18. making decisions based on multiple criteria

8/10/2019 18. Making Decisions Based on Multiple Criteria

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Transportation Decision MakingPrinciples of Project Evaluation and Programming

Chapter 18

Evaluation of Transportation Projectsand Programs Using Multiple Criteria

Kumares C. Sinha and Samuel Labi


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Decision criteria can have multiple dimensions

Dollars

Number of crashes

Acres of land, etc.

All criteria are not of equal importance

For a given criterion, different stakeholders may havedifferent weights.


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Typical Steps in Multi-Criteria

Decision Making

1. EstablishTransportation

Alternatives

3. EstablishCriteria Weights

4. Establish Scale to be Used forMeasuring Levels of Each Criterion

5. Using Scale, Quantify Level(Impact) of Each Criterion for Each

Alternative

2. EstablishEvaluation Criteria

6. Determine Combined Impact of allWeighted Criteria for Each Alternative

Weighting

Amalgamation

Scaling

11. Determine the Best Alternative


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Establishing Weights

Weights reflect the relative importance attached bydecision makers to various criteria

In some cases, the decision maker refers to theagency as well as the facility user. In those cases, the

weight used for each criterion is a weighted average ofthe weights from these two parties.


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Weighting Techniques

1. Equal Weights2. Direct Weighting

3. Derived Weights

4. Delphi Technique

5. Gamble Method

6. Pair-wise comparison: AHP

7. Value Swinging


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Equal Weights - Example

Project Cost 33.3%

Travel Time Saving 33.3%

VOC Saving 33.3%


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Direct Weighting

1. Point Allocation A number of points areallocated among the criteria according to theirimportance.

2. Ranking Simple ordering by decreasingimportance.

Point allocation is preferred because unlike ranking, ityields a cardinal rather that an ordinal scale ofimportance.


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Point Allocation (0-100) Ranking

(Cardinal) (Ordinal)

Project Cost 70 1

TT Saving 50 3

VOC Saving 60 2


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Regression-Based Observer-Derived Weighting

1. Survey respondents assign scores of overallbenefit or desirability for a given combinationof criteria levels achieved by each alternative

2. Weights are then the resulting regressioncoefficients


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( )

2

2

i

i j ji i

j

Minimize

TV w V

= +

i = alternative

j = Criterion

TV = score or desirability


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Regression

7 Respondents

21 Data Points

TV = wcost* Cost + wtime * Time

wcost = 0.214

wtime = 0.786

R2 = 0.98


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Delphi Technique

Individual responses aggregated

Effect of assessment of other respondents

Consensus building

Iterative, generally 2 rounds to achieve stablevalues


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Scaling Methods


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GAMBLE METHOD

1. Carry out an initial ranking of all criteria in order of decreasingimportance. set the first criterion at its most desirable level and

all other criteria at their lest desirable levels

2. Compare between the following two outcomes: Sure thing: The outcome is that the criterion in question is at its

most desirable level while all other criteria at their least desirablelevels

Gamble: In this outcome, all criteria attained their most desirablelevels p% of the time, their least desirable levels (1-p)% of the time

3. At a certain level of p the two situations (sure thing and gamble)are equally desirable. At that level, the value of p representsthe weight for the criterion in question


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Example:

Bus Route Assessment

Headway (from 5 to 15 minutes)

Population Served (from 5,000 to 10,000)

Solution:

1. Sure Thing: Bus headway is 5 minutes and population served is 5,000

2. Gamble: Two outcomes:a. A p% chance of an outcome that headway is 5 minutes and

population is 10,000

b. A (1-p)% chance of an outcome that headway is 15 minutesand population is 5,000.

Suppose the respondent were found to be indifferent between sure

thing and gamble at p = 60%, then, the relative weight for busheadway is 0.6.


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Pair Wire Comparison

Analytical Hierarchy Process (AHP)

12 1

12 2

1 2

1 ...................1/ 1 ...................

... .... .... .... .... .... .......1/ 1/ ..... ... .... 1

n

n

n n

a aa a

a a

= relative importance of two criteria I and j on the basisof a scale of 1 to 9

=

ija

/i jw w


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Table 18.1: Ratios for Pair wise

Comparison Matrix


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Value Swinging Method

1. Consider a hypothetical situation where all criteria at

their worst values2. Determine the criterion for which it is most preferred to

swing from its worst value to best value, all other

criteria remaining at their worst values.3. Repeat steps 1 and 2 for all criteria.

4. Assign the most important criterion the highest weight

in a selected weighting range (100 for 1-100 scale) andthen assign weights to the remaining criteria in

proportion to their rank of importance.


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Scaling of Performance Criteria

Certainty - Value Function

Risk - Utility Function

Uncertainty - Scenario Analysis


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Value Function

a. Direct Rating Method direct assignment

of value to various levels of a criterion

b. Mid Value Splitting Technique based onindifference between changes in levels ofcriterion.

c. Regression based on data from directrating


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Discrete Value Function

Discrete Dis-Utility Function for Performance Measure

of Impact on Natural, Socio-Economic, Historical &Cultural Resources

-100

-80

-60

-40

-20

0

No

Impa

ct

Minor

Impa

ct

Mod

erate

Impact

Major

Impa

ct

Hug

e

Impa

ct

Extreme

Imp

act

Utility


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Continuous Value Function

Dis-Utility Function for Single Performance Measure

of Emissions

-100

-80

-60

-40

-20

0

0 20 40 60 80 100 120

Percentage Increase in Emissions

Utility


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Developed Value Functions


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Utility Function

Direct Questioning Using the GambleApproach

Guaranteed prospect of an outcome vs. riskyprospect of a more favorable outcome.


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Example 18.7

Utility Functions for agency cost, ecological damage, and vulnerablepopulation served.

Solution:

For Agency Cost: Ucost ($30 Million) = 0 (Worst)

Ucost

($ 0 Million) = 1 (Best)

Sure Thing: The outcome is that agency cost is guaranteed to be $20 Million

Gamble: There is a 50% chance that cost is 0 and 50% change it is $30 Million

X50 = $20 Million is the Certainty Equivalent because the expected utility is 0.5


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0

20

40

60

80

100

120

0 5 10 15 20 25 30 35 40 45

Criteria Level

Utility

0

20

40

60

80

100

120

0 5 10 15 20 25 30 35 40 45

Criteria Level

Utility

Cost (in $millions)

Wetland lost in acres (in tens)

Population served (in thousands)


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Combination of Performance Criteria

Pareto Optimality

Difference Approach

Net Utility = U(B) U(C)

NPV = PV (B) PV(C)

Ratio Approach Utility Ratio = U(B)/U(C)

BCR = PV(B) / PV(C)


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Cost Effectiveness

Costs and Benefits are not necessarilyexpressed in the same metrics

Indifference Curves

Tradeoffs marginal rates of substitutionbetween criteria

TV = 2*TTR + PCC


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Indifference Curves Using Mathematical Form of


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Indifference Curves Using Mathematical Form of

Utility/Value Function for Combined Performance

Measures


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Ranking and Rating Method

i i j ij

jScore P w O For each i=


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Impact Index Method

1 2

1max( , ,........, )

tan

( 0.5 0.5)

i j j ij j j j ijj

jj

j

j

jj j nj

j

I R S X e R S X

wR relativeweight for criterion j

w

S scaling factor of measurement X of criterion jX X X

e RN drawn fromarec gular distribution

e

= +

= =

= =

=

+


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Table E18.10.1: Performance of Alternatives

Figure E18 10: Plot of Confidence


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Figure E18.10: Plot of Confidence

Intervals

18. making decisions based on multiple criteria

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