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7/30/2019 Contractor Selection AHP
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Construction Management and Economics (December 2004) 22, 10211032
Construction Management and Economics
ISSN 0144-6193 print/ISSN 1466-433X online 2004 Taylor & Francis Ltd
http://www.tandf.co.uk/journals
DOI: 10.1080/0144619042000202852
*Author for correspondence. E-mail: [email protected]
Contractor selection using the analytic network
process
EDDIE W. L. CHENG and HENG LI*
Department of Building and Real Estate, The Hong Kong Polytechnic University, Hunghom, Kowloon, Hong Kong
Received 30 January 2003; accepted 9 January 2004
Contractor selection is one of the main activities of clients. Without a proper and accurate method for selecting
the most appropriate contractor, the performance of the project will be affected. The multi-criteria decision-
making (MCDM) is suggested to be a viable method for contractor selection. The analytic hierarchy process
(AHP) has been used as a tool for MCDM. However, AHP can only be employed in hierarchical decisionmodels. For complicated decision problems, the analytic network process (ANP) is highly recommended since
ANP allows interdependent influences specified in the model. An example is demonstrated to illustrate how this
method is conducted, including the formation of supermatrix and the limit matrix.
Keywords: Analytic network process, analytic hierarchy process, multi-criteria decision making, contractor
selection
Introduction
Contractor selection is one of the main decisions made
by the clients. In order to ensure that the project can becompleted successfully, the client must select the most
appropriate contractor. This involves a procurement
system that comprises five common process elements:
project packaging, invitation, pre-qualification, short-
listing and bid evaluation (Hatush, 1996; Hatush and
Skitmore, 1997). Moreover, there are methods attemp-
ting to estimate the values of contractors by using various
selection criteria (e.g. Samuelson and Levitt, 1982;
Jaselskis and Russell, 1990). These methods include
multi-criteria decision-making (MCDM), multi-
attribute analysis (MAA), multi-attribute utility theory
(MAUT), multiple regression (MR), cluster analysis
(CA), bespoke approaches (BA), fuzzy set theory (FST)and multivariate discriminant analysis (MDA) (Hatush
and Skitmore, 1997; Holt, 1998; Mahdi et al., 2002).
Selection criteria on the other hand can be classified as
pre-qualification and project-specific (Alarcon and
Mourgues, 2002).
Among those well-known methods, MCDM is
relatively new to be employed to select contractors.
MCDM aims at using a set of criteria for a decision
problem. Since these criteria may vary in the degree of
importance, the analytic hierarchy process (AHP) tech-
nique is employed to prioritize the selection criteria (i.e.assign weights to the criteria). In the existing literature
of contractor selection, studies have utilized AHP to set
up a hierarchical skeleton within which multi-attribute
decision problems can be structured (e.g. Fong and
Choi, 2000; Mahdi et al., 2002). Conceptually, AHP
is only applicable to a hierarchy that assumes a uni-
directional relation between decision levels. The top
level of the hierarchy (apex) is the overall goal for the
decision model, which decomposes to a more specific
level of elements until a level of manageable decision
criteria is met (Meade and Sarkis, 1999). Yet, the strict
hierarchical structure may need to be relaxed whenmodelling a more complicated decision problem that
involves interdependencies between elements of the
same cluster or different clusters. This requires the
generic analytic method the analytic network process
(ANP) that can evaluate multidirectional relationship
among decision elements (Saaty, 1988; Meade and
Sarkis, 1998).
In most studies of contractor selection, selection
criteria are assumed to be independent of each other.
7/30/2019 Contractor Selection AHP
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1022 Cheng and Li
Apparently, these criteria are likely to affect each other.
