multi-criteria decision making for public …

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: [email protected]

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: [email protected]

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

Journal of the Eastern Asia Society for Transportation Studies, Vol. 7, 2007

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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


224

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.


225

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


226

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)


227

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


229

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 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 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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