decision support: multi-attribute methodskt.ijs.si/markobohanec/mspo/en/ds_multiattribute.pdf · 5...

1

Decision Support:

Multi-Attribute Methods

Jožef Stefan International Postgraduate School, Ljubljana

Programme: Information and Communication Technologies [ICT3]

Course Web Page: http://kt.ijs.si/MarkoBohanec/DS/DS.html

Marko Bohanec

Institut Jožef Stefan, Department of Knowledge Technologies, Ljubljana

and

University of Nova Gorica

Decision Analysis

Part 4:

Multi-Attribute Models

Motivation for Multi-Attribute Modeling

So far we have considered single-objective models,

but most of real-life decisions are multiple-objective:

e.g.: price + performance (conflicting)

Influence diagrams facilitate multi-objective modeling to some

degree. However, more is needed in terms of model

development and analysis of decisions. Thus, specialised

models and software.

Multi-attribute modeling is very useful and practical.

ID’s and Multiple ObjectivesVenture

succeeds

or fails

Invest?

Return on

investment

Overall

Satisfaction

Computer

Industry

Growth

Maximize Overall Satisfaction

Return on

InvestmentInvest in

Computer Industry

Questions

1. Have you ever encountered a:– multi-objective decision problem?– multi-attribute model?

When, where, for what kind of problems?

2. Compare multi-attribute models with:– decision trees– influence diagrams

3. Suggest types of decision problems suitable for the application of multi-attribute models

Marko Bohanec

Evaluation Models

EVALUATION

MODEL

options

EVALUATION

ANALYSIS

2

Marko Bohanec


cars

CAR

PRICE

TECH

COMF

lug

pers

doors

safety

maint

buying

problem decomposition

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1

2

3

4

5

digital

photo camera

COMP

functions

multi-attribute model

quality

price

sensor

weight

size

PHOTO

DIM TECH

evaluation

of cameras

body

lens

Marko Bohanec

Multi-Attribute Modelling: Why?• Systematic, structured approach (to difficult real-life problems)• Model development:

– problem decomposition into smaller, less-complex subproblems– requires understanding and careful elaboration of the problem– facilitates and motivates communication and knowledge interchange

• Evaluation:– selection of a single option– option ranking

• Analysis:– “what-if” analysis– sensitivity analysis– explanation:

• how? (evaluation procedure)• why? (selective explanation of advantages/disadvantages)

– option generation

• Contributes to better decisions:– understanding, justification, explanation, documentation

Marko Bohanec

Multi-Attribute Model Structure

a1 a2 a3a1 a2 a3a1 a2 an

X1 X2 Xn

F(X1,X2,…,Xn)

Y

ATTRIBUTES

VALUE

FUNCTION

VALUE

(UTILITY)

OPTIONS

Marko Bohanec

Multi-Attribute Model for Car Selection

a1 a2 a3a1 a2 a3a1 a2 anCARS

PRICE FUEL SAFETY

F(X1,X2,…,Xn)

CAR

ATTRIBUTES

VALUE

FUNCTION

VALUE

Marko Bohanec

Quantitative


VALUE FUNCTION

PRICE FUEL SAFETY

CAR

1

0

50×P1+20×P2 +30×P3

OPTIONS VALUE

1. 22.000 8 6

2. 26.000 6 9

3. 19.000 7 8

63

72

88

3

Marko Bohanec

Qualitative


OPTIONS VALUE

VALUE FUNCTION (DECISION RULES)

PRICE FUEL SAFETY

high high unacc unacc

low low unacc unacc

high low good unacc

med high good unacc

med med acc acc

med med good acc

low low acc acc

low med good good

med low good good

low low good good

CAR

1. med high acc

2. high low good

3. low med acc

unacc

unacc

acc

Marko Bohanec

Hierarchical Multi-Attribute Model

X1 X2 X3 X4 X5

X6

Y

F(X1,X2,X3)

F(X6,X4,X5)

a1 a2 a3 a4 a5

basic attributes

alternatives

aggregate attributes

utility function

utility function

utility value (utility)

value function

aggregate attributes

value function

basic attributes

alternative(option)

Multi-Attribute Modelling: Why?• Systematic, structured approach (to difficult real-life problems)• Model development:

– problem decomposition into smaller, less-complex subproblems– requires understanding and careful elaboration of the problem– facilitates and motivates communication and knowledge interchange

• Evaluation:– selection of a single option– option ranking

• Analysis:– “what-if” analysis– sensitivity analysis– explanation:

• how? (evaluation procedure)• why? (selective explanation of advantages/disadvantages)

– option generation

• Contributes to better decisions:– understanding, justification, explanation, documentation

Multi-Attribute Modelling: How?