For example, Fong and Choi (2000) used a sample
of 13 respondents to identify and prioritize eight un-
correlated criteria (tender price, financial capability,
past performance, past experience, resources, current
workload, past relationship and safety performance) for
contractor selection. In fact, the eight criteria are
interrelated to a certain extent. For example, good past
experience may lead to good safety performance if the
past experience includes good safety records. Good past
performance and experience are good evidence of suc-
cessful projects, which in turn results in strong financial
capability. Resources and financial capability may be
positively correlated. Tender price may be negatively
related to other criteria. Therefore, ANP is more
favourable to be employed in this interdependent
relationship framework. Since ANP is new to the
construction field, this study will demonstrate how to
apply ANP to improve the prioritization of contractor
selection criteria. It is expected that by using ANP,clients are able to establish a complete decision model
without sacrificing the validity due to limitations of the
analytical tool.
Contractor selection
Existing literature on contractor selection mainly deals
with how to identify and assess the criteria to make the
most appropriate decisions (Holt, 1997). A more pro-
mising approach to classifying the contractor selection
criteria has been provided by Hatush and Skitmore
(1997), who focused on two of the five-stage process ofcontractor selection: (1) pre-qualification, and (2) bid
evaluation. Holt (1998) and Valentine (1995) referred
to this as a two-stage procedure: (1) pre-qualification,
and (2) evaluation of tenderers. Figure 1 illustrates a
typical bespoke approach that shows where these stages
are located.
Pre-qualification is the process that compares the key
contractor-organizational criteria among a group of
contractors desirous to tender. Such criteria can be past
performance, past experience, and financial stability. In
order to identify the contractor-organizational criteria,
researchers have proposed useful methods, such as
MAA (e.g. Russell and Skibniewski, 1987; Russell et al.,
1992; Holt et al., 1994).
Evaluation of contractors on the other hand considers
specific criteria that can measure the suitability of con-
tractor for the proposed project (Holt, 1998). Contrac-
tor evaluation is not equivalent to contractor selection.
Specifically, contractor evaluation is the process of
investigating or measuring project-specific attributes,
while contractor selection refers to as the process of
aggregating the results of evaluation to identify
optimum choice. In practice, these two processes are
always grouped together to represent a single procedure
to prioritize the contractors according to the project spe-
cific criteria, which can be office location with respect to
the project, experience in the geographical region, and
experience of the proposed construction methods.
There are methods apt to identify project-specific
criteria. For example, MAUT is one of the current
available techniques (Alarcon and Mourgues, 2002).
MAA, MAUT and AHP are comparable methods
that assign weights to selection criteria (Holt, 1998;
Alarcon and Mourgues 2002). Table 1 illustrates their
respective formula to show why their functions are alike
(Holt, 1998). As shown in Table 1, these contractor
evaluation methods are known to calculate an aggregate
(or composite) score for each criterion. The differences
between these methods are that: (1) MAA and AHP use
Figure 1 A simplified bespoke approach (note: this simpli-
fied bespoke approach (BA) is typically run in a large client in
Hong Kong. It may be different from other BAs (e.g. Holt,
1998)
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1023Contractor selection using analytic network process
simple scoring for rating the criteria, while MAUT
makes use of utility value; and (2) AHP employs pair-
wise comparison for determining the weights, while
MAA and MAUT use simple scoring. Yet, Mahdi et al.(2002) suggested that AHP could be the weighting
method incorporated into MAA or MAUT. When con-
sidering that the criteria are somewhat related and what
Holt (1997) mentioned about the rationalization,
resource saving and objectivity, ANP (analytic network
process) would be a more reliable method to assign
weights to correlated attributes. This paper is not
intended to compare existing contractor evaluation
methods. Those who are interested in knowing more
about other methods may refer to Holt (1998).
