. Kirytopoulos & E. Sachini, “A Case Study for Project and Portfolio Management Information System Selection: a Group AHP-Scoring Model Approach”, International Journal of Project Organisation and Management, to be published in 2010.
P. Fitsilis, V. C. Gerogiannis & M. Tsinidou, “Evaluation of the Factors that Determine Quality in Higher Education. An Empirical Study”, Quality Assurance in Education, Emerald Group Publishing Limited, Vol. 18, Issue 3, pp , 2010.
I LIKE AHP
AND WITH ALL THIS KNOWLEDGE
YOU WILL BE ABLE TO...