Case: Family selecting a car

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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

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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

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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.

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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
  familys 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 familys 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.

Table 1. Properties of the cars.
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Group decision making
The family decided to use Web-HIPREs group
property to support the decision making.
Group members create their own models...
which are combined in the group model
Server
Mother
Internet
Data projector
Father
Son
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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.

In the group hierarchy, the overall value of
each DM is represented as an objective.
DM12 V12 (a1) w1v1(a1) w2v2(a1)
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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

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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.

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The group hierarchy

• Group members value trees are set as objectives

Alternatives
Members
Group

• Each family member has a weight
• In this model equal weights are used
  wi1/3, for i 1,2,3

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Group preferences
To see how the individual models are integrated
in Web-HIPRE see the ltvideo clipgt.

• Family car is the most preferred alternative
• Sports car comes second
• Cross-country vehicle is the least preferred
  alternative

Group decision making with Web-HIPRE

• with sound (3.2Mb)
• no sound (604Kb)
• animation (544Kb)

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Sensitivity analysis

• What if the family members weights wi are not
  equal?
• How sensitive is the model to changes in
  individual preference statements?

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Sensitivity to DMs weights

• The cross-country vehicle becomes familys choice
  if fathers weight increases to 0.76

If mothers weight is close to zero the sports
car becomes the most preferred alternative
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Sensitivity to DMs weights

• If sons 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!
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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

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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.