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MULTI-CRITERIA DECISION MAKING FOR PUBLIC
TRANSPORTATION DEVELOPMENT PROJECTS USING ANALYTIC
NETWORK PROCESS (ANP)
MINTESNOT Gebeyehu
Ph.D. candidate
Graduate School of Engineering
Hokkaido University
North 13, West 8, Kita-Ku, Sapporo,
060-8628, Japan
Fax: +81-11-706-6206
E-mail: mintesnot@gmail.com
Shin- ei TAKANO
Associate Professor
Graduate School of Engineering
Hokkaido University
North 13, West 8, Kita-Ku, Sapporo,
060-8628, Japan
Fax: +81-11-706-6205
E-mail: shey@eng.hokudai.ac.jp
Abstract: In Asian and African developing cities, decisions on transportation projects are made
with capital cost constraints and administrative influences, thus, providing a well-designed public
transport is not a simple task. Therefore, multi-criteria decision-making methods that can
incorporate the conflicting considerations are essential. This case study introduced the application
of ANP for public transportation development programs. Even though ANP is the generalization
of AHP, the results of the two models were compared to see the effects of the feedback, outer and
inner dependences of the elements. According to the result, ANP model give a relative
importance for environmental and socio-economic benefits as a criteria of public transport
development, however, the AHP model turned out to give importance for the capital cost and
capacity. Providing Bus Rapid Transit and Light Rail are the chosen alternatives in the case of
ANP, where as AHP model choose expanding the existing bus services.
Key words: Analytic Hierarchy Process (AHP), Analytic Network Process (ANP), Public
transportation projects
1. INTRODUCTION
Decision-making in transportation projects considers interrelated criteria. Especially in Asian and
African developing cities, decisions are made with capital cost constraints and some
administrative influences. For example, the public transportation in Addis Ababa, the capital city
of Ethiopia, has numerous problems related with socio-economic, political and financial issues.
For several years the city has no well-integrated public transportation. There is only one Bus
Company with limited fleet size, however, the population is growing every year and the socio-
economic settings are becoming complex. People’s mobility pattern is changed with a change of
land use and economic activities. Parallel to these changes, the public transport has not shown
improvements. Buses and taxis are the only public transportation modes, which the residents are
extensively using. Private car is not affordable for the majority of the residents. Therefore, urban
transport improvement and development measures are important in providing an optimal transit
in order to increase accessibility and coverage of public transportations. In the past, several
researches have developed various public transportation improvement programs, and in this
regard, providing a well-designed transport system with increased public transport mode choices
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is indispensable. There have been some studies to propose public transport development
programs in the city of Addis Ababa (e.g., ERA, 2005). However, implementation is not realized
yet because of the multi-facet constraints. For that reason, multi-criteria decision making methods
that can incorporate the conflicting considerations are essential. Therefore, this case study has an
objective of applying the ANP model for prioritize public transport alternatives. Because the
ANP process is based on deriving ratio scale measurements, it can be used to allocate resources
according to their ratio-scale priorities. The Analytic Network Process (ANP), developed by
Thomas L. Saaty, provides a way to input judgments and measurements to derive ratio scale
priorities for the distribution of influence among the factors and groups of factors in the decision.
ANP is the generalization of the Analytic Hierarchy Process (AHP). The basic structures are
networks. Priorities are established in the same way they are in the AHP using pairwise
comparisons and judgments (Jose Fugueira, 2005). The well-known decision theory, the Analytic
Hierarchy Process (AHP) is a special case of the ANP. Both the AHP and the ANP derive ratio
scale priorities for elements and clusters of elements by making paired comparisons of elements
on a common property or criterion.
The Analytic Network Process (ANP) is the most comprehensive framework for the analysis of
societal, governmental and corporate decisions that is available to the decision-maker. It is a
process that allows one to include all the factors and criteria, tangible and intangible that has
bearing on making a best decision. The Analytic Network Process allows both interaction and
feedback within clusters of elements (inner dependence) and between clusters (outer dependence)
with respect to the control criteria. Through its supermatrix, whose elements are themselves
matrices or column priorities, the ANP captures the outcome of dependence and feedback within
and between clusters and elements (Thomas L. Saaty, 1999). Such feedback best captures the
complex effects of interplay in human society, especially when risk and uncertainty are involved.
ANP is a relatively simple, intuitive approach that can be accepted by managers and other
decision-makers (Meade and Presley, 2002).
ANP has been applied for various fields including transportation planning and management.