0. Problem identification

1. Tree (or hierarchy) of attributes

2. Utility functions

3. Evaluation and analysis of alternatives

4+ Implementation

1. Tree of Attributes

Decomposition of the problem to to sub-problems ("Divide and Conquer!")

MAINTENBUYING COMFORTSAFETY

The most difficult stage!

TECH.CHAR.PRICE

CAR

2. Utility Functions (Aggregation)

Aggregation: bottom-up aggregation of attributes’ values

MAINTENBUYING COMFORTSAFETY

TECH.CHAR.PRICE

CAR

75% 25%

SAFETY COMFORT TECH.CH.

low exc unacc

high low unacc

med accept accept

high good exc

4

3. Evaluation and Analysis

• direction: bottom-up

(terminal ⇒root attributes)

• result: each option evaluated

• inacurate/uncertain data?

EVALUATION

CAR

PRICE

TECH

COMF

lug

pers

doors

safety

maint

buying

CAR

PRICE

TECH

COMF

lug

pers

doors

safety

maint

buying

3. Evaluation and Analysis

• interactive inspection

• “what-if” analysis

• sensitivity analysis

• explanation

ANALYSIS

CAR

PRICE

TECH

COMF

lug

pers

doors

safety

maint

buying

CAR

PRICE

TECH

COMF

lug

pers

doors

safety

maint

buying

MADM Tools

1. “Paper and Pencil” (Abacon)

2. Spreadsheets and mathematical modelling

software(MS Excel)

3. Specialized MADM software

Spreadsheet Modelling

Specialized Software (1/4)

Logical Decisionshttp://www.logicaldecisions.com/

Criterium DecisionPlushttp://www.infoharvest.com/

WinPrehttp://www.hut.fi/Units/SAL/

Downloadables/winpre.html

Specialized Software (2/4)

Expert Choice http://www.expertchoice.com/

HiViewhttp://www.catalyze.co.uk/products/hiview

5

Web-HIPRE http://www.hipre.hut.fi/

Specialized Software (3/4) Specialized Software (4/4)

DEXihttp://kt.ijs.si/MarkoBohanec/dexi.html

Vredana

DEX

Exercise

You would like to buy a new laptop computer for your

own purposes (study, internet, fun, ...).

Suggest a suitable set of attributes and

create a tree of attributes.

Consider the guidelines presented on the next two

slides.

Developing Attribute Structure

Three basic strategies:

• Top-Down: Start with the overall evaluation (target

objective), decompose it to sub-goals.

• Bottom-Up: Start with desirable characteristics, sub-

goals. Group them into connected, meaningful sub-trees.

• Middle-Out: Combining the two above. Iteratively

decompose (refine) and group (generalise) attributes.

Developing Attribute Structure

Desirable features of attributes and their structure:

• Completeness: Do not overlook important attributes• Relevance (non-redundancy): Use only relevant

attributes, omit redundant attributes• Minimality: Use a minimal number of attributes• Orthogonality: Basic attributes should be independent of

each other• Operativity: Basic attributes should be easy to assess or

measure• Comprehensibility: Create meaningful sub-trees of inter-

related attributes

Marko Bohanec

Working Example

One Thursday morning, Charles, instead of attending his

Management Science Techniques for Consultants class, was mulling

over his four job offers. His offers came from: Acme Manufacturing,

Bankers Bank, Creative Consulting, and Dynamic Decision Making.

He knew that factors such as location, salary, amount of

management science (which he loved), and long term prospects were

important to him, but he wanted some way to formalize the relative

importance, and some way to evaluate each job offer.

Adapted from: Michael A. Trick, Analytic Hierarchy Process, http://mat.gsia.cmu.edu/mstc/multiple/node4.html

6

Marko Bohanec

Kepner-Tregoe

Kepner, C. H., Tregoe, B. B. (1981).

The New Rational Manager. Princeton Research Press.

