SlideShare a Scribd company logo
Analytical Hierarchy Process
Decision making for
infrastructure alternatives
Authors
Sameer Deo
Duanne Gilmore
32
Contacts
Sameer Deo
Senior Engineer
sameer.deo@arup.com
Duanne Gilmore
Associate
duanne.gilmore@arup.com
arup.com
Summary...........................................................................5
Introduction.......................................................................7
Analytical Hierarchy Process............................................9
	Background....................................................................9
	 Structuring Complexity.................................................9
	Measurement.................................................................9
	Example.........................................................................11
	Synthesis........................................................................11
	 Risks and Variables.......................................................14
	 Inconsistency Ratio.......................................................14
	 Sensitivity Analysis........................................................15
	 Rank Reversal................................................................15
	 Biases.............................................................................16
Case Study 1
California High-Speed Train Project/
Van Nuys Boulevard Grade-Separation Study.................21
	Background....................................................................21
	Methodology..................................................................22
	 Step 1–Structuring Complexity....................................22
	 Step 2–Measurement.....................................................22
	 Step 3– Synthesis............................................................24
	 Advanced Applications..................................................25
	 Grouptime......................................................................25
	 Case Study Conclusions................................................26
	Findings.........................................................................27
Sources...............................................................................29
Contents
©Arup
54
Engineers often make recommendations for project alternatives that
affect multiple stakeholders. Collaborative decision-making for project
alternatives can become challenging for engineers because of the many
opinions — the client, owner, public, architects, and other agencies
and stakeholders, all with different and often conflicting priorities.
The analytical hierarchy process (AHP), a multiple-criteria decision
analysis (MCDA) technique, offers a structured approach to decision
analysis in a multiple-criteria, multiple-stakeholder environment.
AHP begins with setting a goal, developing alternatives that may
be able to meet that goal, and then evaluating each alternative based
upon its ability to meet the stakeholders’ criteria. AHP is utilized in
many different fields, including economics, politics, finance, resource
allocation, conflict resolution, design, architecture, and transportation.
A case study on the California High-Speed Train project using AHP is
applied in this paper to determine the best possible project alternative.
Summary
A30 ©Anthony J. Branco
76
Not everything that counts can be counted
and not everything that can be counted, counts.
Albert Einstein
Infrastructure projects are large, complex, and expensive, and involve
collaborative decision-making among various entities, often with
incompatible ideas that lead to project delays and cost overruns. A
crucial problem engineers face when evaluating project options is
how to scientifically structure the decision-making process, quantify
qualitative human judgment, and then build consensus on a singular
engineering solution that would satisfy multiple stakeholders with
conflicting priorities. During our work on the California High-
Speed Train Project, Arup explored the use of an MCDA technique
as a possible solution for evaluating options for grade separations
(construction cost in excess of US$65b) along the high-speed rail line
in the Los Angeles metropolitan area. Through a case-study approach,
this paper is focused on the application of AHP in evaluating a single
grade separation with multiple design options against a set of criteria
and with multiple stakeholders’ input.
Introduction
98
Analytical Hierarchy Process
has three primary functions: structure,
measurement, and synthesis.
Structuring Complexity
As illustrated in Figure 1, every element
of the hierarchy must ultimately be
related to an alternative. The relationship
must be direct or follow a path, but no
element should be isolated from the
alternatives. Careful consideration
must be given to develop performance
measures and priorities. Determining
which factors to include in the
hierarchical structure as “criteria” is the
most creative part of the AHP process
for the decision-maker.
Measurement
After structuring the problem, AHP
develops a set of priorities for the criteria
used to judge the alternatives using
the Fundamental Scale of Absolute
Numbers (see Table 1). The process of
prioritization resolves the problem of
dealing with different types of scales,
Figure 1: Typical AHP Structure
Goal
Criteria
Alternative #1 Alternative #2 Alternative #3
Criteria Criteria
Background
While teaching at the Wharton School,
Thomas Saaty was troubled by the
communication difficulties between
scientists and lawyers, noting their lack
of a practical and systematic approach
for priority-setting and decision-making.
He set out to find a way for ordinary
people to make complex decisions
(Gass). In his research, Saaty found that
humans often deal with complexity in a
hierarchical way and develop structures
through homogeneous clusters of
factors, with lower levels in the structure
corresponding to increased detail in
criteria.
In 1994, Saaty introduced AHP
as a pair-wise comparison tool for
multi-criteria decision-making. AHP
uses decision analysis mathematics
to determine priorities of various
alternatives using pairwise comparison
of different decision elements with
reference to a common criterion. AHP
1110
since measurements on different
scales cannot be directly evaluated
or combined. AHP uses pairwise
comparisons — directly comparing one
criterion to another, deciding between
the two which is more preferred. AHP
uses pairwise comparisons to determine
which criterion is more important by
comparing each criterion to every
other criterion, one at a time; the extent
preferred is given numerical values
1 through 9 (1 = same importance, 9
= one is extremely more important
than the other). Through these
pairwise comparisons, AHP turns a
multidimensional scaling problem into a
one-dimensional scaling solution.
Example
Suppose a woman is in the market for a
new car and has narrowed her options
to either a fuel-efficient sedan or a
sports car. The decision will be based on
the following metrics: (a) cost, (b) gas
mileage, and (c) style. To the decision-
maker, cost is a little more important
Fundamental Scale
Intensity of
Importance
Definition Explanation
1 equal importance
Two elements contribute equally to
the objective.
3 moderate importance
Experience and judgment
moderately favor one element over
another.
5 strong importance
Experience and judgment strongly
favor one element over another.
7 very strong importance
One element is favored very strongly
over another, its dominance is
demonstrated in practice.
9 extreme importance
The evidence favoring one element
over another is of the highest
possible order of affirmation.
2,4,6,8* values used as a compromise
1.1 - 1.9
when activities are very close a
decimal is added to 1 to show
their difference as appropriate
The option to use decimals can
indicate the relative importance of
similar criteria.
Reciprocals
of above
If Activity A has one of the above non-zero numbers assigned to it
when compared with Activity B, then B has the reciprocal value when
compared with A.
Cost
Gas
Mileage
Style
Cost 1 3 1/7
Gas
Mileage
1/3 1 3
Style 7 1/3 1
Table 2: Pairwise Comparisons
Table 1: Fundamental Scale of Absolute Numbers
*A value range of 1 through 9 makes it simple for the decision-maker to differentiate among
levels of importance. In this model, there are five levels of clear importance, so odd numbers are
normally used. However, even numbers can be used to provide more nuance — if a criterion is
more than “moderately” more important but not “strongly” more important, a value of 4 would
be used.
than gas mileage, so cost compared
to gas mileage receives a value of 3.
Reciprocating the opposite, gas mileage
compared to cost receives a value of 1/3.
Using the Fundamental Scale of Absolute
Numbers, the paired comparisons of the
criteria to the goal are summarized in
Table 2. As shown, style is much more
important than cost while gas mileage
is a little more important than style. The
“1” values diagonally across the table
merely imply that any criterion has equal
importance to itself. Once the criteria
have been prioritized, the alternatives
are then ranked according to how they
perform on each criterion.
It is possible for comparisons to be
inconsistent with each other — in the
example above, cost was assessed as
more important than gas mileage while
gas mileage is more important than style,
and yet style is more important than
cost. This inconsistency will not inhibit
any calculations in the AHP method, but
the inconsistency may indicate that the
scores are not the decision-maker’s true
preferences.
Synthesis
Once comparisons are made, the results
need to be synthesized. Each criterion
is given a numerical weight, determined
through the steps shown in Table 3.
Then each weight is multiplied by a
reciprocal root of the number of criteria
in the decision — for this example, to the
power of 1/3 because there are 3 criteria.
The weight is then determined by each
criterion’s power to the 1/n divided by
the total in that column.
1312
Now that the weights have been
established for each criterion, the
alternatives must compared.
Tables 4–6 show the calculations that
determine each car’s performance in
relation to the weighted criteria. Using
the same calculation as the criteria
weighting process above, these matrices
A B C D E F G
Cost
Gas
Mileage
Style
Product
B x C x D
Power
1/n E^(1/3)
Weight
F/Ftotal
Cost 1 3 1/7 0.429 0.754 0.245
Gas
Mileage
1/3 1 3 1.000 1.000 0.325
Style 7 1/3 1 2.333 1.326 0.431
Total 3.080 1.000
Sedan Sports car Product
Power or
1/n
Weight of
Performance
Sedan 1 3 3.000 1.732 0.750
Sports car 1/3 1 0.333 0.577 0.250
Total 2.309
Sedan Sports car Product
Power or
1/n
Weight of
Performance
Sedan 1 3 3.000 1.732 0.750
Sports car 1/3 1 0.333 0.577 0.250
Total 2.309
Sedan Sports car Product
Power or
1/n
Weight of
Performance
Sedan 1 1/2 0.500 0.707 0.333
Sports car 2 1 2.000 1.414 0.667
Total 2.121
Table 4: Alternatives’ Cost Performance Comparison
Table 5: Alternatives’ Gas Mileage Performance Comparison
Table 6: Alternatives’ Style Performance Comparison
