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.