Characteristics:

• list of attributes

• importance of attributes is expressed by weights∈[0,10]

• alternatives are described by vectors of values∈[0,10]

• evaluation (aggregation) principle: weighted sum

• supported analyses: what-if, sensitivity

Marko Bohanec

Kepner-Tregoe Model

Job Offers

Method: Kepner-Tregoe

alternative

attribute weight value w*v value w*v value w*v value w*v

location 2 4 8 6 12 9 18 1 2

salary 10 1 10 9 90 6 60 4 40

management science 5 4 20 1 5 7 35 6 30

long-term prospects 3 10 30 1 3 6 18 4 12

total 68 110 131 84

A B C D

Marko Bohanec

Kepner-Tregoe: What-If Analysis

Job Offers

Method: Kepner-Tregoe

alternative

attribute weight value w*v value w*v value w*v

location 2 9 18 9 18 9 18

salary 10 6 60 4 40 5 50

management science 5 7 35 6 30 8 40

long-term prospects 3 6 18 6 18 7 21

total 131 106 129

C original C salary- C2

Marko Bohanec

Kepner-Tregoe Model: ChartsWeights

0 2 4 6 8 10 12

location

salary

management

science

long-term

prospects

Attributes

Weights

location; 2

salary; 10

management

science; 5

long-term

prospects; 3

Va lues

0

20

40

60

80

100

120

140

A B

Stanovanje

Value

Attribute Va lues

0 20 40 60 80 100

location

salary

management science

long-term prospec ts

Attribute

V alue

A B C D

Marko Bohanec

Kepner-Tregoe: Sensitivity Analysis

Sensitivity analysis

0

20

40

60

80

100

120

140

0 2 4 6 8 10

Weight of sa lary

Value

A

B

C

D

Marko Bohanec

AHP

AHP: Analytic Hierarchy Process (Thomas Saaty, 1980)

Characteristics:

• based on multiple attribute hierarchies

• assessing weights by a pairwise comparison of attributes

• assessing preferences by a pairwise comparison of alternatives

• consistency analysis

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Marko Bohanec

Hierarchy of Attributes

salarylocation

JOB

longMS

Bankers Creative DynamicAcme

VALUE

(BASIC)

ATTRIBUTES

ALTERNATIVES

WEIGHTS

PREFERENCES

Marko Bohanec

Pairwise Comparison Values

1 Items i and j are of equal importance (preference)

3 Item i is weakly more important (better) than j

5 Item i is strongly more important (better) than j

7 Item i is very strongly more important (better) than j

9 Item i is absolutely more important (better) than j

2,4,6,8 are intermediate values

Marko Bohanec

Assessing Weights

1. Normalize the columns so that the sum equals 1

2. Take the average of rows.

Marko Bohanec

Assessing Preferences (Scores)

For each attribute, e.g., Location, compare alternatives:

1. Normalize the columns so that the sum equals 1

2. Take the average of rows.

Marko Bohanec

Assessing Preferences (Scores)

Scores for all the attributes:

Evaluation:

Acme:

Banks:

Creative: .335

Dynamic: .238

Marko Bohanec

AHP SoftwareCriterium DecisionPlushttp://www.infoharvest.com/

WinPrehttp://www.hut.fi/Units/SAL/

Downloadables/winpre.html

Expert Choice http://www.expertchoice.com/

8

Marko Bohanec

Web-HIPRE http://www.hipre.hut.fi/

Web-HIPRE Software

Marko Bohanec

D-SIGHThttp://www.d-sight.com/

Marko Bohanec

Multicriteria Modeling SoftwareProgram Metoda URL

1000Minds PAPRIKA http://www.1000minds.com

Criterium DecisionPlus AHP, SMART http://www.infoharvest.com/

Decision Deck MCDA http://www.decision-deck.org

Decision Lab PROMETHEE & GAIA http://homepages.ulb.ac.be/~bmaresc/decision_lab.htm

DecisionPad MCDA http://decisionpad.com/

D-SIGHT PROMETHEE http://www.d-sight.com/

Expert Choice AHP http://www.expertchoice.com/

GMAA MCDA http://www.dia.fi.upm.es/~ajimenez/GMAA

HIPRE AHP, SMART http://sal.aalto.fi/en/resources/downloadables/hipre3

Hiview MAUT http://www.catalyze.co.uk/index.php/software/hiview3/

Logical Decisions MCDA http://www.logicaldecisions.com/

MakeItRational AHP http://makeitrational.com/analytic-hierarchy-process/ahp-software

