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Multifactor DecisionMaking
Jaco Wijnmaalenjaco@quartzconsult.c
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FIAP 271
Consistency
Final Decision
AHP Explained
Todays Agenda
Engineeringvs
Management
Objectives
Decision Hierarchy
Pair-wise comparisons
Consistency
Workspace
Pair-wise comparison
Decision Making
MFEP Explained
Application
Opening Screen
Selection
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Objectives
Define and describe
2 types
of scoringmodels.
Use
multi
-
factor scoring
methods to make
decision choices.
Describe how
Analytical Hierarchy Process
can be used to make decision choices.
Understand and use
consistency statistics
to support AHP results.
Understand how
spreadsheets
can be used
to model AHP decision problems.
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Management or Engineering?
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Decision Making
Many decisions may involve a number offactors to consider.
E.g. applying for a new job has many thingsto consider.
Salary,Career opportunities,
Location, etc
Or purchasing a new PC has many factors.Processor speed,
Memory,
Backup service, etc
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Multi-Factor Decision Making
Multifactor Evaluation Process (MFEP)
A more quantitative approach.
Important factors are given an appropriate
weight (relative importance).Each alternative is then evaluated against
these factors.
Totals are added up.
The alternative with the highest score wins.
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Example: Job Application
Alternatives to consider:
Alternative Action Co
Engineering Systems Design Ltd
Product Wiring Inc
Important Factors:
Starting salary
Career opportunitiesLocation
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Factor Weights
Factor Importance (Weight)
Salary 0.3Career Advancement 0.6
Location 0.1
Various factors are weighted according toimportance.
Salary: 0.3
Career advancement opportunities: 0.6
Location: 0.1Important: weights must add up to 1
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Factor Evaluations
Factor AA Co EDS Ltd PW Inc
Salary 0.7 0.8 0.9Career Advancement 0.9 0.7 0.6
Location 0.6 0.8 0.9
Each alternative is given a rating for each
factor considered on a scale of 0 to 1.
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Factor and Alternative
Comparison
With this information it is possible to determine
total weighted evaluation for each alternative.
Each company is given a factor evaluation for
each factor.Factor weights are multiplied by factor
evaluations and added up to get a total
weighted evaluation for each company.
The highest score wins.
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Analytical Hierarchy Process
Break down a big problem into smalldigestible bites.
Prioritise alternatives in decision making
Streamline human decision processes
Easy to use
Well accepted in industry by decision makers
Can be used for multiple decision problems
Very controversial
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Analytical Hierarchy Process
Where many factors are to be evaluatedaccurately, a more scientific approach isneeded.
Analytical Hierarchy Process* involves pair-wise comparisons.
Start by laying out the overall hierarchy of thedecision.
Pair-wise comparison reveals factor weightsand factor evaluations.
Ensure that comparisons are consistent.
* Saaty TL, 1980, The Analytic Hierarchy Process.
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Example: To Buy a Computer
Alternatives:
System 1
System 2
System 3Selection Criteria:
Hardware
SoftwareVendor
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2. Pair-wise Comparison
Intensity ofImportance
Definition Explanation
1 Equally preferred Two activities contribute equally to theobjective
3 Moderately Preferred Experience and judgment slightly favourone activity over another
5
Strongly preferred Experience and judgment strongly or
essentially favour one activity over
another
7 Very strongly preferred An activity is strongly favoured and itsdominance demonstrated in practice
9 Extremely preferred The evidence favouring one activity overanother is of the highest possible order
of affirmation
2, 4, 6, 8 Intermediate values between the twoadjacent judgments
When compromise is needed
Reciprocals of
above nonzero
If activity i has one of the above nonzero numbers assigned to it when
compared with activity j, then j has the reciprocal value when compared with i.
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2. Pair-wise Comparison
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2. Pair-wise Comparison
Consider the following criteria:
1) Compare to
Which is more important?
Say Software Slightly
Hardware Software Vendor
Hardware Software
Hardware Software
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3. Ranking Table
Make a matrix from above comparisons.If judgement value on left from 1, enter actual value.
If judgement value on right from 1, enter reciprocal
value.
Hardware Software Vendor
Hardware 1 1/3 5
Software 1 7
Vendor 1
Hardware Software
VendorHardware
Software Vendor
Its matrix
algebra time!
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3. Ranking Table
To fill in the lower triangular matrix, use thereciprocals of the upper diagonal.
aij = 1/aji
Hardware Software Vendor
Hardware 1 1/3 5
Software 3 1 7
Vendor 1/5 1/7 1
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3. Ranking Table
Add columns togetherHardware Software Vendor
Hardware 1 0.3333 5
Software 3 1 7
Vendor 0.20 0.1429 1
TOTAL 4.20 1.4762 13
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5. Consistency
Have we been consistent in our pair-wisecomparisons?
Consistency ratio is calculated from 4 values:
Consistency vector (CV)Lambda ()
Random index (RI) (read from a table)
Consistency index (CI) (n = no. of variables)
Consistency Ratio (CR)
If CR < 0.10 then our comparisons were
consistent
CI = n
n 1
CR = CIRI
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6. System Selection
Now follow the same procedure to measureeach selection criterion to each alternative
system.
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M Ab t AHP
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More About AHP
It allows multi criteria decision making.Becomes difficult to use when number of criteria oralternatives is high, e.g. higher than 7.
Allows for qualitative as well as quantitative
decision evaluation.Applicable for group decision makingenvironments.
Hidden assumptions like consistency.
Can be cumbersome.Adding or removing a criterion calls for new evaluation.
If consistency does not fit, repeat the evaluation.
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And The Final Outcome
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And The Final Outcome
Options are
Ranked
Highest
Consistency Ratio
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References
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References
Saaty, TL: The Analytic Hierarchy Process;1980.
Render, B; Stair RM: Quantitative Analysis forManagement; 9th Ed;Allyn & Baker.
Triantaphyllou, E; Mann, SH: Using theAnalytic Hierarchy Process for DecisionMaking in Engineering Applications: SomeChallenges; International Journal of IndustrialEngineering: Application and Practice; Vol. 2,
No. 1, pp 35-44; 1995