Table 3: Synthesis of Criteria Weighting Process
Figure 2: Car Hierarchy
Figure 2: Hierarchy with Weights
demonstrate mathematically that the
involved parties believe that the sedan is
three times as cost-effective as the sports
car, has three times the gas mileage, but
only half the style.
AHP objectively advises the decision-
maker to buy the sedan instead of the
sports car.
•	 sedan (0.750)
•	 sports car (0.250)
Sedan performance = (0.245 × 0.750) + (0.325 × 0.750) + (0.431 × 0.333) = 0.571
Sports car performance = (0.245 × 0.250) + (0.325 × 0.250) + (0.431 × 0.667) = 0.430
•	 sedan (0.750)
•	 sports car (0.250)
•	 sedan (0.333)
•	 sports car (0.667)
Goal:
Buy a new car
Criteria:
Gas Mileage (0.325)
Alternative #1:
Sedan
Alternative #2:
Sports car
Criteria:
Cost (0.245)
Criteria:
Style (0.431)
Goal:
Buy a new car
Criteria:
Gas Mileage (0.325)
Criteria:
Cost (0.245)
Criteria:
Style (0.431)
1514
Risks and Variables
Inconsistency Ratio
The inconsistency ratio of a pairwise
comparison matrix identifies the
uniformity of the decision-maker’s
judgments. If A>B and B>C, then
logically, A>C. However, in the example
above, cost was assessed as more
important than gas mileage and gas
mileage as more important than style,
but style as more important than cost.
The inconsistency ratio is a way of
quantifying how applicable this logic is
throughout the pairwise comparison.
AHP assumes that inconsistency is part
of the psychology of human decision-
makers. Extreme judgments, lack
of information, and the structuring
of the problem can all lead to large
inconsistencies. Inconsistency in the
way questions are answered often means
the “intuitiveness” of a result, a key
ingredient for consensus, is lost.
Sensitivity Analysis
Once an AHP problem has been
structured, judgments made, and
a preferred alternative identified,
sensitivity analysis can be performed.
A sensitivity analysis identifies how
sensitive a set of preferences, typically
the ranking of alternatives, are to altering
the criteria upon which they are based.
If the relative importance of a criterion
changes, then it follows that the preferred
alternative may also change. However,
if changing the relative importance of a
criterion has no impact on the preferred
alternative, then it can be reasonably
argued that that particular criterion can
be excluded and consideration given to
more important criteria. Analogous to a
construction schedule where activities on
the critical path warrant more attention
than those with “float,” criteria upon
which the alternatives are dependent
warrant more scrutiny than those that
have little impact on the end result.
Sensitivity analysis can also be used
to assess the impact of a particular
stakeholder or decision-maker on the
preferred alternative. When considering
the judgments from many stakeholders,
it is useful to determine how sensitive
a preferred alternative is to a particular
stakeholder, or to weight the relative
importance of stakeholder’s judgments.
In the context of infrastructure
engineering, sensitivity analysis is a
powerful technique for building consensus.
By mathematically demonstrating that
a particular criterion or decision-maker
has no impact on the ranking of the
alternatives, stakeholders can agree to
disregard that criterion or perspective in
the context of the decision at hand.
The structure of an AHP problem can
lead to inconsistency if it requires
judgment on criteria that are more than
one order of magnitude apart in terms
of their relative importance. The most
extreme judgment that can typically be
made is a nine, or within one magnitude
of difference.
Inconsistency up to 10% is acceptable.
Inconsistency ratios higher than 10%
may be indicative of poor structure,
ambiguity in the questioning, or
disingenuous responses from the
decision-makers. High inconsistency
should be identified, reviewed, and
resolved by improving the problem
structure, clarifying the question, and
revisiting the judgments. Once the
results have been checked for their
inconsistency ratio, a sensitivity analysis
can be performed.
Rank Reversal
If three alternatives are ranked A>B>C,
then adding a much lesser alternative
D should not impact the ranking of
alternatives A, B, and C. However, this
is not always true — the introduction of
a new alternative can change the ranking
of the original alternatives in unintuitive
ways. Rank reversal is a phenomenon of
AHP (and all other MCDA techniques)
where the relative ranking of a set of
alternatives will change whenever
another alternative is added or deleted.
Rank reversal can occur due to the
irrationality of the decision-maker or,
more problematically, as a function of
the mathematics behind AHP. Research
into the causes and potential mitigation
of rank reversal is inconclusive and
thus problematic and often ignored in
all but the most advanced applications
of AHP. Infrastructure engineers often
rearrange priorities and adding and
subtracting alternatives, due to changes
in scope, new information, and design
development. Thus it is important to
be aware of rank reversal as a potential
issue with AHP.
One way to avoid rank reversal is to
measure the alternatives on an absolute
scale rather than a relative scale. In other
words, an alternative is rated against
a benchmark or standard rather than
relative to other alternatives. While
absolute scales preserve rank regardless
of how many alternatives are added
or subtracted, they require a known
benchmark to derive scale. This limits
their functionality when the criteria to be
ranked are intangible, as is often the case
in engineering.
Gerald Desmond Bridge, Long Beach, CA ©Arup
1716
©Arup
1918
Relative measurement, or paired
comparisons, are most widely used
because many scales are intangible and
can only be relatively compared, not
absolutely.
Biases
When using pairwise comparisons
considerations of how we ask the
decision-maker to rank the criteria and
the effect it may have on the results.
First, the framing of the question affects
the answer. For example, within the
boundaries of a pairwise comparison, we
can ask of the decision-maker, “What is
more important: cost or environment?”
Another way to frame the question would
be to ask, “What is more important:
an increase in cost of 2% or obtaining
LEED Platinum status for the project’s
efforts to be sustainable?” The latter is a
more specific, less ambiguous, and well-
defined question, likely to get a different
answer than the former. Ambiguity
can also be used strategically — it can
Descriptive scale Numerical scale Value
None 0 0
A Tad 1 1/9 or 0.1111
Moderate 2 2/9 or 0.2222
Moderate to Good 3 3/9 or 0.3333
Good 4 4/9 or 0.4444
Good to Very Good 5 5/9 or 0.5556
Very Good 6 6/9 or 0.6667
Very Good to Excellent 7 7/9 or 0.7778
Excellent 8 8/9 or 0.8889
Outstanding 9 9/9 or 1.0000
Table 7: Descriptive versus Numerical Scale
promote engagement and discussion
among a group of decision-makers.
Secondly, the type of rating scale
we ask decision-makers to use can
affect results — a numerical scale will
provide outcomes very different from
a descriptive scale. While the decision-
maker’s ratings will inherently be
subjective, descriptive scales are likely
to be more inconsistent than numerical
or graphical scales. For example, a
numerical rating scale of 0 to 9 may
translate to a descriptive scale of “None”
to “Outstanding” with eight gradations
between.
In order to calculate a result, we must
assign a numerical difference between
items on the descriptive scale, for
example, between “Moderate” and
“Moderate to Good.” In Table 6 we
say that the numerical difference is
0.5556 – 0.4444 or 11%. Thus we are
saying “Moderate to Good” is 11%
better than “Moderate,” but how do we
know the decision-makers will assign
the same value to the descriptive scale?
Most software packages also allow
user-defined gradations, so rather than
assuming equal-increment jumps, we
can widen the gap between “Moderate”
and “Moderate to Good” to 18%,
assuming the sum of all gradations
equals 1, and the AHP methodology will
be unaffected. What will change is the
result.
All measurement in AHP is
fundamentally reliant on the scale, so
when structuring an AHP problem,
it is critically important to consider
its effect and the decision-maker’s
interpretation of it on the outcome.
Numerical or graphical scales will
provide the most transparency, but
descriptive scales can be more engaging
and can be intelligently applied to suit
the requirements of a problem, or can
be applied to lean towards a particular
alternative.
©Arup
2120
Case Study 1
California High-Speed Train
Project/Van Nuys Boulevard
Grade-Separation Study
Background
The potential for a structured MCDA methodology such as AHP in
engineering is demonstrated in large infrastructure projects. The
California High-Speed Train Project is one example of a project where
AHP could be implemented to test its applicability and benefits in
alternatives evaluation on infrastructure projects.
Consider the 20-plus grade-separation schemes — in this hypothetical
example, each scheme has 5 distinct locations dependent on preferred
alignment and each location has 8 possible treatments. Thus there are
4,000 possible grade-separation schemes to evaluate. Assume each one
is ranked against 10 key criteria and by 8 executive stakeholders, all of
whom have a preference based on qualitative rather than quantitative
criteria. AHP provides a methodology to structure a problem of this
scale and complexity.
For this case study, a single grade separation, Van Nuys Boulevard, on
a preferred alignment is considered.
California High-Speed Rail ©NC3D Media California High-Speed Rail ©NC3D Media
2322
Methodology
Step 1–Structuring Complexity
AHP begins with an objective, criteria,
and alternatives. The objective is to
find the best alternative for the grade
separation required to cross the high-
speed rail tracks at Van Nuys Boulevard,
in the San Fernando Valley, California.
The key criteria were established as
traffic circulation, right-of-way, utilities
and drainage, constructability, transit,
design compliance, and pedestrian
provision. Lastly, three preferred options
worthy of further consideration were
identified from the initial eight options
shown in Figure 4 — options 1, 2, and 6.
Step 2– Measurement
Once an objective, alternatives, and
criteria are defined, four decision-makers
individually made their judgments
regarding the relative importance of
the criteria and preferences among the
alternatives. The decision-makers made
the pairwise comparisons using the using
an absolute scale (1 to 9). These pairwise
comparisons result in a matrix for each
decision-maker, as shown in Figure 6.
Figure 5: Case Study Hierarchical Structure
Optimum Grade
Separation
VA1 VA2 VA6
Traffic
circulation
Right of
Way
Utilities &
Drainage
Constructability Transit
Compliant
design
Pedestrians
Figure 4: Grade-Separation Treatment Menu
PEDESTRIAN
TRAFFIC
DESIGN
TRANSIT
RIGHT-OF-WAY
CONSTRUCTABILITY
UTILITIES
PEDESTRIAN 1 4 3 1/2 1/4 ... ...
TRAFFIC 1/4 1 6 5 ... ... ...
DESIGN 1/3 1/6 1 2 ... ... ...
TRANSIT 2 1/5 1/2 1 ... ... ...
RIGHT-OF-WAY 4 ... ... ... 1 ... ...