M-MACBETH MACBETH http://www.m-macbeth.com

V.I.S.A MCDA http://www.visadecisions.com

Visual PROMETHEE PROMETHEE & GAIA http://www.promethee-gaia.net/software.html

Visual UTA UTA http://idss.cs.put.poznan.pl/site/visualuta.html

Web-HIPRE SMART..AHP http://www.hipre.hut.fi/

Winpre AHP http://sal.aalto.fi/en/resources/downloadables/winpre

Homework

1. Run Web-HIPRE2. Load one of the existing models (e.g., Cellular Phone)3. Look at all Web-HIPRE’s features for

• describing alternatives• assessing alternatives’ preferences and scores• assessing attributes’ weights

4. Do the following:• evaluation of alternatives• sensitivity analysis

5. Try to make some changes to the model:structure, preferences, weights(but no need to save)

Marko Bohanec

DEX:

Expert System Shell for

Multi-Attribute Decision Making

DEXi:

“DEX for Education”

Computer Program for


1987−1995, DOS

1999→Windows

What is DEX?

Originates in 1980’s

DEX

Multi-Criteria Decision Analysis

•modeling using criteria and utility

functions

•problem decomposition and

structuring

•evaluation and analysis of

decision alternatives

Multi-Criteria Decision Analysis

•modeling using criteria and utility

functions

•problem decomposition and

structuring

•evaluation and analysis of

decision alternatives

Artificial Intelligence

Expert Systems

•qualitative (symbolic) variables

•"if-then" rules

•decision model = knowledge base

•handling imprecision and uncertainty

•transparent models, explanation

Machine Learning

Artificial Intelligence

Expert Systems

•qualitative (symbolic) variables

•"if-then" rules

•decision model = knowledge base

•handling imprecision and uncertainty

•transparent models, explanation

Machine Learning

Fuzzy sets

•verbal measures

•fuzzy operators

Fuzzy sets

•verbal measures

•fuzzy operators

9

DEX

Method for qualitative multi-attribute modeling

DEX is similar to other multi-attribute methods:

1. Multiple attributes, hierarchically structured

2. Evaluation of alternatives: bottom-up aggregation

CAR

TECH.CH.PRICE

COMFORTSAFETYMAINTBUYING FUEL

Some CarSome Car

DEX


DEX is different from other multi-attribute methods:

1. Attributes are discrete, symbolic, qualitative

CAR

TECH.CH.PRICE


Numeric (quantitative):

BUYING = 12.233 €

numeric scale, e.g. R+

Symbolic (qualitative):

BUYING = medium

scale: {high, medium, low}

DEX



2. Evaluation of alternatives (aggregation) is defined by decision rules

CAR

TECH.CH.PRICE


PRICE = 75%*BUYING + 25%*MAINTPRICE = 75%*BUYING + 25%*MAINT

75%75% 25%25%

DEX



2. Evaluation of alternatives (aggregation) is defined by decision rules

CAR

TECH.CH.PRICE

COMFORTSAFETY

MAINTBUYING

FUEL

PRICE = 75%*BUYING + 25%*MAINTPRICE = 75%*BUYING + 25%*MAINT

75%75% 25%25%FUEL SAFETY COMFORT TECH.CH.

high good exc unacc

low bad med unacc

... ... ... ...

med good med good

DEX History

1980 20001990 2010

Methodology

•initial development

Software

•DECMAK

•“toolbag”

First applications

•HW and SW selection

•personnel mgmt

•nursery schools

DECMAK

Methodology

•integration

Software

•DEX

•Vredana

National applications

•Housing Fund

•Ministry Sci-Tech

•Talent System

•industry

•medicine

Related

•HINT

Methodology

•further improvement

Software

•DEXi

Education

International applications

•Sol-Eu-Net

•agronomy, GMO

•project evaluation

•finance

Related

•model revision, proDEX

DEX DEXi

Marko Bohanec

DEXi

A simple computer program for MADM that facilitates:

• Creation and editing of– model structure (tree of attributes)

– value scales of attributes

– decision rules (incl. using weights)

– options and their descriptions (data)

• Evaluation of options (can handle missing values)

• Presentation of evaluation results with:– tables

– charts

• Analyses: “what-if”, “±1”, selective explanation, comparison

• Preparing reports and charts

Computer Program for


10

Marko Bohanec

DEXi Model Attribute Scale Job unacc; acc; good; exclocation unacc; acc; goodsalary unacc; acc; goodsatisfaction unacc; acc; goodMS unacc; acc; goodlong unacc; acc; good

