Introduction to Value Tree Analysis

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


Contents

About the introduction Basic concepts A job selection problem Problem structuring Preference elicitation Results and sensitivity analysis


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


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


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


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


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


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


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


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


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


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.


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


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


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


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)


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


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)


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


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


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



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.


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)


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


Video Clip: Using direct rating in Web-HIPRE with sound (.avi 1.17 MB)no sound (.avi 217 KB)animation (.gif 142 KB)


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



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)


Video Clip: Using SMART in Web-HIPRE with sound (.avi 1.12 MB)no sound (.avi 209 KB)animation (.gif 133 KB)


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=


Video Clip: Using AHP in Web-HIPRE with sound (.avi 1.97 MB)no sound (.avi 377 KB)animation (.gif 204 KB)


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


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


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.


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.


Video Clip: Viewing the results in Web-HIPRE with sound (.avi 1.58 MB)no sound (.avi 286 KB)animation (.gif 213 KB)


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



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



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.


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


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

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Introduction to Value Tree Analysis

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