introduction to value tree analysis
DESCRIPTION
Introduction to Value Tree Analysis. Evatech seminar. eLearning resources / MCDA team Director prof. Raimo P. Hämäläinen Helsinki University of Technology Systems Analysis Laboratory http://www.eLearning.sal.hut.fi. Contents. About the introduction Basic concepts - PowerPoint PPT PresentationTRANSCRIPT
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Introduction to Value Tree Analysis
eLearning resources / MCDA team
Director prof. Raimo P. Hämäläinen
Helsinki University of Technology
Systems Analysis Laboratory
http://www.eLearning.sal.hut.fi
Evatech seminar
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Contents
About the introduction Basic concepts A job selection problem Problem structuring Preference elicitation Results and sensitivity analysis
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
About the introduction
This is a brief introduction to multiple criteria decision analysis and specifically to value tree analysis
After reading the material you should know basic concepts of value tree analysis how to construct a value tree how to use the Web-HIPRE software in simple
decision making problems to support your decision
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Basic concepts
Objective is a statement of something that one desires to achieve for example; “more wealth”
Attribute indicates the level to which an objective is achieved in a
given decision alternative for example by selecting a certain job offer you may get
3000 €/month
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Value function
Value function v(x) assigns a number i.e. value to each attribute level x.
Value describes subjective desirability of the corresponding attribute level.
For example:
value
Size of the ice cream cone
1
value
1
Working hours / day
Basic concepts
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Value tree
In a value tree objectives are organised hierarchically
Ideal car
overall objective
Driving
Economy
sub-objectives attributes alternatives
Top speed
Acceleration
Price
Expenses
• Each objective is defined by sub-objectives or attributes
• There can be several layers of objectives
• Attributes are added under the lowest level of objectives
• Decision alternatives are connected to the attributes
Citroen
VW Passat
Audi A4
Basic concepts
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Phases of value tree analysis
Note: Only the highlighted parts are covered in this mini intro
The aim of the Problem structuring is to createa better understanding of the problem
Decision context is a setting in which the decision occurs
In Preference elicitation DM’s preferencesover a set of objectives is estimated and measured
The aim of the Sensitivity analysis is to explorehow changes in the model influence the recommended decision
Basic concepts
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Decision context is the setting in which the decision occurs
Use the figure to define the decision context for the Job selection problem.
· Start with the easiest.
· Proceed to more complicated areas.
· At the end, select and highlight the most important ones.
How does the nature of possible job opportunities affect the decision context?
See the “Problem structuring / Defining the decision context” section in the theory part.
Problem structuring
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Identifying decision alternatives
Identify possible decision alternatives To stimulate the process
a) use fundamental objectives If there were only one objective, two objectives...
b) use means objectives
c) remove constraints If time were no concern...
c) use different perspectives How would you see the situation after ten years?
See the “Problem structuring / Generating and identifying decision alternatives” section in the theory part.
Problem structuring
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A job selection problem
Assume that you have four job offers to choose between;
1) a place as a researcher in a governmental research institute
2) a place as a consultant in a multinational consulting firm
3) a place as a decision analyst in a large domestic firm
4) a place in a small IT firm
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Generating objectives
List all the objectives that you find relevant Specify their meaning carefully
object direction
You may use Wish list Alternatives:
What makes the difference between the alternatives? Consequences Different perspectives
See the “Problem structuring / Identifying and generating objectives” section in the theory part.
Problem structuring
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Possible objectiveswith their descriptions
What other objectives might there be?
objective description
networkingMaximise new contacts with persons and bodies who can potentially influence your personal career opportunitites.
continuing education Maximise possibilities for continuing education.
fit with interests Maximise the match between tasks and personal interests.
tasks diversity Maximise possibilities for carrying out different tasks.
challengeMaximise the correspondence between task requirements and professional skills and opportunities for further professional growth.
working environment Maximise the positive effect of working environment.atmosphere Maximise the positive effect of corporate culture and atmosphere.
facilitiesMaximise the positive effect of facilities and physical working environment.
starting salary Maximise the starting salary.expected salary in 3
yearsMaximise the expected salary in three years.
fringe benefits Maximise fringe benefits.
effects on leisure time Mimimise the extent to which the work constrains the leisure time.
working hours Minimise working hours.
daily commuting Minimise daily commuting.
business travel Minimise the amount of extended trips.
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Hierarchical organisation of objectives
1) Identify the overall objective.
2) Clarify its meaning with more specific sub-objectives. Add the sub-
objectives to the next level of the hierarchy.
3) Continue recursively until an attribute can be associated with each
lowest level objective.
4) Add the decision alternatives to the hierarchy and link them to the
attributes.