Tables location salary satisfaction Job 33% 33% 33% 1 unacc * * unacc2 * unacc * unacc3 * * unacc unacc4 acc acc >=acc acc5 acc >=acc acc acc6 >=acc acc acc acc7 acc good good good8 good acc good good9 good good acc good10 good good good exc MS long satisfaction 50% 50% 1 unacc * unacc2 * unacc unacc3 acc acc acc4 >=acc good good5 good >=acc good

Marko Bohanec

DEXi Evaluation

Evaluation results Attribute A B C D Job unacc unacc acc unacclocation acc acc good unaccsalary unacc good acc acc

satisfaction good unacc acc goodMS acc unacc acc good

long good unacc acc acc

location

satisfactionsalary

location

acc

acc

B

location

satisfactionsalary

location

acc

acc

location

satisfactionsalary

location

acc acc

acc acc

D

location

satisfactionsalary

location

acc

acc

Marko Bohanec

Stages of MADM with DEXi

0. Problem Identificationa. problem formulation

b. formation of a decision-making group

c. selection of decision-support methodology

1. Identification of Attributes

a. unstructured list of attributes

b. hierarchy (tree) of attributes

c. measurement scales

2. Definition of Utility Functions (Decision Rules)

3. Evaluation and Analysis of Options

a. description of options (data acquisition)

b. evaluation of options

c. analysis

4. Implementation

Stages of MADM (with DEXi)

0. Problem Identificationa. problem formulation

b. formation of a decision-making group

c. selection of decision-support methodology

1. Identification of Attributes

a. unstructured list of attributes

b. hierarchy (tree) of attributes

c. measurement scales

2. Definition of Utility Functions (Decision Rules)

3. Evaluation and Analysis of Options

a. description of options (data acquisition)

b. evaluation of options

c. analysis

4. Implementation

knowledge acquisition

DECOMPOSITION

AGGREGATION

EXPLOITATION

1.a: Unstructured List of Attributes

Problem in Personnel Management:

Select of a Candidate for a Job (e.g., a project manager)

• education

• age

• experience

• references

• knowledge

• work approach

• ability to work in a group

• leadership

• organizational abilities

• loyalty

• intelligence

• communicativity

• character

• health

• …

Do not overlook important attributes!

11

1.b: Tree of Attributes

Create meaningful, related groups

Avoid aggregate attributes having more than three descendants

Employ

Educat Years Personal

Formal For.Lang Exper Age Abilit

Comm Leader

Test

1.b: Tree of Attributes

1.c: Scales

Scales are discrete, typically ordered from bad to good

Values should distinguish between importantly different characteristics

Their number should gradually increase from bottom to the root

Employ



Comm Leader

Test

unacc, acc, good, exc

unacc, acc, good unacc, acc, good

unacc, acc, good

prim/sec,

high,

univ,

MSc,

PhD

no, pas, act none,

to1year,

1-5,

6-8,

more

18-20,

21-25,

26-40,

41-55,

more

D, C, B, A

poor, aver,

good, exc

less, approp, more

1.c: Scales

2: Decision rules

Personal

Abilit

Comm Leader

Test

Utility Functions, Bottom-Up Aggregation

Comm Leader Abilit

poor less unacc

poor approp unacc

poor more unacc

aver less unacc

aver approp acc

aver more acc

good less unacc

good approp acc

good more good

exc less unacc

exc approp good

exc more good

2: Decision rules

12

3.a: Description of Options

Employ



Comm Leader

Test

Candidate Formal For.Lang Exper Age Comm Leader Test

A MSc pas to1year 21-25 good more B

B PhD act more 26-40 aver less B

3.a: Description of Options

3.bc: Evaluation and Analysis of Options

1. Evaluation• proceeds from bottom (basic attributes) to the root• result: qualitative evaluation of each option• handles missing (DEXi) or imprecise (DEX) option values

2. Analysis• interactive inspection of results• what-if analysis• analyses:

• compare options• “±1” analysis• selective explanation

• reports• charts

3.b: Evaluation of an Option

Employ



Comm Leader

Test

good

acc goodacc

good

MSc pas to1year 21-25 B

good more

Candidate A

3.b: Evaluation of Options 3.c: What-If Analysis

MScMSc

⇓⇓⇓⇓

PhD

⇐⇐⇐⇐ no effectEmploy



Comm Leader

Test

good

acc goodacc

good

pas to1year 21-25 B

good more

Candidate A

13

3.c: What-If Analysis

good ⇒⇒⇒⇒ exc

acc ⇒⇒⇒⇒ good

pas

⇓⇓⇓⇓

act

MSc

Employ



Comm Leader

Test

good

acc

goodacc

good

pas to1year 21-25 B

good more

Candidate A

3.c: What-If Analysis

3.c: “±1” Analysis 3.c: Compare options

3.c: Selective Explanation

Employ



Comm Leader

Test

unacc

good unaccgood

PhD act more 26-40 B

aver less

unacc

Candidate B

3.c: Selective Explanation

14

Charts and Reports DEX and DEXi: Experience

• Wide applicability to various application areas

• Usually, solutions are specific (non-general)

