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

Systems Analysis Laboratory Helsinki University of Technology eLearning / MCDA

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 Systems Analysis Laboratory Helsinki University of Technology eLearning / MCDA

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.

Systems Analysis Laboratory Helsinki University of Technology eLearning / MCDA

Problem description

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.

Table 1. Properties of the cars .

price persons pieces of luggages top speed (km/hour) gasoline consumption sports car family car cross-country

31000 3 1 240 9

(l/100km) acceleration, 0 to 100km/h (1/s)

7.5

27000 4 2 180 7 10.2

37000 5 4 160 10.4

11.8

Systems Analysis Laboratory Helsinki University of Technology eLearning / MCDA

Group decision making

The family decided to use Web HIPRE’s 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

Systems Analysis Laboratory Helsinki University of Technology

Son

eLearning / MCDA

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.

V

(

a j

) 

i n

  1

w i v i

(

a j

) In the group hierarchy, the overall value of each DM is represented as an objective.

DM1&2: V 1&2 (a 1 ) = w 1 v 1 (a 1 ) + w 2 v 2 (a 1 ) Systems Analysis Laboratory Helsinki University of Technology eLearning / MCDA

Value trees for car selection

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 Systems Analysis Laboratory Helsinki University of Technology eLearning / MCDA

Value trees for car selection

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.

Systems Analysis Laboratory Helsinki University of Technology eLearning / MCDA

The group hierarchy

• Group members’ value trees are set as objectives Group Members Alternatives • Each family member has a weight • In this model equal weights are used

w i

=1/3, for

i

=1,2,3 Systems Analysis Laboratory Helsinki University of Technology eLearning / MCDA

Group preferences

To see how the individual models are integrated in Web-HIPRE see the

   Family car is the most preferred alternative Sports car comes second Cross-country vehicle is the least preferred alternative Systems Analysis Laboratory Helsinki University of Technology eLearning / MCDA • • • Group decision making with Web-HIPRE with sound no sound animation (3.2Mb) (604Kb) (544Kb)

Sensitivity analysis

 What if the family members weights

w

i equal?

are not  How sensitive is the model to changes in individual preference statements?

Systems Analysis Laboratory Helsinki University of Technology eLearning / MCDA

Sensitivity to DM’s weights

 The cross-country vehicle becomes family’s choice if father’s weight increases to 0.76 Systems Analysis Laboratory Helsinki University of Technology eLearning / MCDA If mother’s weight is close to zero the sports car becomes the most preferred alternative

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!

Systems Analysis Laboratory Helsinki University of Technology eLearning / MCDA

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 Systems Analysis Laboratory Helsinki University of Technology eLearning / MCDA

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.

Systems Analysis Laboratory Helsinki University of Technology eLearning / MCDA