Piantanakulchai (2005) applied ANP model for highway corridor planning. The research
demonstrates how to empirically prioritize a set of alternatives by using ANP model. The paper
first reviews the planning issues related to the highway corridor planning. Then related
characteristics were used to structure the ANP model and scores were computed for prioritizing
the potential highway alignments. Shang et.al (2004) explored the potential of applying the
analytic network process (ANP) to evaluate transportation projects in Ningbo, China.
In this current study, the ANP is implemented as a decision making tool for public transportation
development programs. The following sections will explain the theoretical background of AHP
and ANP, the problem description, the decision model, the pairwise comparison and the synthesis
with benefit-cost analysis.
2. METHODOLOGY
2.1. Analytic Hierarchy Process (AHP)
The Analytic Hierarchy Process (AHP) for decision structuring and decision analysis was first
introduced by Saaty (Thomas L. Saaty, 1994; 1996 (1)). AHP allows a set of complex issues that
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have an impact on an overall objective to be compared with the importance of each issue relative
to its impact on the solution of the problem. AHP models a decision-making framework that
assumes a unidirectional hierarchical relationship among decision levels. The top element of the
hierarchy is the overall goal for the decision model. The hierarchy decomposes to a more specific
attribute until a level of manageable decision criteria is met. The hierarchy is a type of system
where one group of entities influences another set of entities (Meade and Presley, 2002). AHP
was developed due to the need to include criteria that are not measurable in an absolute sense.
The fact that AHP allows subjective judgments as well as quantitative information to enter into
the evaluation process simultaneously and provides decision- makers with better communication
make it an appealing decision-making aid (Shang et. al., 2004). The shortcoming of AHP is that
many decision problems can not be structure hierarchically because they involve the interaction
and dependence of higher level elements on lower level elements. Not only does the importance
of the criteria determines the importance of the alternatives as in a hierarchy, but also the
importance of the alternatives themselves determines the importance of the criteria (Thomas L.
Saaty, 1996 (2))
2.2. Analytic Network Process (ANP)
It is a suitable multi-criteria decision analysis (MCDA) to evaluate alternatives. It is a
generalization of the Analytic Hierarchy Process (AHP). The basic structures are networks. The
feedback structure does not have the top-to-bottom form of hierarchy but looks more like a
network, with cycles connecting its components of elements, which we can no longer call levels.
A network has cluster or elements, with the elements being connected to elements in another
cluster (outer dependence) or the same cluster (inner dependence). The priorities derived from the
pairwise comparison matrices are entered as parts of columns of a supermatrix. The supermatrix
represents the influence priority of an element on the left of the matrix on an element at the top of
the matrix (Thomas L. Saaty, 1996, Jose Figueira et.al, 2005).Whereas AHP models a decision
making framework that assumes a unidirectional hierarchical relationship among decision levels,
ANP allows for more complex interrelationships among the decision levels and attributes
(Thomas L. Saaty, 1999). Typically in AHP, the hierarchy decomposes from the general to a
more specific attribute until a level of manageable decision criteria is met. ANP does not require
this strictly hierarchical structure. Two-way arrows (or arcs) represent interdependence among
attributes and attribute levels, or if within the same level of analysis, a looped arc. The directions
of the arcs signify dependence. Arcs emanate from an attribute to other attributes that may
influence it. The relative importance or strength of the impacts on a given element is measured on
a ratio scale similar to AHP. A priority vector may be determined by asking the decision maker
for a numerical weight directly, but there may be less consistency, since part of the process of
decomposing the hierarchy is to provide better definitions of higher level attributes. The ANP
approach is capable of handling interdependence among elements by obtaining the composite
weights through the development of a “supermatrix.” (Meade and Presley, 2002, Thomas L.
Saaty, 1999)
3. PROCEDURES OF ANP
1. Develop the decision model: it can be represented as a directed hierarchy (like AHP) or the
hierarchy of networks with feedbacks. The relevant goal, criteria, alternatives, cost and
benefits, considerations etc. form a cluster and each cluster may have its elements in it.
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Elements are the entities in the system that interacts with each other. They could be a unit of
decision makers, stakeholders, criteria or sub criteria (if exists), possible outcomes, and
alternatives etc. In complex system which contains a great number of elements it would be
very time consuming to measure relative importance of each element with every single
element in the system. Instead, elements which share similar characteristics are usually
grouped into cluster. The determination of relative weights mentioned above is based on
pairwise comparison as in the standard AHP (Piantanakulchi, 2005)
Figure 1 Framework of the AHP and ANP model
2. Perform a pairwise comparison among the clusters and elements interacting in the decision
system using a scale of preference as given in table 1.