AHP and ANP
AHP and ANP are two separate concepts introduced by
Saaty (1980, 1996). Saaty (1980) first developed the
AHP, which helps to establish decision models through
a process that contains both qualitative and quantitative
components. Qualitatively, it helps to decompose a
decision problem from the top overall goal to a set of
manageable clusters, sub-clusters, and so on down to
the final level that usually contains scenarios or alterna-
tives. The clusters or sub-clusters can be forces,
attributes, criteria, activities, objectives, etc. Quantita-
tively, it uses pair-wise comparison to assign weights to
the elements at the cluster and sub-cluster levels and
finally calculates global weights for assessment taking
place at the final level. Each pair-wise comparison
measures the relative importance or strength of the
elements within a cluster by using a ratio scale. One of
the main functions of AHP is to calculate the consis-
tency ratio to ascertain that the matrices are appropriate
for analysis (Saaty, 1980). Nevertheless, AHP models
assume that there are unidirectional relationships
between clusters of different decision levels along the
hierarchy and uncorrelated elements within each cluster
as well as between clusters. It is not appropriate for
models that specify interdependent relationships
in AHP. ANP is then developed to enhance the toolsanalytical power.
ANP is a generic form of AHP and allows for more
complex interdependent relationships among elements
(Saaty, 1996). It is also known as the systems-with-
feedback approach (Meade and Sarkis, 1998). Inter-
dependence can occur in several ways: (1) uncorrelated
elements are connected, (2) uncorrelated levels are con-
nected and (3) dependence of two levels is two-way (i.e.
bi-directional). Figure 2 illustrates examples of these
interdependencies. By incorporating interdependencies
Table 1 Comparison of MAA, MAUT and AHP
Method Formula Description
Multi-attribute n ACrj is the aggregate score for contractorj;
analysis (MAA) ACrj= SVijWi Vijis the attribute iscore with respect to contractorj;
i = 1 n is the number of attributes considered in the analysis;
Wi is the weighting indices to Vi
Multi-attribute utility n ACrj is the aggregate score for contractorj;theory (MAUT) ACrj= SUijWi Uijis the attribute iscore with respect to contractorj;
i = 1 n is the number of attributes considered in the analysis;
Wi is the weighting indices to UiAnalytic hierarchy n Cri is the composite score for contractor i;
process (AHP) Cri= SciVij ciis the relative weight for Viwith respect to contractorj;
i = 1 and Vijis the selection criterion iwith respect to contractorj
Note: Partially adapted from Holt (1998).
Figure 2 Examples of interdependence (notes: (1) uncorre-
lated elements are connected; (2) uncorrelated levels are
connected; (3) dependence of two levels is two-way (i.e.
bi-directional)
7/30/2019 Contractor Selection AHP
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1024 Cheng and Li
Figure3
Hierarchicalstructureofcontractorselection(source:FongandChoi,2000)
7/30/2019 Contractor Selection AHP
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1025Contractor selection using analytic network process
(i.e. addition of the feedback loops in the model), a
supermatrix will be developed. The supermatrix
adjusts the relative importance weights in individual
matrices to form a new overall matrix with the eigen-
vectors of the adjusted relative importance weights
(Meade and Sarkis, 1998). According to Sarkis (1999),
ANP comprises four main steps:
(1) Conducting pair-wise comparisons on the
elements at the cluster and sub-cluster levels;
(2) Placing the resulting relative importance
weights (eigenvectors) in submatrices within the
supermatrix;
(3) Adjusting the values in the supermatrix so that
the supermatrix can achieve column stochastic;
and
(4) Raising the supermatrix to limiting powers until
the weights have converged and remain stable.
Methodology
The current study revises the hierarchical model of
Fong and Choi (2000) by adding interdependent influ-
ences at the selection criteria level. Figure 3 illustrates
the original model being composed of four levels. At the
top level is the decision problem itself, while the bottom
level comprises the three decision alternatives (i.e. con-
tractor candidates). The criteria and sub-criteria repre-
sent the middle two levels. Figure 4 illustrates a general
view of the new decision network model. In this model,
the main difference from the original model is that there
Figure 4 The ANP network component
is a feedback loop in the selection criteria level. It is
assumed that the eight selection criteria are interdepen-
dent. Figure 4 also illustrates a clearer view of the inter-
relationship structure by the callout box. Moreover,
only four of the eight criteria have sub-criteria (see
Figure 3). It is worth noting that sub-criteria decom-
posed from their respective criterion are not assumed tobe interdependent.