5) Iterate the steps 1- 4, until you are satisfied with the structure.
Problem structuring
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
A preliminary objectives hierarchy with alternatives illustrated with Web-HIPRE
Note: • Alternatives are shown in yellow in Web-HIPRE.
• Only the fundamental objectives are included.
• All objectives are assumed to be preferentially independent.
Is there anything you would like to change?
Does the value tree satisfy the conditions listed in the “Checking the structure” section?
Problem structuring - Hierarchical organisation of objectives
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Checking the structure
The hierarchy requires further modification; Networking may be difficult to measure and there is
no real information available on it either. According to the DM
Task diversity is not relevant; tasks are likely to change over time, and all job offers have some variability.
Facilities have only a minor importance. Daily commuting may be neglected because it is almost
the same for all jobs.
Problem structuring - Hierarchical organisation of objectives
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
The objectives hierarchy for the job selection problem
Decision alternatives
Attributes
Overall objective
Sub-objectives
Problem structuring
Video Clip: Structuring a value tree in Web-HIPREwith sound (.avi 3.3MB) no sound (.avi 970KB )animation (.gif 475KB)
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Specifying attributes
Attributes measure the degree to which objectives are achieved.
Attributes should be comprehensive and understandable
Attribute levels define unambiguously the extent to which an objective is achieved.
measurable It is possible to measure DM’s preferences for different attribute levels.
1) Specify attributes for each lowest level objective.
2) Assess the alternatives’ consequences with respect to those attributes.
For more see the “Specification of attributes” section in the theory part.
Problem structuring
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Consequences
Attribute Research Institute Consulting Firm Large Corporation Small IT Firmcontinuing education 3 3 1 2
starting salary/€ 1900 2700 2200 2300expected salary
in 3 years/€ 2500 3500 2800 3000
hours / week 37.5 55 40 42.5atmosphere 3.2 2.5 3.7 4.5
travelling days / year 20 160 100 30
Problem structuring
Video Clip: Entering the consequences of the alternatives in Web-HIPRE with sound (.avi 1.33 MB)no sound (.avi 230 KB)animation (.gif 165 KB)
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Preference elicitation: an overview
The aim is to measure DM’s preferences on each objective.
First, single attribute value functionsvi are determined for all attributes Xi.
Value
Attribute level
Second, the relative weights of the attributes wi are determined.
1/4 1/8 3/8 1/4
n
iiiin xvwxxxV
121 )(),...,,(
Finally, the total value of an alternative a with consequences Xi(a)=xi (i=1..n)
is calculated as
Value elicitation
Weight elicitation
vi(x) [0,1]1
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Single attribute value function elicitation in brief
1) Set attribute ranges All alternatives should be within
the range. Large range makes it difficult to
discriminate between alternatives. New alternatives may lay
outside the range if it is too small.
2) Estimate value functions for attributes Assessing the form of value function Direct rating Bisection Difference standard sequence Category estimation Ratio estimation AHP
Possible ranges for the “working hours/d“ attribute
Note:Methods used in this case are shown in bold
Preference elicitation
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Setting attributes’ ranges
No new job offers expected Analysis is used to compare only the existing
alternatives
small ranges are most appropriateAttribute Research Institute Consulting Firm Large Corporation Small IT Firm Rangecontinuing education 3 3 1 2 1 - 3
starting salary/€ 1900 2700 2200 2300 1900 - 2300
expected salary in 3
years/€2500 3500 2800 3000 2500 - 3500
hours / week 37.5 55 40 42.5 37.5 - 55atmosphere 3.2 2.5 3.7 4.5 2.5 - 4.5
travelling days / year 20 160 100 30 20 - 160
Preference elicitation
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Assessing the form of value function
Is the value function• increasing or decreasing?• linear?
Is an increase at the end of the attribute scale more important than a same sized increase at the beginning of the scale?
You can use Bisection method to ease the assessment.More about the Bisection method (optional)
Value scale
Attribute level scale
In the following video clip the Bisection method is used to estimate a point from the value curve.Web-HIPRE uses exponential approximation to estimate the rest of the value function.
Preference elicitation
Video Clip: Assessing the form of the value function with bisection method in Web-HIPRE with sound (.avi 1.69 MB)no sound (.avi 303 KB)animation (.gif 180 KB)
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Direct rating
1) Rank the alternatives
2) Give 100 points to the best alternative
3) Give 0 points to the worst alternative
4) Rate the remaining alternatives between 0 and 100
Note that direct rating:
• is most appropriate when the performance levels of an attribute can be judged only with subjective measures
• can be used also for weight elicitation
Preference elicitation
Video Clip: Using direct rating in Web-HIPRE with sound (.avi 1.17 MB)no sound (.avi 217 KB)animation (.gif 142 KB)
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
About weight elicitation
In the Job selection case hierarchical weighting is used.