Table 1 Scale of preference between two elements
Level of
importance Definition Explanation
1 Equally preferred Two activities contribute equally to the objective
3 Moderately
preferred
Experience and judgment slightly favor one activity over
the other
5 Strongly preferred Experience and judgment strongly or essentially favor one
activity over the other
7 Very strongly
preferred
An activity is strongly favored over another and its
dominance demonstrated in practice
9 Extremely
preferred
The evidence favoring one activity over another is of the
highest degree possible of affirmation
2, 4, 6, 8 Intermediate values Used to represent compromise between the preferences
listed above
Reciprocals Reciprocals for inverse comparison
Cluster 2
Element 1
Element 2
Element 3
Cluster 1
Element 1
Element 2
Element 3
Cluster 3
Element 1
Element 2
Element 3
Cluster 4
Element 1
Element 2
Element 3
Outer dependence
Inner dependence
Feedback GOAL
Criteria 2
Criteria 3
Criteria 1
Alternative
2
Alternative
3
Alternative
1
AHP STRUCTURE
ANP STRUCTURE
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When n elements in the cluster (e.g., criteria) are compared in a pairwise mode with respect to a
common property or controlling element (e.g., goal element), n(n-1)/2 questions are needed to
elicit value judgments from the decision maker and fill up the pairwise comparison matrix.
(1)
3. Calculate the local priority weight (eigenvector) of the matrix obtained from step 2. Measure
the consistency using the following formula:
CR=RIn
n
)1(
max
−
−λ (2)
Where λmax is the principal eigenvalue, n is number of elements to be compared and RI is the
random consistency index given in the following table that depends on n. Saaty recommends that
the CR (consistency ratio) must be less than 0.1 to 0.2 for the judgment to be considered
acceptable (Satty, 1980).
n 1 2 3 4 5 6 7 8 9 10
RI 0 0 0.58 0.9 1.12 1.24 1.32 1.41 1.45 1.49
4. Form the initial supermatrix from the priority indices (eigenvectors) obtained in step 3.
5. Transform the initial (unweighted) supermatrix to the weighted or stochastic supermatrix by
cluster weighting and normalization so that the column sum equal to 1.
6. Finally compute the limiting priorities of the weighted supermatrix. This can be done by
raising the weighted matrix to the large power until it converges to the limit.
limWk
(4)
k→∞
Then, these priorities are normalized according to the clusters to provide the overall relative
priorities.
1 … a1n
. . . . . . . . . an1 … 1
A= Where aij = 1/aji
wi1j1 wi1j2… wi1jnj
wi2j1 wi2j2 … wi2jnj
. . .
. . .
winj1 winj2 … winjnj
Wij=
C1
C2
CN
e11 e12 …e1n1 e21 e22 …e2n2 eN1 eN2 …eNnN
W11 W12… W1N
W21 W22 … W2N
. .
. .
WN1 WN2 … WNN
C1 C2 CN
e11
e12
.
e1n1
e21
e22
.
e2n2
.
eN1
eN2
.
.eNnN
W=
Wij is the eigenvector or priority weight
(3)
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4. PROBLEM DESCRIPTION AND BACKGROUND OF THE CASE STUDY AREA
Addis Ababa is the capital city of the Federal Democratic Republic of Ethiopia, located in the
centre of the country. Established in 1886, the city has experienced several planning changes that
have influenced its physical and social growth. The area of Addis Ababa is 530.14 square
kilometers. The current population of the city is 2.57 million (2005 estimate), which is about 3.9
percent of the population of Ethiopia. It also represents about 26 percent of the urban population
of Ethiopia. Addis Ababa has an aggregate population density of 4847.8 persons per square
kilometer. Public transport in the city consists of conventional bus services provided by the
publicly owned Anbessa City Bus Enterprise, taxis operated by the private sector, and buses used
exclusively for the employees of large government and private companies. The role of bicycles in
urban transport is insignificant because of topographic inconvenience (The World Bank African
Region Scoping Study, 2002). Buses provide 40% of the public transport in the city where as
taxis account for 60% (ERA, 2005). There is no rail transit within the city.