CONSTRUCTABILITY ... ... ... ... ... 1 ...
UTILITIES ... ... ... ... ... ... 1
Figure 6: Pairwise comparison matrix
2524
Step 3–Synthesis
Synthesis is the stage between making
pairwise comparisons and arriving
at a preferred alternative, essentially
the mathematical theory behind AHP.
Squaring the pairwise comparison
matrix and summing and normalizing
the rows results in a vector with 7 rows
(1 for each criterion), which represents
the relative weighting of the criteria.
This vector will always be 1 column by
n rows, where n equals the number of
criteria.
Once the pairwise comparisons are
synthesized for the criteria, resulting in
criteria vector C, we repeat the process
on the alternatives.
The alternatives’ performances
concerning each criterion are pairwise
compared to each other. The comparison
values are then synthesized to obtain
an n x m matrix, where n is the number
of criteria and m is the number of
alternatives. Thus we get a 3 x 7
alternatives matrix A, as shown in
Figure 8.
Multiplying the criteria vector C by the
alternatives matrix A, and normalizing
the result, produces a 3 x 1 vector R,
which represents the ranked alternatives.
R is the preference vector, which in
this case translates to 33.31% for VA1,
31.07% for VA2, and 35.62% VA6 —
thus VA6 is the preferred alternative.
The percentages demonstrate the relative
C =
0.2096 PEDESTRIAN
0.2053 TRAFFIC
0.1863 DESIGN
0.1803 TRANSIT
0.1408 RIGHT-OF-WAY
0.0447 CONSTRUCTABILITY
0.0329 UTILITIES
Figure 7: Criteria vector showing relative weighting of the criteria
A =
0.293
VA1
PEDS 0.113
VA1
TRAF 0.293
VA1
DESN 0.113
VA1
TRAN 0.396
VA1
ROW 0.220
VA1
CONS 0.703
VA1
UTIL
0.113
VA2
PEDS 0.040
VA2
TRAF 0.362
VA2
DESN 0.259
VA2
TRAN 0.431
VA2
ROW 0.362
VA2
CONS 0.255
VA2
UTIL
0.113
VA6
PEDS 0.293
VA6
TRAF 0.362
VA6
DESN 0.425
VA6
TRAN 0.113
VA6
ROW 0.293
VA6
CONS 0.255
VA6
UTIL
Figure 8: Alternatives matrix showing to what extent each alternative satisfies the criteria
C x A = R =
0.331 VA1
0.3107 VA2
0.3562 VA6
Figure 9: Rankings vector showing extent to which each alternative satisfies the objective
strength of the alternative in terms of
satisfying the objective, in this instance
the optimum grade separation. The
difference between the percentages of
the alternatives gives an indication of
how preferred they are. In this instance,
all alternatives are relatively close, a
reflection of the similarity of the impacts
of each alternative.
Advanced Applications
The results can be interrogated once
synthesis has been performed in order
to build consensus among the decision-
makers and apply sensitivity analysis,
altering our judgments and changing our
assumptions to evaluate the impact on
our preferred alternative.
In our case study, there were multiple
decision-makers. During synthesis this
is accounted for by using a mean average
of their individual judgments. Another
option at this stage would be to weight
the decision-makers themselves, making
one person more influential than another,
a situation inherent to any decision-
making process.
Sensitivity analysis can also be
performed to determine how sensitive
our ranked alternatives are to the
pairwise comparisons, for example,
by selectively excluding particular
criteria or decision-makers’ judgments.
Sensitivity analysis can explore a
wide range of methods, in which case
software proves critical to avoiding
laborious calculations. In this case study,
hand calculations have been employed
in parallel to running the software
to confirm our methodology, but for
problems with larger numbers of criteria
or alternatives, or to perform robust
sensitivity analyses, hand calculations
and spreadsheets become impractical.
Grouptime
During the synthesis, a function of the
software called grouptime was used.
This was a platform for discussing the
weighting of the criteria and ranking
of the alternatives. Until this stage the
four decision-makers had made the
judgments independently based on their
own experience and knowledge of the
project. Using grouptime, these decision-
makers were brought together and could
argue the case for their judgments and
see the sensitivity of the rankings to
their weighted criteria. For example, one
criterion could be ignored altogether
to determine the extent of impact,
if any, on the ranking of the results.
Changing decision-maker’s judgments
or ignoring them entirely is also an
option. The possibilities for analysis and
interrogation were numerous and their
value immeasurable.
2726
California High-Speed Rail Grade Separation Schematic California High-Speed Rail Grade Separation Schematic
Case Study Conclusions
In this case study, utilizing AHP as a
decision-making methodology allowed
the project team to arrive at a preferred
alternative in an efficient manner with
input from each stakeholder. AHP is not
only tried and tested, but structured,
transparent, and justifiable to the client
and wider stakeholders. For the purposes
of this paper, a single grade separation on
Van Nuys Boulevard was investigated.
Historically, across the California
High-Speed Train Project, as many as 50
grade separations have been considered,
each with eight possible alternatives.
For a large number of these alternatives
the weighting of the criteria, and thus
the first half of the AHP synthesis,
may be identical. It would be unusual
to have different criteria and different
weighting of those criteria for each of
the 50 schemes. Pairwise comparisons
of the criteria rarely vary greatly across
similar locations. For example, within
a city we may consistently judge utility
diversions as less important than right-
of-way land take, or traffic circulation
as more important than constructability.
Assuming our criteria weighting for
Van Nuys is applicable at other locations
within the San Fernando Valley, this
case study provides a foundation to
implement an AHP analysis to multiple
scenarios without replicating the entire
process. These economies of scale would
further add value and efficiency to the
decision-making process of large-scale
infrastructure projects. Opportunities to
develop generalized criteria weighting
within a company or for a particular
client open up exciting possibilities to
harness the power of AHP analysis.
With a complex infrastructure project
such as the California High-Speed Train
Project, where many stakeholders hold
differing, often strong, opinions, AHP
is ideally suited not only to structure
the complexity of the problem but
also to build consensus among the
stakeholders in regards to an alternative.
Lack of consensus and a lack of belief
in a solution often stall or inhibit
funding and forward movement of
large schemes. Stakeholders often find
themselves entrenched in unswaying
beliefs and unwillingness to buy into and
support a compromise for the greater
good of a project. AHP could provide
all stakeholders space to share their
preferences and critical transparency
to interrogate their relative importance.
Using a robust and measurable decision-
making process can help ensure that
the project team chooses the correct
alternative that everyone can believe in
and support moving forward.
Findings
AHP methodology brings a powerful,
transparent, and structured approach to
decisions on infrastructure projects. Too
often significant decisions in traditional
option analysis are determined by
subjective, biased, or even random
factors — the opinion of “the loudest
voice in the room” or simply the last
issue identified, as it is fresh on the
minds of the decision-makers. Older
issues tend to be underestimated as we
become desensitized to them through
their numerous tablings at progress
meetings. Often, the extrovert’s issues
are always critical, while the introvert’s
are forgotten or underestimated. The
decision process is plagued by a lack of
structure, a bias toward the loudest voice,
and a general fatigue in considering
historical issues. AHP provides a
documentable and replicable way of
structuring problems involving multiple
criteria. The vast body of academic study
and accompanying literature, as well as
commercially available software, provide
confidence in AHP as a decision-making
tool. AHP provides a platform for group
decision-making, allowing a spectrum of
stakeholders to have their voices heard
and critically build consensus through
early involvement and collaboration.
This research has established that the
AHP process is a relevant and useful
technique in the decision-making
process for infrastructure projects. The
study has shown that even when a result
has been determined, a professional and
pragmatic view is needed to draw an
actionable conclusion.
2928
Sources
1.	 Forman, Ernest H. and Saul I. Gass. “The Analytic Hierarchy Process – An
Exposition.” Operations Research, 49.4 (2001): 469-486. Print.
2.	 Piantanakulchai, Mongkut and Nattapon Saengkhao. “Evaluation of Alternatives
in Transportation Planning Using Multi-Stakeholders Multi-Objectives AHP
Modeling.” Proceedings of the Eastern Asia Society of Transportation Studies,
Vol. 4 (2003): 1613-1628. Print.
3.	 Saaty, Thomas L. and Luis G. Vargas. Models, Methods, Concepts & Applications
of the Analytic Hierarchy Process. Boston: Kluwer Academics, 2001. Print.
4.	 Sadasivuni, Raviraj, Charles G. O’Hara, Rodrigo Nobrega, and Jeramiah Dumas.
“A Transportation Corridor Case Study for Multi-Criteria Decision Analysis.”
ASPRS 2009 Annual Conference. 9 Mar. 2009, Baltimore. Starkville: Mississippi
State University, n.d. Print.
5.	 Shin, Yong B., Seungho Lee, Sun Gi Chun, and Dalsang Chung. “A Critical
Review of Popular Multi-Criteria Decision Making Methodologies.” Issues in
Information Systems, 14.1 (2013): 358-365. Print.
6.	 Triantaphyllou, Evangelos and Stuart H. Mann. “Using the Analytic Hierarchy
Process for Decision Making in Engineering Applications: Some Challenges.”
International Journal of Industrial Engineering: Applications and Practice, 2.1
(1995): 35-44. Print.
©Arup
Gerald Desmond Bridge, Long Beach, CA ©Arup
3130
About Arup
Arup is the creative force at the heart of many of the world’s most
prominent projects in the built environment and across industry.
We offer a broad range of professional services that combine to make a
real difference to our clients and the communities in which we work.
We are truly global. From 92 offices in 40 countries, our 12,000
planners, designers, engineers, consultants and technical specialists
deliver innovative projects across the world with creativity and passion.
Founded in 1946 with an enduring set of values, our unique
trust ownership fosters a distinctive culture and an intellectual
independence that encourages collaborative working. This is reflected
in everything we do, allowing us to develop meaningful ideas,
help shape agendas and deliver results that frequently surpass the
expectations of our clients.
We shape a better world.
Contributors
Josh Bird
Engineer
Josue Enriquez
Engineer
Mackenzie Van Thof
Graduate Engineer
Daleen Saah
GIS Consultant
Jesse Vernon
Technical Editor
Precila Disman
Josephine Donde
Business Development
Doreen Patron
Graphic Design
Acknowledgements
Tony Marshall
Tim Corcoran
Richard Prust
AHP Paper

