ch12 multi criteria decision making

8/4/2019 Ch12 Multi Criteria Decision Making

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Multiple Criteria Decision Making

I. Multifactor decision making II. Multicriteria decision making

Luu Van ThanhSource: Dr. Ho Thanh Phong


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Many decision-making problems involve a number ofcriteria. The criteria, also called attribute or factor , not objectives . always conflict with each others.

Distinguish between multi-objective and multi-criteria:

Quantitative methods1. Introduction

Multi-objective Multi-criteriaSolutions Not available, unlimited Available, limited

MethodsMathematical programming(basically on Linear Programming)

Specialized methods


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Examples:

Buying a new or used car : criteria are price, RAM,software adaptability, . . .

Selecting a job : criteria are salary, location, career

Selecting a person for a special position : criteriaare degree, skills, public relations . . .

Because there are many factors to be considered, a

quantitative approach is often used


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2. Multi-factor decision making

In multi-factor decision making, individualsubjectively and intuitively consider the various

factors in making their selection.

All of the important factors can be given appropriate

weights and each alternatives can be evaluated in

terms of these factors.

This approach is called the Multi-Factor Evaluation

Process (MFEP)


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Example: Steve Markel, an undergraduate business

major, is looking at several job opportunities.According to Steve, three important factors in

selecting a good job are:

Salary Career advancement

Location


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Step 1: Give weight to each factor

Step 2: Choose the most important alternatives ( non- dominated alternatives) e.g. Jobs at AA, BB and CC companies

Step 3: Evaluate the 3 factors on each of these jobs

Table 11.1. Factor weightsFACTOR WEIGHT

Salary 0.3Career advancement 0.6Location 0.1

FACTOR AA BB CCSalary 0.7 0.8 0.9Career advancement 0.9 0.7 0.6Location 0.6 0.8 0.9

Table 11.2. Factor Evaluations


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Step 4: Determine a total weighted evaluation for each of the job

FACTOR WEIGHT FACTOR EVALUATION WEIGHTED EVALUSalary 0.3 x 0.7 = 0.21

Career advancement 0.6 x 0.9 = 0.54Location 0.1 x 0.6 = 0.06Total 1 0.81

Table 11.3. Evaluation of AA Co.

FACTOR WEIGHT FACTOR EVALUATION WEIGHTED EVALUSalary 0.3 x 0.8 = 0.24Career advancement 0.6 x 0.7 = 0.42Location 0.1 x 0.8 = 0.08Total 1 0.74

Table 11.4. Evaluation of BB Co.

FACTOR WEIGHT FACTOR EVALUATION WEIGHTED EVALUSalary 0.3 x 0.9 = 0.27Career advancement 0.6 x 0.6 = 0.36Location 0.1 x 0.9 = 0.09

Total 1 0.72

Table 11.5. Evaluation of CC Co.


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Step 5: Compare the final total weighted and give decisionCompare the total weighted evaluation, AA Co. receives the

highest value


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3. Multicriteria Decision Making In situations when we can not assign evaluations and

weights to the various decision factors, the multifactor

evaluation process should not be used.

In these cases, Multicriteria decision approachs will beused:

Utility Theory - Prof. Ralph Keeney ,Analytic Hierarchy Process (AHP) - Prof. ThomasSaaty (1980).ELECTREE I and II - Prof. Roy (1967),PROMETHEE - Prof. J.P. Brans (1982)


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3.1. The Hierarchy:

This process involves pair wise comparisons. Startedby laying out the overall hierarchy of the decision.

The decision includes the determinations of factors to

be considered, sub-factors , and eventually thealternatives.


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Example: Buying car the best car

There are three criteria:CostQuality

SafetyComfortability

MaintenanceInsurance

Services

Concept of dominanceapplied for screeningalternatives before using

AHP.

And three alternatives:Honda, Mercedes, Hyundai


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Select the"best" car

COST Maintenance Quality

ServiceInsurance

Honda Mercedes Huyndai

Level 0

Level 1

Criteria

Level 2

Sub-criteria

Alternatives

Fig. 11.1 The Hierarchy for problem Buying the best car


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3.2 Computational procedure We will use the above car example to illustrate the procedure. The

Hierarchy diagram is shown in Figure 11.1.