Figure 2 The city of Addis Ababa
The city is currently experiencing a horizontal growth, but the bus service has not exhibited
growth proportionate enough to accommodate this. The analysis results of the transit availability
indices show that only the center of the city is being served by the existing bus networks while
urban expansion areas have low transit availability (Mintesnot & Takano, 2006). Taxis have
many constraints in their operation including bad behavior of divers, excessive fare, and high
accident rate. The road network of Addis Ababa is limited in extent and right of way. Its capacity
is low, on-street parking is prevalent and the pavement condition is deteriorating. Despite a large
volume of pedestrians, there are no walkways over a large length (63%) of the roadway network.
This is a major concern, especially as it contributes to the increased pedestrian involvement in
traffic accidents (10,189 accidents occurred in 2004) (ERA, 2005). The city’s traffic and
transportation problems are numerous and highly linked with the socio-economic condition of
citizens, the financial and institutional matters, management and politics. The major problem is
luck of well-integrated public transportation modes such as bus rapid transit and light rail transit.
For the 3 million population city, providing a regular bus service with only one Bus Company of
limited fleet size can not cater the demand.
Addis Ababa
Inner Zone
Intermediate Zone
Expansion Zone
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Figure 3 Problem description
5. FORMING THE HIERARCHICAL NETWORKS
Based on the problem descriptions, the hierarchical networks are generated. Five links are created
with nodes to be the goal, the criteria and the alternatives. The dominance between the three
clusters (goal, criteria and alternatives) and among the elements is formulated. The goal, which is
developing well-integrated public transportation in the city, is formed to have dominance on both
the criteria and the alternatives. The feedback link is also created to weigh the criteria in terms of
the alternatives. An inner dependence is formulated that the criteria ‘capital cost’ would have
relative dominance on the other criteria, as for a project under financial constraints, other criteria
are also influenced by the capital cost.
Figure 4 Decision Model
Public transportation problems
Buses are the only public transit mode in the city. There is no
rail transit or bus priority lane. Only one Bus Company with
limited fleet size is providing a service for 3 million Pop.
Big gap b/n
demand and supply
Poor Accessibility
Low bus frequency
Poor bus information system
Developing well-integrated
public transportation in
the city
Capital cost
BRT LRT Co
nfl
icti
ng
con
sid
erat
ion
s fo
r
pu
blic
tra
nsp
ort
d
evel
op
men
t
AHP??
ANP??
Cluster 1
GOAL
Cluster 2
ALTERNATIVES EXB
BRT
LRT
BRT-LRT
Cluster 2
CRITERIA
1
2
3
5
4EB
SEB
CA
CC
Benefits Cost
Control hierarchy LINK 1- Goal to
criteria- outer
dependence
LINK 2- Criteria to
alternatives- outer
dependence
LINK 3-
Alternatives to
criteria- feedback
LINK 4- Among
criteria- inner
dependence
LINK 5- Goal to
alternatives- outer
dependence
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Table 2 Clusters and elements in the decision model
CLUSTERS ELEMENTS EXPLANATIONS
Goal To develop an integrated public transportation in the city of Addis Ababa
Capital cost (CC) Investment for construction, equipment, facilities etc.
Capacity (CA) Carrying capacity to tackle the travel demand
Environmental benefit (EB) Reduction of CO2, noise, etc.
Criteria
Socio-economic benefit
(SEB)
Creating employment and other economic activities, social
interactions, benefits in reducing accidents, etc
Expand existing bus
service (EXB)
Adding the number of buses and extending bus route
networks to the urban expansion areas
Introduce Bus Rapid
Transit (BRT)
Bus Rapid Transit development with bus priority lanes,
having the existing bus networks as a feeder routes
Introduce Light Rail
Transit (LRT)
Light Rail Transit development at high travel demand areas,
having the existing bus networks as feeder routes
Alternatives
The combination of
BRT and LRT
Implementing both the Bus Rapid Transit and Light Rail
Transit, having the existing bus networks as feeder routes
6. PAIRWISE COMPARISON MATRIX
Pairwise comparison is a method implemented to decision-making using AHP. To make a
pairwise comparison, one needs a hierarchic or network structure to represent the problem, as
well as pairwise comparisons to establish relations within the structure. The pairwise
comparisons are the steps in AHP and ANP where the decision maker will compare two
components at a time with respect to the upper level cluster or element. In the discrete case these
comparisons lead to dominance matrices, from which ratio scales are derived in the form of
principal eigenvectors. These matrices are positive and reciprocal, e.g., aij=1/aij. In this study 11
sets of pairwise comparisons are formulated for 5 identified links in which the relationship is
created. Link I is the pairwise comparison between the goal and the criteria. It is an outer
dependence, assuming the goal has dominance over the criteria. In Link II the pairwise
comparison between the criteria and the alternatives is created. It is obvious that in any decision
making process the criteria affect the choices. Link III is created to make a feedback influence
from the alternatives towards the criteria. In real situations, unlike hierarchical considerations in
AHP, the choices can have dominance on the criteria. Link IV is the inner dependence among the
criteria. In this case only one criteria (capital cost) is chosen to have a dominance on the rest of
the criteria. The last link, link V is the outer dependence between the goal and the alternatives.