More Related Content

What's hot

Factor Analysis for Exploratory Studies
Factor Analysis for Exploratory StudiesFactor Analysis for Exploratory Studies
Factor Analysis for Exploratory Studies
Manohar Pahan
 
Multi criteria decision making
Multi criteria decision makingMulti criteria decision making
Multi criteria decision making
Kartik Bansal
 
Factor analysis ppt
Factor analysis pptFactor analysis ppt
Factor analysis ppt
Mukesh Bisht
 
Decision Making Using The Analytic Hierarchy Process
Decision Making Using The Analytic Hierarchy ProcessDecision Making Using The Analytic Hierarchy Process
Decision Making Using The Analytic Hierarchy Process
Vaibhav Gaikwad
 
ESTIMATING R 2 SHRINKAGE IN REGRESSION
ESTIMATING R 2 SHRINKAGE IN REGRESSIONESTIMATING R 2 SHRINKAGE IN REGRESSION
ESTIMATING R 2 SHRINKAGE IN REGRESSION
International Journal of Technical Research & Application
 
s.analysis
s.analysiss.analysis
s.analysis
kavi ...
 
Factor analysis
Factor analysisFactor analysis
Factor analysis
nurul amin
 
Unit iv statistical tools
Unit iv statistical toolsUnit iv statistical tools
Unit iv statistical tools
sujianush
 
Factor analysis
Factor analysisFactor analysis
Factor analysis
緯鈞 沈
 
Multi criteria decision support system on mobile phone selection with ahp and...
Multi criteria decision support system on mobile phone selection with ahp and...Multi criteria decision support system on mobile phone selection with ahp and...
Multi criteria decision support system on mobile phone selection with ahp and...Reza Ramezani
 
Research Methology -Factor Analyses
Research Methology -Factor AnalysesResearch Methology -Factor Analyses
Research Methology -Factor AnalysesNeerav Shivhare
 
Chapter 12
Chapter 12Chapter 12
Chapter 12bmcfad01
 
Exploratory Factor Analysis
Exploratory Factor AnalysisExploratory Factor Analysis
Exploratory Factor Analysis
Daire Hooper
 
Spss cross classification
Spss cross classificationSpss cross classification
Factor Analysis with an Example
Factor Analysis with an ExampleFactor Analysis with an Example
Factor Analysis with an Example
Seth Anandaram Jaipuria College
 
Introduction to Mediation using SPSS
Introduction to Mediation using SPSSIntroduction to Mediation using SPSS
Introduction to Mediation using SPSS
smackinnon
 
Cannonical Correlation
Cannonical CorrelationCannonical Correlation
Cannonical Correlationdomsr
 
Multiple Criteria for Decision
Multiple Criteria for DecisionMultiple Criteria for Decision
Multiple Criteria for Decision
Subhash sapkota
 
Binary OR Binomial logistic regression
Binary OR Binomial logistic regression Binary OR Binomial logistic regression
Binary OR Binomial logistic regression
Dr Athar Khan
 
Kappa statistics
Kappa statisticsKappa statistics
Kappa statistics
AmeyDhatrak
 

What's hot (20)

Factor Analysis for Exploratory Studies
Factor Analysis for Exploratory StudiesFactor Analysis for Exploratory Studies
Factor Analysis for Exploratory Studies
 
Multi criteria decision making
Multi criteria decision makingMulti criteria decision making
Multi criteria decision making
 
Factor analysis ppt
Factor analysis pptFactor analysis ppt
Factor analysis ppt
 
Decision Making Using The Analytic Hierarchy Process
Decision Making Using The Analytic Hierarchy ProcessDecision Making Using The Analytic Hierarchy Process
Decision Making Using The Analytic Hierarchy Process
 
ESTIMATING R 2 SHRINKAGE IN REGRESSION
ESTIMATING R 2 SHRINKAGE IN REGRESSIONESTIMATING R 2 SHRINKAGE IN REGRESSION
ESTIMATING R 2 SHRINKAGE IN REGRESSION
 
s.analysis
s.analysiss.analysis
s.analysis
 
Factor analysis
Factor analysisFactor analysis
Factor analysis
 
Unit iv statistical tools
Unit iv statistical toolsUnit iv statistical tools
Unit iv statistical tools
 
Factor analysis
Factor analysisFactor analysis
Factor analysis
 
Multi criteria decision support system on mobile phone selection with ahp and...
Multi criteria decision support system on mobile phone selection with ahp and...Multi criteria decision support system on mobile phone selection with ahp and...
Multi criteria decision support system on mobile phone selection with ahp and...
 
Research Methology -Factor Analyses
Research Methology -Factor AnalysesResearch Methology -Factor Analyses
Research Methology -Factor Analyses
 
Chapter 12
Chapter 12Chapter 12
Chapter 12
 
Exploratory Factor Analysis
Exploratory Factor AnalysisExploratory Factor Analysis
Exploratory Factor Analysis
 
Spss cross classification
Spss cross classificationSpss cross classification
Spss cross classification
 
Factor Analysis with an Example
Factor Analysis with an ExampleFactor Analysis with an Example
Factor Analysis with an Example
 
Introduction to Mediation using SPSS
Introduction to Mediation using SPSSIntroduction to Mediation using SPSS
Introduction to Mediation using SPSS
 
Cannonical Correlation
Cannonical CorrelationCannonical Correlation
Cannonical Correlation
 
Multiple Criteria for Decision
Multiple Criteria for DecisionMultiple Criteria for Decision
Multiple Criteria for Decision
 
Binary OR Binomial logistic regression
Binary OR Binomial logistic regression Binary OR Binomial logistic regression
Binary OR Binomial logistic regression
 
Kappa statistics
Kappa statisticsKappa statistics
Kappa statistics
 

Viewers also liked

the-changing-nature-of-financial-and-professional-services-in-the-city
the-changing-nature-of-financial-and-professional-services-in-the-citythe-changing-nature-of-financial-and-professional-services-in-the-city
the-changing-nature-of-financial-and-professional-services-in-the-cityKerri Bridges
 
Jatin Joshi Resume
Jatin Joshi ResumeJatin Joshi Resume
Jatin Joshi ResumeJatin Joshi
 
Slide share assignment
Slide share assignmentSlide share assignment
Slide share assignment
jesswilton
 
Questionnaire results
Questionnaire resultsQuestionnaire results
Questionnaire results
jamiedavismedia
 
Los numeros en Ingles
Los numeros en InglesLos numeros en Ingles
Los numeros en Ingles
n04s08f1995d
 
คู่มือ การใส่รูปภาพ
คู่มือ การใส่รูปภาพคู่มือ การใส่รูปภาพ
คู่มือ การใส่รูปภาพ
soysuda
 
1.2 secuencia revisión de propiedades
1.2 secuencia revisión de propiedades1.2 secuencia revisión de propiedades
1.2 secuencia revisión de propiedades
Sandy Anaya
 
Idiopathic scoliosis
Idiopathic scoliosis Idiopathic scoliosis
Idiopathic scoliosis
Rifhan Kamaruddin
 
количество информации
количество информацииколичество информации
количество информации
UriyK
 
Shooting script template (completed) (1)
Shooting script template (completed) (1)Shooting script template (completed) (1)
Shooting script template (completed) (1)
brxns
 
Palestinians Envision Life Without Occupation
Palestinians Envision Life Without OccupationPalestinians Envision Life Without Occupation
Palestinians Envision Life Without Occupation
irumshiekh
 
Light Tech Capabilities Statement1-12
Light Tech Capabilities Statement1-12Light Tech Capabilities Statement1-12
Light Tech Capabilities Statement1-12Kenneth Owens
 
Первые шаги с Farmasi 2016
Первые шаги с Farmasi 2016Первые шаги с Farmasi 2016
Первые шаги с Farmasi 2016
Яна Іванова
 
Research into radio trailers
Research into radio trailersResearch into radio trailers
Research into radio trailers
Zoheb Ashraf
 
от улыбки
от улыбкиот улыбки
от улыбки
yakushenkova
 
Mis diapositivas
Mis diapositivasMis diapositivas
Mis diapositivas
peluchin555
 

Viewers also liked (18)

the-changing-nature-of-financial-and-professional-services-in-the-city
the-changing-nature-of-financial-and-professional-services-in-the-citythe-changing-nature-of-financial-and-professional-services-in-the-city
the-changing-nature-of-financial-and-professional-services-in-the-city
 
Jatin Joshi Resume
Jatin Joshi ResumeJatin Joshi Resume
Jatin Joshi Resume
 
Slide share assignment
Slide share assignmentSlide share assignment
Slide share assignment
 
