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Transcript of ELearning / MCDA Systems Analysis Laboratory Helsinki University of Technology Case: Family...
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Case: Family selecting a car
eLearning resources / MCDA team
Director prof. Raimo P. Hämäläinen
Helsinki University of Technology
Systems Analysis Laboratory
http://www.eLearning.sal.hut.fi
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Group decision-making with value trees
About the case Problem description Group decision making Weighted arithmetic mean method Value trees for car selection Group hierarchy Group preferences Sensitivity analysis
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
About the case
The purpose is to illustrate group decision-making with value trees. Note, this is only one possible approach to group decision making.
The weighted arithmetic mean method is applied to aggregate individual opinions into a group value tree.
For basics of the value tree analysis, see the Job selection problem and the related theory parts.
Problem description
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Family buying a car
A family is buying a new car and they have to make a choice between three options. The first
option, a sports car, is the absolute favorite of family’s son, who have had the licence just for
a couple of months. However, his father is concerned with the space requirements and prefers
a cross-country vehicle, which would be far more spacious and perfectly suitable for his
fishing trips. The last option, a family car, the favorite of family’s mother, lags behind in
performance fot the sports car and is not as spacious as the cross-country vehicle, but
consumes considerably less, and most importantly, is far more cheaper than the others.
Properties of the cars are presented in Table 1.
sports car family car cross-countryprice 31000 27000 37000
persons 3 4 5pieces of luggages
1 2 4
top speed (km/hour)
240 180 160
gasoline consumption
(l/100km)9 7 10.4
acceleration, 0 to 100km/h (1/s)
7.5 10.2 11.8
Table 1. Properties of the cars.
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Group decision making
Data projector
The family decided to use Web-HIPRE’s group property to support the decision making.
Father
Internet
Mother
Son
Group members create their own models...
…which are combined in the group model
Server
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Weighted arithmetic mean method
1) Preferences of individual DMs are modelled with a value tree.
2) The overall value is calculated as a weighted sum of individual values.
DM1&2: V1&2 (a1) = w1v1(a1) + w2v2(a1)
)()(1
ji
n
iij avwaV
In the group hierarchy, the overall value of each DM is represented as an objective.
Value trees for car selection
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Value trees of the mother and the father
Mother and father decided to use similar value trees
Note:• Individual value trees need not be identical, but• all models have to have same alternatives• The model is available in Web-HIPRE
Value trees for car selection
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Value tree of the son
As the son is not concerned with money he decided to use this value tree
For more about• Problem structuring• Preference elicitation
see Job selection case and corresponding sections in the theory part.
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
The group hierarchy
• Group members’ value trees are set as objectives
• Each family member has a weight
• In this model equal weights are used wi=1/3, for i =1,2,3
AlternativesMembersGroup
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Group preferences
Family car is the most preferred alternative
Sports car comes second Cross-country vehicle is
the least preferred alternative
To see how the individual models are integrated in Web-HIPRE see the <video clip>.
• with sound (3.2Mb) • no sound (604Kb)• animation (544Kb)
Group decision making with Web-HIPRE
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Sensitivity analysis
What if the family members weights wi are not equal?
How sensitive is the model to changes in individual preference statements?
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Sensitivity to DM’s weights
The cross-country vehicle becomes family’s choice if father’s weight increases to 0.76
If mother’s weight is close to zero the sports car becomes the most preferred alternative
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Sensitivity to DM’s weights
If son’s weight is more than 0.66 sports car becomes the most preferred alternative
The results are not sensitive to the changes in group members weights!
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Sensitivity to individual preference statements
For example, assume that the “economy” objective becomes more important due to tightened loan terms
Modify individual preference statements accordingly
Check for changes in the group model Repeat with other objectives
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Conclusion
Family car is the recommended solution, i.e. the most preferred alternative.
The solution is not sensitive to family members’ weights.
However, it may be sensitive to individual preference statements. This issue would still require further analysis.