The detailed characteristics of the pairwise comparison are discussed in the next sections based
on the aggregated (through consensus) responses of certain respondents.
6.1. Outer dependence between the goal and criteria
In this case, the relative importance of the criteria with respect to the goal is formulated. Among
the four chosen criteria, capital cost is found out to be relatively the most important consideration
for developing integrated public transportation in the city. Knowing the financial situation of the
national as well as the municipal governments, one may not be surprised that the capital cost is an
important consideration for huge projects like public transport development in the city. The
second important criterion is the capacity in which the proposed public transport would cater the
existing high demand. The environmental benefit and socio-economic benefits got small value in
terms of the goal.
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Table 3 Pairwise comparison matrix of criteria in terms of goal
Goal CC CA EB SEB e-vector
CC 1 3 7 7 0.5655
CA 1/3 1 5 5 0.2802
EB 1/7 1/5 1 1/3 0.0553
SEB 1/7 1/5 3 1 0.0990
λmax=4.3537 CI=0.1179 CR=0.1310
6.2. Outer dependence between the criteria and alternatives
This step measures the relative preference of alternatives in terms of the criteria. This can answer
which alternative is preferable in terms of each criteria and it directly leads to the synthesis, if
AHP model is considered. In the case of ANP, further networks should be analyzed in order to
get a synthesis result. According to the result of this pairwise comparison, expanding existing bus
service is favored in terms of capital cost, as it is fairly cheaper than developing BRT or LRT.
With respect to capacity, the combination of BRT and LRT is preferred as it can accommodate
high number of users at a time. Environmental benefit favors LRT; coinciding with the real
situation in which LRT uses electric power, so that it reduces gas emission. Socio-economic
benefit favors the combination of BRT and LRT.
Table 4 Pairwise comparison matrix of alternatives in terms of capital cost
CC EXB BRT LRT BRT-LRT e-vector
EXB 1 3 5 7 0.5579
BRT 1/3 1 3 5 0.2633
LRT 1/5 1/3 1 3 0.1219
BRT-LRT 1/7 1/5 1/3 1 0.0569
λmax=4.1767 CI=0.0589 CR=0.0654
Table 5 Pairwise comparison matrix of alternatives in terms of capacity
CA EXB BRT LRT BRT-LRT e-vector
EXB 1 1/3 1/5 1/7 0.0569
BRT 3 1 1/3 1/5 0.1219
LRT 5 3 1 1/3 0.2633
BRT-LRT 7 5 3 1 0.5579
λmax=4.1767 CI=0.0589 CR=0.0654
Table 6 Pairwise comparison matrix of alternatives in terms of EB
EB EXB BRT LRT BRT-LRT e-vector
EXB 1 1 1/9 1/5 0.0685
BRT 1 1 1/5 1/3 0.0894
LRT 9 5 1 3 0.5831
BRT-LRT 5 3 1/3 1 0.2589
λmax=4.1236 CI=0.0412 CR=0.0458
Table 7 Pairwise comparison matrix of alternatives in terms of SEB
SEB EXB BRT LRT BRT-LRT e-vector
EXB 1 1/3 1/3 1/5 0.0765
BRT 3 1 1/3 1/5 0.1360
LRT 3 3 1 1/3 0.2445
BRT-LRT 5 5 3 1 0.5430
λmax=4.2691 CI=0.0897 CR=0.0997
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6.3. Feedback between the criteria and alternatives
Up to this step, the hierarchy of levels was discussed without considering the feedback and the
inner dependence. However, in reality, there is the two way influence between the criteria and the
alternatives. i.e. the alternatives affect the criteria too. That is what AHP can’t do because of the
inflexible nature of hierarchies, but possible in ANP. In this case study, the pairwise matrix to
measure relative dominance of the criteria in terms of the alternatives is formulated. The criteria
‘capacity’ is relatively important in terms of an alternative ‘expanding the existing bus service’.
According to the previous AHP output, expanding the existing bus service is relatively cheap;
therefore, the probable consideration would not be capital cost but tackling the existing demand.
