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Transportation Decision Making Principles of Project Evaluation and Programming
Chapter 18Evaluation of Transportation Projects and Programs Using Multiple Criteria
Kumares C. Sinha and Samuel Labi
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Decision criteria can have multiple dimensionsDollarsNumber of crashesAcres of land, etc.
All criteria are not of equal importance
For a given criterion, different stakeholders may have different weights.
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Typical Steps in Multi-Criteria Decision Making
1. Establish Transportation Alternatives
3. Establish Criteria Weights
4. Establish Scale to be Used for Measuring Levels of Each Criterion
5. Using Scale, Quantify Level (Impact) of Each Criterion for Each
Alternative
2. Establish Evaluation Criteria
6. Determine Combined Impact of all Weighted Criteria for Each Alternative
Weighting
Amalgamation
Scaling
11. Determine the Best Alternative
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Establishing Weights
Weights reflect the relative importance attached by decision makers to various criteria
In some cases, the decision maker refers to the agency as well as the facility user. In those cases, the weight used for each criterion is a weighted average of the weights from these two parties.
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Weighting Techniques1. Equal Weights2. Direct Weighting3. Derived Weights4. Delphi Technique5. Gamble Method6. Pair-wise comparison: AHP7. 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 are allocated among the criteria according to their importance.
2. Ranking – Simple ordering by decreasing importance.
Point allocation is preferred because unlike ranking, it yields a cardinal rather that an ordinal scale of importance.
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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 overall “benefit” or “desirability” for a given combination of criteria levels achieved by each alternative
2. Weights are then the resulting regression coefficients
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( )2
2
i
i j ji ij
Minimize
TV w V
ε
ε= +
∑∑
i = alternativej = CriterionTV = score or desirability
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Regression
7 Respondents21 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 stable values
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Scaling Methods
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GAMBLE METHOD
1. Carry out an initial ranking of all criteria in order of decreasing importance. 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 desirable levelsGamble: In this outcome, all criteria attained their most desirable levels 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’ represents the weight for the criterion in question
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Example:
Bus Route AssessmentHeadway (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 5,0002. 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 minutes and population is 5,000.
Suppose the respondent were found to be indifferent between surething and gamble at p = 60%, then, the relative weight for bus headway is 0.6.
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Pair Wire ComparisonAnalytical 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 basis of 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 values
2. 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) and then 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 on “indifference” between changes in levels of criterion.
c. Regression – based on data from direct rating
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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
Impact
Minor
Impact
ModerateIm
pact
Major
Impact
Huge
Impact
Extreme
Impact
Utility
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Continuous Value Function
Dis-Utility Function for Single Performance Measure of Emissions
-100
-80
-60
-40
-20
00 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 Gamble Approach
Guaranteed prospect of an outcome vs. risky prospect of a more favorable outcome.
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Example 18.7
Utility Functions for agency cost, ecological damage, and vulnerable population 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
Util
ity
0
20
40
60
80
100
120
0 5 10 15 20 25 30 35 40 45
Criteria Level
Util
ity
Cost (in $millions)
Wetland lost in acres (in tens)
Population served (in thousands)
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Combination of Performance Criteria
Pareto Optimality
Difference ApproachNet Utility = U(B) – U(C)NPV = PV (B) – PV(C)
Ratio ApproachUtility Ratio = U(B)/U(C)BCR = PV(B) / PV(C)
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Cost Effectiveness
Costs and Benefits are not necessarily expressed in the same metrics
Indifference CurvesTradeoffs – marginal rates of substitution between criteria
TV = 2*TTR + PCC
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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 ijj
Score 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
jj
jj j nj
j
I R S X e R S X
wR relativeweight for criterion jw
S scaling factor of measurement X of criterion j X X X
e RN drawn fromarec gular distribution
e
= +
= =
= =
=
− ≤ ≤+
∑
∑
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Table E18.10.1: Performance of Alternatives
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Figure E18.10: Plot of Confidence Intervals