1. Model development time• heavily problem-dependent: from hours to months

• typical: 2 to 15 days

2. The most difficult stage• designing the tree of attributes

3. Appropriate decision problems• many attributes (> 15)

• many options (> 10)

• prevailing qualitative decision-making, judgment

• inaccurate or missing data

• group decision making (communication and explanation)

• sufficient resources available (expertise, time)

DEX in DEXi: Future

• Combined qualitative and quantitative models

• Extensions:

• Data Mining (e.g. machine learning of models by HINT)

• Data Bases, Data Warehouses, OLAP

• Software:

• “Dex Machine”: Low-level OO library for QQ models

• Various types and levels of GUI

DEX and DEXi: Summary

1. Combination of

multi-attribute decision making and expert systems

2. Characteristics:

• qualitative (symbolic) decision making

• explanation and analysis

• active support in the acquisition of decision rules

3. Applicability:

• for complex real-world problems

• over 50 real-life applications

Exercise

1. Take one of the already defined “empty” models

shown on the next slide

2. Define all utility functions (decision rules) in that model

3. Define and describe a few (about 4) options

4. Evaluate and analyse the options

5. Extend the model:

• add and/or refine a few attributes

(including their scales and rules)

• repeat the steps 2, and 4.

6. Prepare and print out (or save) a report

ModelsProgrammer’s Performance Attribute Description

PROGRAMMER Programmer's PerformanceKNOWLEDGE Knowledge of the Programmer

EXPER Working ExperienceSPECIAL Specialized Knowledge

WORK Quality of Programmer's WorkQUALITY Quality of the ResultsEFFECTIVE Work Effectivenes: Are the results delivered in time?

APPROACH Working Approach

TEAM Attitude to Team WorkPERSONAL Personal Characteristics

INITIATIVE Self InitiativenessCREATIVE Creativity

Attribute Description

PROGRAMMER Programmer's PerformanceKNOWLEDGE Knowledge of the Programmer

EXPER Working ExperienceSPECIAL Specialized Knowledge

WORK Quality of Programmer's WorkQUALITY Quality of the ResultsEFFECTIVE Work Effectivenes: Are the results delivered in time?

APPROACH Working Approach

TEAM Attitude to Team WorkPERSONAL Personal Characteristics

INITIATIVE Self InitiativenessCREATIVE Creativity


PORTABLE Portable computerCOMMERCIAL

PRICE [ in Euro ]IMAGE

TECHNICALINTERNAL

PROCESSORMEMORYDISK

EXTERNAL

MONITORKEYBOARD

AUTONOMY


PORTABLE Portable computerCOMMERCIAL

PRICE [ in Euro ]IMAGE

TECHNICALINTERNAL

PROCESSORMEMORYDISK

EXTERNAL

MONITORKEYBOARD

AUTONOMY

Portable Computer


ENTERP Performance evaluation of enterprisesFINANC

RETURN

PROFITPROF-AB

LIQUIDECONOMIC

PRODUCTCAPACITY


ENTERP Performance evaluation of enterprisesFINANC

RETURN

PROFITPROF-AB

LIQUIDECONOMIC

PRODUCTCAPACITY

Performance Evaluation of Companies Attribute Description

CAR Quality of a car

PRICE Price of a car

BUY.PRICE Buying priceMAINT.PRICE Maintenance price

TECH.CHAR. Technical characteristicsCOMFORT Comfort

#PERS Maximum number of passengers#DOORS Number of doorsLUGGAGE Size of the luggage boot

SAFETY Car's safety


CAR Quality of a car

PRICE Price of a car

BUY.PRICE Buying priceMAINT.PRICE Maintenance price

TECH.CHAR. Technical characteristicsCOMFORT Comfort

#PERS Maximum number of passengers#DOORS Number of doorsLUGGAGE Size of the luggage boot

SAFETY Car's safety

Car Selection

Also available: Employ

decision support: multi-attribute methodskt.ijs.si/markobohanec/mspo/en/ds_multiattribute.pdf · 5...

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