‘Capital cost’ is the first consideration with respect to alternative ‘introducing BRT’ with the e-
vector of 0.5579. The same dominance is observed in the case of alternative ‘introducing LRT’
with the e-vector of 0.6248. Both alternatives require a huge investment for implementation, thus
it is not surprising that the important factor for alternatives ‘the combination of BRT and LRT’ is
the ‘capital cost’.
Table 8 Pairwise comparison matrix of criteria in terms of EXB
EXB CC CA EB SEB e-vector
CC 1 1/5 3 1/3 0.1360
CA 5 1 5 3 0.5430
EB 1/3 1/5 1 1/3 0.0765
SEB 3 1/3 3 1 0.2445
λmax=4.2691 CI=0.0897 CR=0.0997
Table 9 Pairwise comparison matrix of criteria in terms of BRT
BRT CC CA EB SEB e-vector
CC 1 3 7 5 0.5579
CA 1/3 1 5 3 0.2633
EB 1/7 1/5 1 1/3 0.0569
SEB 1/5 1/3 3 1 0.1219
λmax=4.1767 CI=0.0589 CR=0.0654
Table 10 Pairwise comparison matrix of criteria in terms of LRT
LRT CC CA EB SEB e-vector
CC 1 3 9 7 0.6248
CA 1/3 1 3 3 0.2221
EB 1/9 1/3 1 1 0.0740
SEB 1/7 1/3 1 1 0.0790
λmax=4.0136 CI=0.0045 CR=0.0050
Table 11 Pairwise comparison matrix of criteria in terms of BRT-LRT
BRT-LRT CC CA EB SEB e-vector
CC 1 5 9 5 0.6157
CA 0 1 5 3 0.2212
EB 0 0 1 0 0.0489
SEB 0 0 3 1 0.1143
λmax=4.3214 CI=0.1071 CR=0.1190
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6.4. Inner dependence among the criteria
Among the criteria, it is understood that only ‘capital cost’ could have dominance over the
remaining criteria. For example, high capacity public transportation requires high investment and
environmental friendly public transport also has to do with cost. Therefore, the inner dependence
between the capital cost and other criteria is formulated. Leaving the dominance of capital cost
over itself, capacity is found out to be important criteria that affect the criteria ‘capital cost’
Table 12 Pairwise comparison matrix of CC in terms of other criteria
CC CC CA EB SEB e-vector
CC 1 3 5 5 0.5230
CA 1/3 1 5 5 0.3132
EB 1/5 1/5 1 1 0.0819
SEB 1/5 1/5 1 1 0.0819
λmax=4.2498 CI=0.0833 CR=0.0925
6.5. Outer dependence between the goal and the alternatives
Unlike hierarchical consideration of AHP, ANP allows the bottom-up relationship of cluster and
elements. Not only the relative importance of the criteria in terms of goal is derived, but in real
situation, the goal has a direct effect on the alternatives. The general vision of the project can be
derived from this step. In this case study, Introducing the combination of BRT and LRT is
favored with respect to the goal of developing an integrated public transportation in the city (e-
vector = 0.6679). LRT got the second biggest e-vector (0.2633). Expanding the existing bus
service is the least preferable with respect to the goal.
Table 13 Pairwise comparison matrix of alternatives in terms of the goal
Goal EXB BRT LRT
BRT-
LRT e-vector
EXB 1 1/3 1/5 1/7 0.0569
BRT 3 1 1/3 1/5 0.1219
LRT 5 3 1 1/3 0.2633
BRT-LRT 7 5 3 1 0.5579
λmax=4.1767 CI=0.0589 CR=0.0654
7. INITIAL, WEIGHTED AND LIMITED SUPERMATRICES
Recalling the theoretical explanation in step 4 of section 3, CN denotes the Nth
cluster, eNn denotes
the nth
element in the Nth
cluster, and Wij block matrix consists of the collection of the priority
weight vectors (w) of the influence of the elements in the ith
cluster with respect to the jth
cluster.
If the ith
cluster has no influence to the jth
cluster then Wij = 0. The matrix obtained in this step is
called the initial supermatrix. As stated earlier, the pairwise comparison is performed and the
eigenvector obtained from cluster level comparison as well as the element level comparison (e.g.,
the criterion capital cost and other criteria) are used to form the initial supermatrix. The initial
(unweighted) supermatrix can be transformed to the stochastic (weighted) supermatrix by cluster
weighting and normalization so that the column sum equal to one (see table 15). The stable
limiting priorities of the weighted supermatrix can be calculated by raising the stochastic
supermatrix to a large power until it converges to the limit as indicated in equation 4.