Hinduism
HinduismHinduism
Hinduism
 
Questionnaire results
Questionnaire resultsQuestionnaire results
Questionnaire results
 
Los numeros en Ingles
Los numeros en InglesLos numeros en Ingles
Los numeros en Ingles
 
คู่มือ การใส่รูปภาพ
คู่มือ การใส่รูปภาพคู่มือ การใส่รูปภาพ
คู่มือ การใส่รูปภาพ
 
1.2 secuencia revisión de propiedades
1.2 secuencia revisión de propiedades1.2 secuencia revisión de propiedades
1.2 secuencia revisión de propiedades
 
Idiopathic scoliosis
Idiopathic scoliosis Idiopathic scoliosis
Idiopathic scoliosis
 
CERN_Seminar_KVelissaridis
CERN_Seminar_KVelissaridisCERN_Seminar_KVelissaridis
CERN_Seminar_KVelissaridis
 
количество информации
количество информацииколичество информации
количество информации
 
Shooting script template (completed) (1)
Shooting script template (completed) (1)Shooting script template (completed) (1)
Shooting script template (completed) (1)
 
Palestinians Envision Life Without Occupation
Palestinians Envision Life Without OccupationPalestinians Envision Life Without Occupation
Palestinians Envision Life Without Occupation
 
Light Tech Capabilities Statement1-12
Light Tech Capabilities Statement1-12Light Tech Capabilities Statement1-12
Light Tech Capabilities Statement1-12
 
Первые шаги с Farmasi 2016
Первые шаги с Farmasi 2016Первые шаги с Farmasi 2016
Первые шаги с Farmasi 2016
 
Research into radio trailers
Research into radio trailersResearch into radio trailers
Research into radio trailers
 
от улыбки
от улыбкиот улыбки
от улыбки
 
Mis diapositivas
Mis diapositivasMis diapositivas
Mis diapositivas
 

Similar to AHP Paper

AHP technique a way to show preferences amongst alternatives
AHP technique a way to show preferences amongst alternativesAHP technique a way to show preferences amongst alternatives
AHP technique a way to show preferences amongst alternatives
ijsrd.com
 
AHP model for qualitative research study
AHP model for qualitative research studyAHP model for qualitative research study
AHP model for qualitative research study
NagarajNavalgund
 
Decision Support Systems in Clinical Engineering
Decision Support Systems in Clinical EngineeringDecision Support Systems in Clinical Engineering
Decision Support Systems in Clinical EngineeringAsmaa Kamel
 
Multi Criteria Decision Making Methodology on Selection of a Student for All ...
Multi Criteria Decision Making Methodology on Selection of a Student for All ...Multi Criteria Decision Making Methodology on Selection of a Student for All ...
Multi Criteria Decision Making Methodology on Selection of a Student for All ...
ijtsrd
 
Analytical Hierarchy Process (AHP)
Analytical Hierarchy Process (AHP)Analytical Hierarchy Process (AHP)
Analytical Hierarchy Process (AHP)
SakshiAggarwal98
 
30 14 jun17 3may 7620 7789-1-sm(edit)new
30 14 jun17 3may 7620 7789-1-sm(edit)new30 14 jun17 3may 7620 7789-1-sm(edit)new
30 14 jun17 3may 7620 7789-1-sm(edit)new
IAESIJEECS
 
Poonam 20ahluwalia-131008015758-phpapp02
Poonam 20ahluwalia-131008015758-phpapp02Poonam 20ahluwalia-131008015758-phpapp02
Poonam 20ahluwalia-131008015758-phpapp02PMI_IREP_TP
 
Poonam ahluwalia
Poonam ahluwaliaPoonam ahluwalia
Poonam ahluwaliaPMI2011
 
Selection of Fuel by Using Analytical Hierarchy Process
Selection of Fuel by Using Analytical Hierarchy ProcessSelection of Fuel by Using Analytical Hierarchy Process
Selection of Fuel by Using Analytical Hierarchy Process
IJERA Editor
 
Analytic Network Process
Analytic Network ProcessAnalytic Network Process
Analytic Network Process
Amir NikKhah
 
Project104_Group173_Draft_Proposal
Project104_Group173_Draft_ProposalProject104_Group173_Draft_Proposal
Project104_Group173_Draft_ProposalSarp Uzel
 
PRIORITIZING THE BANKING SERVICE QUALITY OF DIFFERENT BRANCHES USING FACTOR A...
PRIORITIZING THE BANKING SERVICE QUALITY OF DIFFERENT BRANCHES USING FACTOR A...PRIORITIZING THE BANKING SERVICE QUALITY OF DIFFERENT BRANCHES USING FACTOR A...
PRIORITIZING THE BANKING SERVICE QUALITY OF DIFFERENT BRANCHES USING FACTOR A...
ijmvsc
 
AHP_Report_EM-206.ppt
AHP_Report_EM-206.pptAHP_Report_EM-206.ppt
AHP_Report_EM-206.ppt
GeorgeGomez31
 
Application of the analytic hierarchy process (AHP) for selection of forecast...
Application of the analytic hierarchy process (AHP) for selection of forecast...Application of the analytic hierarchy process (AHP) for selection of forecast...
Application of the analytic hierarchy process (AHP) for selection of forecast...
Gurdal Ertek
 
AHP-ANALYTIC HIERARCHY PROCESS- How To Slove AHP in Excel
AHP-ANALYTIC HIERARCHY PROCESS- How To Slove AHP in ExcelAHP-ANALYTIC HIERARCHY PROCESS- How To Slove AHP in Excel
AHP-ANALYTIC HIERARCHY PROCESS- How To Slove AHP in Excel
Megha Ahuja
 
Entropy-weighted similarity measures for collaborative recommender systems.pdf
Entropy-weighted similarity measures for collaborative recommender systems.pdfEntropy-weighted similarity measures for collaborative recommender systems.pdf
Entropy-weighted similarity measures for collaborative recommender systems.pdf
Malim Siregar
 
IM426 3A G5.ppt
IM426 3A G5.pptIM426 3A G5.ppt
IM426 3A G5.ppt
MohamedSalem979344
 
Factor Analysis in Research
Factor Analysis in ResearchFactor Analysis in Research
Factor Analysis in ResearchQasim Raza
 
A041130105
A041130105A041130105
A041130105
IOSR-JEN
 

Similar to AHP Paper (20)

AHP technique a way to show preferences amongst alternatives
AHP technique a way to show preferences amongst alternativesAHP technique a way to show preferences amongst alternatives
AHP technique a way to show preferences amongst alternatives
 
AHP model for qualitative research study
AHP model for qualitative research studyAHP model for qualitative research study
AHP model for qualitative research study
 
Decision Support Systems in Clinical Engineering
Decision Support Systems in Clinical EngineeringDecision Support Systems in Clinical Engineering
Decision Support Systems in Clinical Engineering
 
Multi Criteria Decision Making Methodology on Selection of a Student for All ...
Multi Criteria Decision Making Methodology on Selection of a Student for All ...Multi Criteria Decision Making Methodology on Selection of a Student for All ...
Multi Criteria Decision Making Methodology on Selection of a Student for All ...
 
Analytical Hierarchy Process (AHP)
Analytical Hierarchy Process (AHP)Analytical Hierarchy Process (AHP)
Analytical Hierarchy Process (AHP)
 
30 14 jun17 3may 7620 7789-1-sm(edit)new
30 14 jun17 3may 7620 7789-1-sm(edit)new30 14 jun17 3may 7620 7789-1-sm(edit)new
30 14 jun17 3may 7620 7789-1-sm(edit)new
 
Poonam 20ahluwalia-131008015758-phpapp02
Poonam 20ahluwalia-131008015758-phpapp02Poonam 20ahluwalia-131008015758-phpapp02
Poonam 20ahluwalia-131008015758-phpapp02
 
Poonam ahluwalia
Poonam ahluwaliaPoonam ahluwalia
Poonam ahluwalia
 
Selection of Fuel by Using Analytical Hierarchy Process
Selection of Fuel by Using Analytical Hierarchy ProcessSelection of Fuel by Using Analytical Hierarchy Process
Selection of Fuel by Using Analytical Hierarchy Process
 
AJSR_23_01
AJSR_23_01AJSR_23_01
AJSR_23_01
 
Analytic Network Process
Analytic Network ProcessAnalytic Network Process
Analytic Network Process
 
Project104_Group173_Draft_Proposal
Project104_Group173_Draft_ProposalProject104_Group173_Draft_Proposal
Project104_Group173_Draft_Proposal
 
PRIORITIZING THE BANKING SERVICE QUALITY OF DIFFERENT BRANCHES USING FACTOR A...
PRIORITIZING THE BANKING SERVICE QUALITY OF DIFFERENT BRANCHES USING FACTOR A...PRIORITIZING THE BANKING SERVICE QUALITY OF DIFFERENT BRANCHES USING FACTOR A...
PRIORITIZING THE BANKING SERVICE QUALITY OF DIFFERENT BRANCHES USING FACTOR A...
 
AHP_Report_EM-206.ppt
AHP_Report_EM-206.pptAHP_Report_EM-206.ppt
AHP_Report_EM-206.ppt
 
Application of the analytic hierarchy process (AHP) for selection of forecast...
Application of the analytic hierarchy process (AHP) for selection of forecast...Application of the analytic hierarchy process (AHP) for selection of forecast...
Application of the analytic hierarchy process (AHP) for selection of forecast...
 