1) Weights are defined for each hierarchical level...
2) ...and multiplied down to get the final lower level weights.
0.6 0.4
0.7 0.3 0.2 0.6 0.2
0.6 0.4
0.7 0.3 0.2 0.6 0.2
Multiply
0.42 0.18 0.08 0.24 0.08
In the following the use of different weight elicitation methods is presented...
To improve the quality of weight estimates• use several weight elicitation methods• iterate until satisfactory weights are reached
Preference elicitation
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
SMART
1) Assign 10 points to the least important attribute (objective)
wleast = 10
2) Compare other attributes with xleast and weigh them
accordinglywi > 10, i least
3) Normalise the weights
w’k = wk/(iwi ), i =1...n, n=number of attributes (sub-objectives)
Preference elicitation
Video Clip: Using SMART in Web-HIPRE with sound (.avi 1.12 MB)no sound (.avi 209 KB)animation (.gif 133 KB)
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
AHP1) Compare each pair of
sub-objectives or attributes under an objective
2) Store preference ratios in a comparison matrix
for every i and j, give rij, the ratio of importance between
the ith and jth objective (or attribute, or alternative)
Assign A(i,j) = rij
3) Check the consistency measure (CM)
If CM > 0.20 identify and eliminate inconsistencies
in preference statements
nnn
n
rr
rr
...
.........
...
1
111
A=
Preference elicitation
Video Clip: Using AHP in Web-HIPRE with sound (.avi 1.97 MB)no sound (.avi 377 KB)animation (.gif 204 KB)
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Web-HIPRE example
The weights for the attributes under the “Compensation” objective in the job selection problem are determined with the SMART method.
Weight Elicitation Methods: SMART
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Weighting attributes under the “Compensation” objective
• ”Fringe benefits” is the least important attribute 10 points
• ”Starting salary” is the second most important with 40 points
• ”Expexted salary in 3 years” is the most important attribute with 65 points.
points
normalised weights
Weight Elicitation Methods: SMART
• with sound (1.2Mb) • no sound (200Kb)• animation (130Kb)
SMART
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Used preference elicitation methods
The job selection value tree with used preference elicitation methods shown in Web-HIPRE:
SMART
Assessing the form of the value function (Bisection method)
AHP
Direct rating
Results & sensitivity analysis
Note: Only the highlighted methods are covered in this introduction.
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Recommended decision
Small IT firm is the recommended alternative with the highest total value (0.442)
Large corporation and consulting firm options are almost equally preferred (total values 0.407 and 0.405 respectively)
Research Institute is clearly the least preferred alternative (total value of 0.290)
Solution of the job selection problem in Web-HIPRE. Only first-level objectives are shown.
Results & sensitivity analysis
Video Clip: Viewing the results in Web-HIPRE with sound (.avi 1.58 MB)no sound (.avi 286 KB)animation (.gif 213 KB)
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
One-way sensitivity analysis
What happens to the solution of the job selection problem if one of the parameters affecting the solution changes? What if, for example the working hours in the IT firm alternative increase to 50 h/week or the salary in the Research Institute rises to 2900 euros/month?
In other words, how sensitive our solution is to changes in the objective weights, single attribute value functions or attribute ratings
In one-way sensitivity analysis one parameter is varied at time Total values of decision alternatives are drawn as a function of the
variable under consideration Next, we apply one-way sensitivity analysis to the job selection case
Results & sensitivity analysis
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Changes in “working hours” attribute
If working hours in the IT firm rise to 53 h/week or over and nothing else in the model changes, Large Corporation becomes the most preferred alternative
If working hours in the Consulting firm were 47 h/week or less instead of the current 55 h/week, it would be considered the best alternative
Results & sensitivity analysis
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Changes in “working hours” attribute
Changes in the weekly working hours in Large corporation‘s job offer would not affect the recommended solution even if they decreased to zero. The ranking order of the other alternatives would change though.
Changes in the weekly working hours in the Research Institute‘s job offer don‘t have any effect on the solution or on the preference order of rest of the alternatives.
Results & sensitivity analysis
Video Clip: Sensitivity analysis in Web-HIPRE with sound (.avi 1.60 MB)no sound (.avi 326 KB)animation (.gif 239 KB)
21.04.23
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Conclusion
Small IT Firm is the recommended solution, i.e. the most preferred alternative
The solution is not sensitive to changes in the weights of the first level objectives or weekly working hours of any single alternative
Sensitivity to other aspects of the model requires further studying, however
Results & Sensitivity Analysis