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Table 14 Initial supermatrix
GOAL EXB BRT LRT BRT/LRT CC CA EB SEB
GOAL 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
EXB 0.0569 1.0000 0.0000 0.0000 0.0000 0.5579 0.0569 0.0685 0.0765
BRT 0.1219 0.0000 1.0000 0.0000 0.0000 0.2633 0.1219 0.0894 0.1360
LRT 0.2633 0.0000 0.0000 1.0000 0.0000 0.1219 0.2633 0.5831 0.2445
BRT/LRT 0.5579 0.0000 0.0000 0.0000 1.0000 0.0569 0.5579 0.2589 0.5430
CC 0.5655 0.1360 0.5579 0.6248 0.6157 0.5230 0.0000 0.0000 0.0000
CA 0.2802 0.5430 0.2633 0.2221 0.2212 0.3132 1.0000 0.0000 0.0000
EB 0.0553 0.0765 0.0569 0.0740 0.0489 0.0819 0.0000 1.0000 0.0000
SEB 0.0990 0.2445 0.1219 0.0790 0.1143 0.0819 0.0000 0.0000 1.0000
sum 3.0000 3.0000 3.0000 3.0000 3.0000 3.0000 3.0000 3.0000 3.0000
Table 15 Weighted supermatrix
GOAL EXB BRT LRT BRT/LRT CC CA EB SEB
GOAL 0.3333 0.3333 0.3333 0.3333 0.3333 0.3333 0.3333 0.3333 0.3333
EXB 0.0190 0.3333 0.0000 0.0000 0.0000 0.1860 0.0190 0.0228 0.0255
BRT 0.0406 0.0000 0.3333 0.0000 0.0000 0.0878 0.0406 0.0298 0.0453
LRT 0.0878 0.0000 0.0000 0.3333 0.0000 0.0406 0.0878 0.1944 0.0815
BRT/LRT 0.1860 0.0000 0.0000 0.0000 0.3333 0.0190 0.1860 0.0863 0.1810
CC 0.1885 0.0453 0.1860 0.2083 0.2052 0.1743 0.0000 0.0000 0.0000
CA 0.0934 0.1810 0.0878 0.0740 0.0737 0.1044 0.3333 0.0000 0.0000
EB 0.0184 0.0255 0.0190 0.0247 0.0163 0.0273 0.0000 0.3333 0.0000
SEB 0.0330 0.0815 0.0406 0.0263 0.0381 0.0273 0.0000 0.0000 0.3333
sum 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
Table 16 Limited supermatrix
GOAL EXB BRT LRT BRT/LRT CC CA EB SEB
GOAL 0.3333 0.3333 0.3333 0.3333 0.3333 0.3333 0.3333 0.3333 0.3333
EXB 0.0564 0.0564 0.0564 0.0564 0.0564 0.0564 0.0564 0.0564 0.0564
BRT 0.0509 0.0509 0.0509 0.0509 0.0509 0.0509 0.0509 0.0509 0.0509
LRT 0.0810 0.0810 0.0810 0.0810 0.0810 0.0810 0.0810 0.0810 0.0810
BRT/LRT 0.1450 0.1450 0.1450 0.1450 0.1450 0.1450 0.1450 0.1450 0.1450
CC 0.1471 0.1471 0.1471 0.1471 0.1471 0.1471 0.1471 0.1471 0.1471
CA 0.1168 0.1168 0.1168 0.1168 0.1168 0.1168 0.1168 0.1168 0.1168
EB 0.0254 0.0254 0.0254 0.0254 0.0254 0.0254 0.0254 0.0254 0.0254
SEB 0.0440 0.0440 0.0440 0.0440 0.0440 0.0440 0.0440 0.0440 0.0440
8. SYNTHESIS AND DISCUSSION
The target of the analysis is to synthesize the priorities of alternatives. The AHP model can be
synthesized by considering only the three links (goal→criteria→alternatives) whereas in ANP the
limiting priorities gives the result after normalizing the result according to clusters to provide the
overall relative priorities. In the distributive mode, the weight of the alternatives or the criteria
can be obtained from the limit supermatrix, which is normalized to yield a unique estimate of a
ratio scale underlying the judgments. In ideal mode, the weights of the alternatives or the criteria
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obtained from the limit supermatrix are divided by the value of the highest rated alternative. In
this manner the newly added alternative that is dominated everywhere can not cause reversal in
the ranks of the existing alternatives (Thomas L. Saaty, 1994)
According to the AHP model, the importance of the capital cost exhibited with higher
eigenvector (0.5655) followed by the capacity (0.2802). This relative importance of the criteria in
terms of the goal brought a synthesis result of choosing alternative 1 which is expanding the
existing bus service in the city followed by the combination of BRT and LRT. Without
considering the feedback (outer dependence) and the inner dependence, environmental and socio-
economical benefits got a little attention with eigenvector of 0.0553 and 0.0990 respectively. It is
obvious that, one who considers the capital cost would definitely go for the cheapest alternative
instead of investing on BRT and LRT. However, with the consideration of inner dependence,
feedback and outer dependence (ANP model), the relative importance of the criteria is changed
(not in sequence but in value). The environmental and socio-economical benefits got a higher
value which indicates that a strong relation between the cluster and elements give a more clear
result. According to the ANP model, the combination of BRT and LRT got a first priority
followed by introducing LRT. Expanding the existing bus service got the third ranking.