AHP-ANALYTIC HIERARCHY PROCESS- How To Slove AHP in Excel
AHP-ANALYTIC HIERARCHY PROCESS- How To Slove AHP in ExcelAHP-ANALYTIC HIERARCHY PROCESS- How To Slove AHP in Excel
AHP-ANALYTIC HIERARCHY PROCESS- How To Slove AHP in Excel
 
Entropy-weighted similarity measures for collaborative recommender systems.pdf
Entropy-weighted similarity measures for collaborative recommender systems.pdfEntropy-weighted similarity measures for collaborative recommender systems.pdf
Entropy-weighted similarity measures for collaborative recommender systems.pdf
 
IM426 3A G5.ppt
IM426 3A G5.pptIM426 3A G5.ppt
IM426 3A G5.ppt
 
Factor Analysis in Research
Factor Analysis in ResearchFactor Analysis in Research
Factor Analysis in Research
 
A041130105
A041130105A041130105
A041130105
 

AHP Paper

  • 1. Analytical Hierarchy Process Decision making for infrastructure alternatives Authors Sameer Deo Duanne Gilmore
  • 2. 32 Contacts Sameer Deo Senior Engineer sameer.deo@arup.com Duanne Gilmore Associate duanne.gilmore@arup.com arup.com Summary...........................................................................5 Introduction.......................................................................7 Analytical Hierarchy Process............................................9 Background....................................................................9 Structuring Complexity.................................................9 Measurement.................................................................9 Example.........................................................................11 Synthesis........................................................................11 Risks and Variables.......................................................14 Inconsistency Ratio.......................................................14 Sensitivity Analysis........................................................15 Rank Reversal................................................................15 Biases.............................................................................16 Case Study 1 California High-Speed Train Project/ Van Nuys Boulevard Grade-Separation Study.................21 Background....................................................................21 Methodology..................................................................22 Step 1–Structuring Complexity....................................22 Step 2–Measurement.....................................................22 Step 3– Synthesis............................................................24 Advanced Applications..................................................25 Grouptime......................................................................25 Case Study Conclusions................................................26 Findings.........................................................................27 Sources...............................................................................29 Contents
  • 3. ©Arup 54 Engineers often make recommendations for project alternatives that affect multiple stakeholders. Collaborative decision-making for project alternatives can become challenging for engineers because of the many opinions — the client, owner, public, architects, and other agencies and stakeholders, all with different and often conflicting priorities. The analytical hierarchy process (AHP), a multiple-criteria decision analysis (MCDA) technique, offers a structured approach to decision analysis in a multiple-criteria, multiple-stakeholder environment. AHP begins with setting a goal, developing alternatives that may be able to meet that goal, and then evaluating each alternative based upon its ability to meet the stakeholders’ criteria. AHP is utilized in many different fields, including economics, politics, finance, resource allocation, conflict resolution, design, architecture, and transportation. A case study on the California High-Speed Train project using AHP is applied in this paper to determine the best possible project alternative. Summary
  • 4. A30 ©Anthony J. Branco 76 Not everything that counts can be counted and not everything that can be counted, counts. Albert Einstein Infrastructure projects are large, complex, and expensive, and involve collaborative decision-making among various entities, often with incompatible ideas that lead to project delays and cost overruns. A crucial problem engineers face when evaluating project options is how to scientifically structure the decision-making process, quantify qualitative human judgment, and then build consensus on a singular engineering solution that would satisfy multiple stakeholders with conflicting priorities. During our work on the California High- Speed Train Project, Arup explored the use of an MCDA technique as a possible solution for evaluating options for grade separations (construction cost in excess of US$65b) along the high-speed rail line in the Los Angeles metropolitan area. Through a case-study approach, this paper is focused on the application of AHP in evaluating a single grade separation with multiple design options against a set of criteria and with multiple stakeholders’ input. Introduction
  • 5. 98 Analytical Hierarchy Process has three primary functions: structure, measurement, and synthesis. Structuring Complexity As illustrated in Figure 1, every element of the hierarchy must ultimately be related to an alternative. The relationship must be direct or follow a path, but no element should be isolated from the alternatives. Careful consideration must be given to develop performance measures and priorities. Determining which factors to include in the hierarchical structure as “criteria” is the most creative part of the AHP process for the decision-maker. Measurement After structuring the problem, AHP develops a set of priorities for the criteria used to judge the alternatives using the Fundamental Scale of Absolute Numbers (see Table 1). The process of prioritization resolves the problem of dealing with different types of scales, Figure 1: Typical AHP Structure Goal Criteria Alternative #1 Alternative #2 Alternative #3 Criteria Criteria Background While teaching at the Wharton School, Thomas Saaty was troubled by the communication difficulties between scientists and lawyers, noting their lack of a practical and systematic approach for priority-setting and decision-making. He set out to find a way for ordinary people to make complex decisions (Gass). In his research, Saaty found that humans often deal with complexity in a hierarchical way and develop structures through homogeneous clusters of factors, with lower levels in the structure corresponding to increased detail in criteria. In 1994, Saaty introduced AHP as a pair-wise comparison tool for multi-criteria decision-making. AHP uses decision analysis mathematics to determine priorities of various alternatives using pairwise comparison of different decision elements with reference to a common criterion. AHP
  • 6. 1110 since measurements on different scales cannot be directly evaluated or combined. AHP uses pairwise comparisons — directly comparing one criterion to another, deciding between the two which is more preferred. AHP uses pairwise comparisons to determine which criterion is more important by comparing each criterion to every other criterion, one at a time; the extent preferred is given numerical values 1 through 9 (1 = same importance, 9 = one is extremely more important than the other). Through these pairwise comparisons, AHP turns a multidimensional scaling problem into a one-dimensional scaling solution. Example Suppose a woman is in the market for a new car and has narrowed her options to either a fuel-efficient sedan or a sports car. The decision will be based on the following metrics: (a) cost, (b) gas mileage, and (c) style. To the decision- maker, cost is a little more important Fundamental Scale Intensity of Importance Definition Explanation 1 equal importance Two elements contribute equally to the objective. 3 moderate importance Experience and judgment moderately favor one element over another. 5 strong importance Experience and judgment strongly favor one element over another. 7 very strong importance One element is favored very strongly over another, its dominance is demonstrated in practice. 9 extreme importance The evidence favoring one element over another is of the highest possible order of affirmation. 2,4,6,8* values used as a compromise 1.1 - 1.9 when activities are very close a decimal is added to 1 to show their difference as appropriate The option to use decimals can indicate the relative importance of similar criteria. Reciprocals of above If Activity A has one of the above non-zero numbers assigned to it when compared with Activity B, then B has the reciprocal value when compared with A. Cost Gas Mileage Style Cost 1 3 1/7 Gas Mileage 1/3 1 3 Style 7 1/3 1 Table 2: Pairwise Comparisons Table 1: Fundamental Scale of Absolute Numbers *A value range of 1 through 9 makes it simple for the decision-maker to differentiate among levels of importance. In this model, there are five levels of clear importance, so odd numbers are normally used. However, even numbers can be used to provide more nuance — if a criterion is more than “moderately” more important but not “strongly” more important, a value of 4 would be used. than gas mileage, so cost compared to gas mileage receives a value of 3. Reciprocating the opposite, gas mileage compared to cost receives a value of 1/3. Using the Fundamental Scale of Absolute Numbers, the paired comparisons of the criteria to the goal are summarized in Table 2. As shown, style is much more important than cost while gas mileage is a little more important than style. The “1” values diagonally across the table merely imply that any criterion has equal importance to itself. Once the criteria have been prioritized, the alternatives are then ranked according to how they perform on each criterion. It is possible for comparisons to be inconsistent with each other — in the example above, cost was assessed as more important than gas mileage while gas mileage is more important than style, and yet style is more important than cost. This inconsistency will not inhibit any calculations in the AHP method, but the inconsistency may indicate that the scores are not the decision-maker’s true preferences. Synthesis Once comparisons are made, the results need to be synthesized. Each criterion is given a numerical weight, determined through the steps shown in Table 3. Then each weight is multiplied by a reciprocal root of the number of criteria in the decision — for this example, to the power of 1/3 because there are 3 criteria. The weight is then determined by each criterion’s power to the 1/n divided by the total in that column.