The key to using AHP is pairwise comparison. There are 9 levelsof comparison:1. Equally preferred

2. Equally to moderately preferred3. Moderately preferred4. Moderately to strongly preferred5. Strongly preferred

6. Strongly to very strongly preferred7. Very strongly preferred8. Very to extremely strongly preferred9. Extremely preferred


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The levels of 2, 4, 6, 8 is the intermediate ones. Thecorresponding scores range from 1 to 9.

The comparison process begins from the lowest levelto the highest one. We illustrate here the highest levelcomparison.

Step 1: Criterion comparisonTable 11.6 Criterion comparison

Price Mantenance Quality

Price 1 3 5

Maintenance 1/3 1 2

Quality 1/5 1/2 1


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Normalize values:The number in the matrix are divided by their respective column

totals as follow: ( Table 11.7. Value normalization)

Find the average of the various rows from the matrix asfollows: (Column vector)

The process is repeated for the sub-criteria until theevaluation for all other alternatives. This example will besupported by a software named Expert Choice.

Price Maintenance QualityPrice 0.652 0.667 0.625Maintenance 0.217 0.222 0.25Quality 0.131 0.111 0.125

AveragePrice 0.648Mainternance 0.23

Quality 0.122


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Step 2: Determining the Consistency Ratio - CR

In practical problems, we are not always able to establish the

bridging relation in pairwise comparisons.

For example, alternative A may be better than B, B may be

better than C but this does not always mean that A is better

than C.

This shows the realistic characteristic of practical problems

which is called inconsistency.


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Inconsistency is real but its volume should not be too

big, hence showing that the evaluation is not accurate.

To assess the inconsistency of each level, Consistency

Ratio- CR is used. If CR is equal or lower than 0.1, it

means that the decision makers evaluation is relatively

consistent. In contrary, re-evaluation of relevant level

should be carried out.

Determining CR process follows 3 steps


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1. Determining the Consistency vector We begin by determining the weighted sum vector.This is done by multiplying the column vector times thepairwise comparison matrix.Column vector:

Pairwise comparison matrix:

Price 0.648

Mainternance = 0.230Quality 0.122

1 3 5

1/3 1 21/5 1/2 1


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After multiplying the matrix, we get weighted sum vector:

1.9480.6900.366

Consistency vector = Weighted sum vector/ Column vectorConsistency vector:

1.948 / 0.648 3.006

0.690 / 0.230 = 3.00

0.366 / 0.122 3.00


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2. Determining and the Consistency Index-CI is characteristic value or Eigen value of comparison matrix

(remember that this matrix is squared). The value of is simplythe average value of the consistency vector:

= (3.006+3.0+3.0) / 3 = 3.002The formula for CI is:

CI = (3.002 - 3) / (3 - 1) = 0.001

3. Determining the Consistency Ratio-CR The formula of CR is:

1n

nCI

RI

CI CR


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Where RI (Random Index) is determined from belowtable:

Therefore, with n = 3, we get RI = 0.58

CR = 0.001 / 0.58 = 0.0017Since 0< CR < 0.1 , we accept this result and move to thelower level. The procedure is repeated till the lowest level.

n RI

2 0.003 0.584 0.905 1.126 1.24

7 1.328 1.41


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Continue for other levels:

For subcriteria Insurance Service:

Insurance Service

Insurance 1 3

Service 1/3 1

HONDA 25000

MER. 60000

VOLVO 65000

Honda Mer Volvo

Honda 1 1/3

Mer 3 1 2

Volvo 4 1/2 1

For Cost correspondingwith three alternatives:

For Insurance:

Honda Mer Volvo

Honda 1 3 4

Mer 1/3 1 2

Volvo 1/4 1/2 1

For Service

Honda Mer Volvo

Honda 1 1/4 1/5

Mer 4 1 1/2

Volvo 5 2 1

For Quality

And make your final evaluation (students self develop this evaluation)


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Notes: In general, the evaluation scores are collected frommany experts and the average scores is used in thepairwise comparison matrix.The AHP solving is computer-aided by Expert Choice

(EC) software.- Building structure of problem !!!- Enter judgments (Pairwise Comparisons)- Analysis the weights- Sensitivity Analysis- Advantages and disadvantages- Miscellaneous

ch12 multi criteria decision making

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