Therefore, environmental and socio-economical consideration contributed for the change of the
result.
Table 17 Synthesized result
ANP AHP
Clusters and elements Raw Distributive Ideal Distributive
EXB 0.0564 0.1692 0.3890 0.3428
BRT 0.0509 0.1528 0.3513 0.2015
LRT 0.0810 0.2431 0.5588 0.1992
BRT & LRT 0.1450 0.4350 1.0000 0.2566
Cluster sum 0.3333 1.0000 2.2991 1.0000
CC 0.1471 0.4414 1.0000 0.5655
CA 0.1168 0.3504 0.7937 0.2802
EB 0.0254 0.0762 0.1725 0.0553
SEB 0.0440 0.1321 0.2992 0.0990
Cluster sum 0.3333 1.0000 2.2654 1.0000
Figure 5 Synthesis results of alternatives Figure 6 Criteria weights in terms of the goal
0
0.1
0.2
0.3
0.4
0.5
EXB
BRT
LRT
BRT & LRT
ANP AHP
0
0.1
0.2
0.3
0.4
0.5
0.6
CC CA EB SEB
Criteria
Weig
ht
ANP AHP
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The study is extended to the benefit-cost analysis based in the eigenvector weights of the criteria
except the cost. The estimated capital costs are normalized to be considered as a ‘cost’ in the
analysis. The priority weights of other criteria are considered as the ‘benefit’. Environmental and
socio-economic benefits are originally designed as ‘benefit’, and the providing high capacity is
added as a benefit of providing an integrated public transportation in the city. According to the
result, the combination of BRT and LRT got higher benefit over the cost followed by expanding
the existing bus.
Table 18 Benefit-Cost analysis Capital cost Priority Index (PI) or Benefit
Alternatives Estimated Normalized(a) CA EB SEB
PI-
ANP(b)
PI/
Cost(b/a)
EXB 15METB/km* 0.0667 0.0569 0.0685 0.0765 0.1692 2.538
BRT 35 METB/km* 0.1556 0.1219 0.0894 0.1360 0.1528 0.982
LRT 100 METB/km* 0.4444 0.2633 0.5831 0.2445 0.2431 0.547
BRT-LRT 75 METB/km* 0.3333 0.5579 0.2589 0.5430 0.4350 1.305
Sum 220 METB/km 1 1 1 1 1 *METB/km = Million Ethiopian Birr (1USD = 8.8 ETB)
*The costs for BRT and LRT are estimated by the Addis Ababa Master Plan Revision Office
2.538
0.982285714
0.546975
1.305
0.00
0.50
1.00
1.50
2.00
2.50
3.00
Alternatives
PI/c
ap
ita
l c
os
t
Series1 2.538 0.982285714 0.546975 1.305
EXB BRT LRT BRT-LRT
Figure 7 Benefit-cost results
9. CONCLUSIONS
In this paper, the multi-criteria decision making model is explored using supermatrix approach
for public transport development programs. Analytic Network Process (ANP) is developed based
on the hierarchical model (AHP) and the results are compared. The ANP signifies better the
complex real-world problem as it allows for feedback and interdependency among various
decision levels such as clusters and elements. The relative dominance of the criteria with respect
to the goal can be shown clearly in ANP. The model can be developed further by performing a
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multi-participant decision making process, by diversifying criteria, and the control hierarchy.
Since the public transportation projects face diversified, conflicting and interrelated
considerations, additional factors should be added to utilize the model fully. The decision maker
should be carefully selected comprising the technical, political and community representatives.
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