  • 7. 1312 Now that the weights have been established for each criterion, the alternatives must compared. Tables 4–6 show the calculations that determine each car’s performance in relation to the weighted criteria. Using the same calculation as the criteria weighting process above, these matrices A B C D E F G Cost Gas Mileage Style Product B x C x D Power 1/n E^(1/3) Weight F/Ftotal Cost 1 3 1/7 0.429 0.754 0.245 Gas Mileage 1/3 1 3 1.000 1.000 0.325 Style 7 1/3 1 2.333 1.326 0.431 Total 3.080 1.000 Sedan Sports car Product Power or 1/n Weight of Performance Sedan 1 3 3.000 1.732 0.750 Sports car 1/3 1 0.333 0.577 0.250 Total 2.309 Sedan Sports car Product Power or 1/n Weight of Performance Sedan 1 3 3.000 1.732 0.750 Sports car 1/3 1 0.333 0.577 0.250 Total 2.309 Sedan Sports car Product Power or 1/n Weight of Performance Sedan 1 1/2 0.500 0.707 0.333 Sports car 2 1 2.000 1.414 0.667 Total 2.121 Table 4: Alternatives’ Cost Performance Comparison Table 5: Alternatives’ Gas Mileage Performance Comparison Table 6: Alternatives’ Style Performance Comparison Table 3: Synthesis of Criteria Weighting Process Figure 2: Car Hierarchy Figure 2: Hierarchy with Weights demonstrate mathematically that the involved parties believe that the sedan is three times as cost-effective as the sports car, has three times the gas mileage, but only half the style. AHP objectively advises the decision- maker to buy the sedan instead of the sports car. • sedan (0.750) • sports car (0.250) Sedan performance = (0.245 × 0.750) + (0.325 × 0.750) + (0.431 × 0.333) = 0.571 Sports car performance = (0.245 × 0.250) + (0.325 × 0.250) + (0.431 × 0.667) = 0.430 • sedan (0.750) • sports car (0.250) • sedan (0.333) • sports car (0.667) Goal: Buy a new car Criteria: Gas Mileage (0.325) Alternative #1: Sedan Alternative #2: Sports car Criteria: Cost (0.245) Criteria: Style (0.431) Goal: Buy a new car Criteria: Gas Mileage (0.325) Criteria: Cost (0.245) Criteria: Style (0.431)
  • 8. 1514 Risks and Variables Inconsistency Ratio The inconsistency ratio of a pairwise comparison matrix identifies the uniformity of the decision-maker’s judgments. If A>B and B>C, then logically, A>C. However, in the example above, cost was assessed as more important than gas mileage and gas mileage as more important than style, but style as more important than cost. The inconsistency ratio is a way of quantifying how applicable this logic is throughout the pairwise comparison. AHP assumes that inconsistency is part of the psychology of human decision- makers. Extreme judgments, lack of information, and the structuring of the problem can all lead to large inconsistencies. Inconsistency in the way questions are answered often means the “intuitiveness” of a result, a key ingredient for consensus, is lost. Sensitivity Analysis Once an AHP problem has been structured, judgments made, and a preferred alternative identified, sensitivity analysis can be performed. A sensitivity analysis identifies how sensitive a set of preferences, typically the ranking of alternatives, are to altering the criteria upon which they are based. If the relative importance of a criterion changes, then it follows that the preferred alternative may also change. However, if changing the relative importance of a criterion has no impact on the preferred alternative, then it can be reasonably argued that that particular criterion can be excluded and consideration given to more important criteria. Analogous to a construction schedule where activities on the critical path warrant more attention than those with “float,” criteria upon which the alternatives are dependent warrant more scrutiny than those that have little impact on the end result. Sensitivity analysis can also be used to assess the impact of a particular stakeholder or decision-maker on the preferred alternative. When considering the judgments from many stakeholders, it is useful to determine how sensitive a preferred alternative is to a particular stakeholder, or to weight the relative importance of stakeholder’s judgments. In the context of infrastructure engineering, sensitivity analysis is a powerful technique for building consensus. By mathematically demonstrating that a particular criterion or decision-maker has no impact on the ranking of the alternatives, stakeholders can agree to disregard that criterion or perspective in the context of the decision at hand. The structure of an AHP problem can lead to inconsistency if it requires judgment on criteria that are more than one order of magnitude apart in terms of their relative importance. The most extreme judgment that can typically be made is a nine, or within one magnitude of difference. Inconsistency up to 10% is acceptable. Inconsistency ratios higher than 10% may be indicative of poor structure, ambiguity in the questioning, or disingenuous responses from the decision-makers. High inconsistency should be identified, reviewed, and resolved by improving the problem structure, clarifying the question, and revisiting the judgments. Once the results have been checked for their inconsistency ratio, a sensitivity analysis can be performed. Rank Reversal If three alternatives are ranked A>B>C, then adding a much lesser alternative D should not impact the ranking of alternatives A, B, and C. However, this is not always true — the introduction of a new alternative can change the ranking of the original alternatives in unintuitive ways. Rank reversal is a phenomenon of AHP (and all other MCDA techniques) where the relative ranking of a set of alternatives will change whenever another alternative is added or deleted. Rank reversal can occur due to the irrationality of the decision-maker or, more problematically, as a function of the mathematics behind AHP. Research into the causes and potential mitigation of rank reversal is inconclusive and thus problematic and often ignored in all but the most advanced applications of AHP. Infrastructure engineers often rearrange priorities and adding and subtracting alternatives, due to changes in scope, new information, and design development. Thus it is important to be aware of rank reversal as a potential issue with AHP. One way to avoid rank reversal is to measure the alternatives on an absolute scale rather than a relative scale. In other words, an alternative is rated against a benchmark or standard rather than relative to other alternatives. While absolute scales preserve rank regardless of how many alternatives are added or subtracted, they require a known benchmark to derive scale. This limits their functionality when the criteria to be ranked are intangible, as is often the case in engineering. Gerald Desmond Bridge, Long Beach, CA ©Arup
  • 10. 1918 Relative measurement, or paired comparisons, are most widely used because many scales are intangible and can only be relatively compared, not absolutely. Biases When using pairwise comparisons considerations of how we ask the decision-maker to rank the criteria and the effect it may have on the results. First, the framing of the question affects the answer. For example, within the boundaries of a pairwise comparison, we can ask of the decision-maker, “What is more important: cost or environment?” Another way to frame the question would be to ask, “What is more important: an increase in cost of 2% or obtaining LEED Platinum status for the project’s efforts to be sustainable?” The latter is a more specific, less ambiguous, and well- defined question, likely to get a different answer than the former. Ambiguity can also be used strategically — it can Descriptive scale Numerical scale Value None 0 0 A Tad 1 1/9 or 0.1111 Moderate 2 2/9 or 0.2222 Moderate to Good 3 3/9 or 0.3333 Good 4 4/9 or 0.4444 Good to Very Good 5 5/9 or 0.5556 Very Good 6 6/9 or 0.6667 Very Good to Excellent 7 7/9 or 0.7778 Excellent 8 8/9 or 0.8889 Outstanding 9 9/9 or 1.0000 Table 7: Descriptive versus Numerical Scale promote engagement and discussion among a group of decision-makers. Secondly, the type of rating scale we ask decision-makers to use can affect results — a numerical scale will provide outcomes very different from a descriptive scale. While the decision- maker’s ratings will inherently be subjective, descriptive scales are likely to be more inconsistent than numerical or graphical scales. For example, a numerical rating scale of 0 to 9 may translate to a descriptive scale of “None” to “Outstanding” with eight gradations between. In order to calculate a result, we must assign a numerical difference between items on the descriptive scale, for example, between “Moderate” and “Moderate to Good.” In Table 6 we say that the numerical difference is 0.5556 – 0.4444 or 11%. Thus we are saying “Moderate to Good” is 11% better than “Moderate,” but how do we know the decision-makers will assign the same value to the descriptive scale? Most software packages also allow user-defined gradations, so rather than assuming equal-increment jumps, we can widen the gap between “Moderate” and “Moderate to Good” to 18%, assuming the sum of all gradations equals 1, and the AHP methodology will be unaffected. What will change is the result. All measurement in AHP is fundamentally reliant on the scale, so when structuring an AHP problem, it is critically important to consider its effect and the decision-maker’s interpretation of it on the outcome. Numerical or graphical scales will provide the most transparency, but descriptive scales can be more engaging and can be intelligently applied to suit the requirements of a problem, or can be applied to lean towards a particular alternative. ©Arup
  • 11. 2120 Case Study 1 California High-Speed Train Project/Van Nuys Boulevard Grade-Separation Study Background The potential for a structured MCDA methodology such as AHP in engineering is demonstrated in large infrastructure projects. The California High-Speed Train Project is one example of a project where AHP could be implemented to test its applicability and benefits in alternatives evaluation on infrastructure projects. Consider the 20-plus grade-separation schemes — in this hypothetical example, each scheme has 5 distinct locations dependent on preferred alignment and each location has 8 possible treatments. Thus there are 4,000 possible grade-separation schemes to evaluate. Assume each one is ranked against 10 key criteria and by 8 executive stakeholders, all of whom have a preference based on qualitative rather than quantitative criteria. AHP provides a methodology to structure a problem of this scale and complexity. For this case study, a single grade separation, Van Nuys Boulevard, on a preferred alignment is considered. California High-Speed Rail ©NC3D Media California High-Speed Rail ©NC3D Media
  • 12. 2322 Methodology Step 1–Structuring Complexity AHP begins with an objective, criteria, and alternatives. The objective is to find the best alternative for the grade separation required to cross the high- speed rail tracks at Van Nuys Boulevard, in the San Fernando Valley, California. The key criteria were established as traffic circulation, right-of-way, utilities and drainage, constructability, transit, design compliance, and pedestrian provision. Lastly, three preferred options worthy of further consideration were identified from the initial eight options shown in Figure 4 — options 1, 2, and 6. Step 2– Measurement Once an objective, alternatives, and criteria are defined, four decision-makers individually made their judgments regarding the relative importance of the criteria and preferences among the alternatives. The decision-makers made the pairwise comparisons using the using an absolute scale (1 to 9). These pairwise comparisons result in a matrix for each decision-maker, as shown in Figure 6. Figure 5: Case Study Hierarchical Structure Optimum Grade Separation VA1 VA2 VA6 Traffic circulation Right of Way Utilities & Drainage Constructability Transit Compliant design Pedestrians Figure 4: Grade-Separation Treatment Menu PEDESTRIAN TRAFFIC DESIGN TRANSIT RIGHT-OF-WAY CONSTRUCTABILITY UTILITIES PEDESTRIAN 1 4 3 1/2 1/4 ... ... TRAFFIC 1/4 1 6 5 ... ... ... DESIGN 1/3 1/6 1 2 ... ... ... TRANSIT 2 1/5 1/2 1 ... ... ... RIGHT-OF-WAY 4 ... ... ... 1 ... ... CONSTRUCTABILITY ... ... ... ... ... 1 ... UTILITIES ... ... ... ... ... ... 1 Figure 6: Pairwise comparison matrix
  • 13. 2524 Step 3–Synthesis Synthesis is the stage between making pairwise comparisons and arriving at a preferred alternative, essentially the mathematical theory behind AHP. Squaring the pairwise comparison matrix and summing and normalizing the rows results in a vector with 7 rows (1 for each criterion), which represents the relative weighting of the criteria. This vector will always be 1 column by n rows, where n equals the number of criteria. Once the pairwise comparisons are synthesized for the criteria, resulting in criteria vector C, we repeat the process on the alternatives. The alternatives’ performances concerning each criterion are pairwise compared to each other. The comparison values are then synthesized to obtain an n x m matrix, where n is the number of criteria and m is the number of alternatives. Thus we get a 3 x 7 alternatives matrix A, as shown in Figure 8. Multiplying the criteria vector C by the alternatives matrix A, and normalizing the result, produces a 3 x 1 vector R, which represents the ranked alternatives. R is the preference vector, which in this case translates to 33.31% for VA1, 31.07% for VA2, and 35.62% VA6 — thus VA6 is the preferred alternative. The percentages demonstrate the relative C = 0.2096 PEDESTRIAN 0.2053 TRAFFIC 0.1863 DESIGN 0.1803 TRANSIT 0.1408 RIGHT-OF-WAY 0.0447 CONSTRUCTABILITY 0.0329 UTILITIES Figure 7: Criteria vector showing relative weighting of the criteria A = 0.293 VA1 PEDS 0.113 VA1 TRAF 0.293 VA1 DESN 0.113 VA1 TRAN 0.396 VA1 ROW 0.220 VA1 CONS 0.703 VA1 UTIL 0.113 VA2 PEDS 0.040 VA2 TRAF 0.362 VA2 DESN 0.259 VA2 TRAN 0.431 VA2 ROW 0.362 VA2 CONS 0.255 VA2 UTIL 0.113 VA6 PEDS 0.293 VA6 TRAF 0.362 VA6 DESN 0.425 VA6 TRAN 0.113 VA6 ROW 0.293 VA6 CONS 0.255 VA6 UTIL Figure 8: Alternatives matrix showing to what extent each alternative satisfies the criteria C x A = R = 0.331 VA1 0.3107 VA2 0.3562 VA6 Figure 9: Rankings vector showing extent to which each alternative satisfies the objective strength of the alternative in terms of satisfying the objective, in this instance the optimum grade separation. The difference between the percentages of the alternatives gives an indication of how preferred they are. In this instance, all alternatives are relatively close, a reflection of the similarity of the impacts of each alternative. Advanced Applications The results can be interrogated once synthesis has been performed in order to build consensus among the decision- makers and apply sensitivity analysis, altering our judgments and changing our assumptions to evaluate the impact on our preferred alternative. In our case study, there were multiple decision-makers. During synthesis this is accounted for by using a mean average of their individual judgments. Another option at this stage would be to weight the decision-makers themselves, making one person more influential than another, a situation inherent to any decision- making process. Sensitivity analysis can also be performed to determine how sensitive our ranked alternatives are to the pairwise comparisons, for example, by selectively excluding particular criteria or decision-makers’ judgments. Sensitivity analysis can explore a wide range of methods, in which case software proves critical to avoiding laborious calculations. In this case study, hand calculations have been employed in parallel to running the software to confirm our methodology, but for problems with larger numbers of criteria or alternatives, or to perform robust sensitivity analyses, hand calculations and spreadsheets become impractical. Grouptime During the synthesis, a function of the software called grouptime was used. This was a platform for discussing the weighting of the criteria and ranking of the alternatives. Until this stage the four decision-makers had made the judgments independently based on their own experience and knowledge of the project. Using grouptime, these decision- makers were brought together and could argue the case for their judgments and see the sensitivity of the rankings to their weighted criteria. For example, one criterion could be ignored altogether to determine the extent of impact, if any, on the ranking of the results. Changing decision-maker’s judgments or ignoring them entirely is also an option. The possibilities for analysis and interrogation were numerous and their value immeasurable.
  • 14. 2726 California High-Speed Rail Grade Separation Schematic California High-Speed Rail Grade Separation Schematic Case Study Conclusions In this case study, utilizing AHP as a decision-making methodology allowed the project team to arrive at a preferred alternative in an efficient manner with input from each stakeholder. AHP is not only tried and tested, but structured, transparent, and justifiable to the client and wider stakeholders. For the purposes of this paper, a single grade separation on Van Nuys Boulevard was investigated. Historically, across the California High-Speed Train Project, as many as 50 grade separations have been considered, each with eight possible alternatives. For a large number of these alternatives the weighting of the criteria, and thus the first half of the AHP synthesis, may be identical. It would be unusual to have different criteria and different weighting of those criteria for each of the 50 schemes. Pairwise comparisons of the criteria rarely vary greatly across similar locations. For example, within a city we may consistently judge utility diversions as less important than right- of-way land take, or traffic circulation as more important than constructability. Assuming our criteria weighting for Van Nuys is applicable at other locations within the San Fernando Valley, this case study provides a foundation to implement an AHP analysis to multiple scenarios without replicating the entire process. These economies of scale would further add value and efficiency to the decision-making process of large-scale infrastructure projects. Opportunities to develop generalized criteria weighting within a company or for a particular client open up exciting possibilities to harness the power of AHP analysis. With a complex infrastructure project such as the California High-Speed Train Project, where many stakeholders hold differing, often strong, opinions, AHP is ideally suited not only to structure the complexity of the problem but also to build consensus among the stakeholders in regards to an alternative. Lack of consensus and a lack of belief in a solution often stall or inhibit funding and forward movement of large schemes. Stakeholders often find themselves entrenched in unswaying beliefs and unwillingness to buy into and support a compromise for the greater good of a project. AHP could provide all stakeholders space to share their preferences and critical transparency to interrogate their relative importance. Using a robust and measurable decision- making process can help ensure that the project team chooses the correct alternative that everyone can believe in and support moving forward. Findings AHP methodology brings a powerful, transparent, and structured approach to decisions on infrastructure projects. Too often significant decisions in traditional option analysis are determined by subjective, biased, or even random factors — the opinion of “the loudest voice in the room” or simply the last issue identified, as it is fresh on the minds of the decision-makers. Older issues tend to be underestimated as we become desensitized to them through their numerous tablings at progress meetings. Often, the extrovert’s issues are always critical, while the introvert’s are forgotten or underestimated. The decision process is plagued by a lack of structure, a bias toward the loudest voice, and a general fatigue in considering historical issues. AHP provides a documentable and replicable way of structuring problems involving multiple criteria. The vast body of academic study and accompanying literature, as well as commercially available software, provide confidence in AHP as a decision-making tool. AHP provides a platform for group decision-making, allowing a spectrum of stakeholders to have their voices heard and critically build consensus through early involvement and collaboration. This research has established that the AHP process is a relevant and useful technique in the decision-making process for infrastructure projects. The study has shown that even when a result has been determined, a professional and pragmatic view is needed to draw an actionable conclusion.
  • 15. 2928 Sources 1. Forman, Ernest H. and Saul I. Gass. “The Analytic Hierarchy Process – An Exposition.” Operations Research, 49.4 (2001): 469-486. Print. 2. Piantanakulchai, Mongkut and Nattapon Saengkhao. “Evaluation of Alternatives in Transportation Planning Using Multi-Stakeholders Multi-Objectives AHP Modeling.” Proceedings of the Eastern Asia Society of Transportation Studies, Vol. 4 (2003): 1613-1628. Print. 3. Saaty, Thomas L. and Luis G. Vargas. Models, Methods, Concepts & Applications of the Analytic Hierarchy Process. Boston: Kluwer Academics, 2001. Print. 4. Sadasivuni, Raviraj, Charles G. O’Hara, Rodrigo Nobrega, and Jeramiah Dumas. “A Transportation Corridor Case Study for Multi-Criteria Decision Analysis.” ASPRS 2009 Annual Conference. 9 Mar. 2009, Baltimore. Starkville: Mississippi State University, n.d. Print. 5. Shin, Yong B., Seungho Lee, Sun Gi Chun, and Dalsang Chung. “A Critical Review of Popular Multi-Criteria Decision Making Methodologies.” Issues in Information Systems, 14.1 (2013): 358-365. Print. 6. Triantaphyllou, Evangelos and Stuart H. Mann. “Using the Analytic Hierarchy Process for Decision Making in Engineering Applications: Some Challenges.” International Journal of Industrial Engineering: Applications and Practice, 2.1 (1995): 35-44. Print. ©Arup
  • 16. Gerald Desmond Bridge, Long Beach, CA ©Arup 3130 About Arup Arup is the creative force at the heart of many of the world’s most prominent projects in the built environment and across industry. We offer a broad range of professional services that combine to make a real difference to our clients and the communities in which we work. We are truly global. From 92 offices in 40 countries, our 12,000 planners, designers, engineers, consultants and technical specialists deliver innovative projects across the world with creativity and passion. Founded in 1946 with an enduring set of values, our unique trust ownership fosters a distinctive culture and an intellectual independence that encourages collaborative working. This is reflected in everything we do, allowing us to develop meaningful ideas, help shape agendas and deliver results that frequently surpass the expectations of our clients. We shape a better world. Contributors Josh Bird Engineer Josue Enriquez Engineer Mackenzie Van Thof Graduate Engineer Daleen Saah GIS Consultant Jesse Vernon Technical Editor Precila Disman Josephine Donde Business Development Doreen Patron Graphic Design Acknowledgements Tony Marshall Tim Corcoran Richard Prust