Pair-wise comparisons
The normal procedure of a pair-wise comparison is to
invite experts to compare two sub-clusters elements
with respect to their respective clusters element. Saaty
(1980) has developed a 9-point priority scale of mea-
surement, with a score of 1 representing equal impor-
tance of the two compared elements and 9 being
overwhelming dominance of one element (row element)
over another element (column element). When there is
overwhelming dominance of a column element over arow element, a score of 1/9 is given. Figures 5 and 6
provide an illustration of the use of the scale to represent
the judgments generated in this study.
After having consulted with five construction pro-
fessionals, the pair-wise comparisons in this paper are
of three bases. First, this paper adopts the original
pair-wise comparison results in Fong and Choi (2000)
who compared the criteria and sub-criteria for the three
candidates, which had fifteen sets of judgment matrices.
Second, this paper adjusted part of the original relative
weights of the criteria with respect to the top goal and
7/30/2019 Contractor Selection AHP
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1026 Cheng and Li
those of the sub-criteria with respect to their respective
criteria. Figure 5 presents these five sets of judgment
matrices. Third, for synthesizing the relative weights
among the criteria, other pair-wise comparisons have
to be made for this study. This is to compare two criteria
with respect to a selected criterion. This requires
establishing eight additional sets of judgment matrices
for analysis. Figure 6 presents these eight paired
comparison matrices. For example, with respect to the
criterion tender price, financial capability is relatively
Figure 5 Relative weights of criteria and sub-criteria
more important than safety performance. Noteworthy,
clients should develop their own set of scores for
the criteria and sub-criteria matching their project
requirements.
Relative weights of elements and consistency
ratio of matrices
After the pair-wise comparison matrices are developed,
a vector of priorities (i.e. a proper or eigen vector) in
7/30/2019 Contractor Selection AHP
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1027Contractor selection using analytic network process
Figure 6 Criteria interdependency comparisons
7/30/2019 Contractor Selection AHP
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1028 Cheng and Li
Figure 6 Continued
7/30/2019 Contractor Selection AHP
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1029Contractor selection using analytic network process
each matrix is calculated and is then normalized to
sum to 1.0 or 100 per cent. This is done by dividing
the elements of each column of the matrix by the sum
of that column (i.e. normalizing the column); then,
obtaining the eigen vector (eVector) by adding the
elements in each resulting row (to obtain a row sum)
and dividing this sum by the number of elements in
the row (to obtain priority or relative weight)(Cheng and Li, 2002). Moreover, for ascertaining the
consistency of the judgment matrices, Saaty (1994)
suggested three threshold levels: (1) 0.05 for 3-by-3
matrix; (2) 0.08 for 4-by-4 matrix; and (3) 0.1 for all
other matrices. Those who want to know the algo-
rithm for computing consistency ratio may refer to
Saaty (1980) and Cheng and Li (2001). Figures 5 and
6 present the relative weights (priorities) and the CR
values for the comparison matrices.
Supermatrix and the limit matrix
With interdependent influences, the system that con-
sists of cluster and sub-cluster matrices must translate
to a supermatrix. This can be achieved by entering the
local priority vectors in the supermatrix, which in turn
obtains global priorities. Table 2 shows the super-
matrix for the ANP decision model. It contains the
weights (or priorities) for the judgment matrices.
After entering the sub-matrices into the super-
matrix and completing the column stochastic, the
supermatrix is then raised to sufficient large power
until convergence occurs (Saaty, 1996; Meade and
Sarkis, 1998). Table 3 presents the final limit matrix.
Each column is the same and provides the localrelative weights of individual sets of elements.
Discussions
The limit matrix shows the local relative weights for
all the elements in the supermatrix. In order to ascer-
tain the value of ANP, results of the normalized rela-
tive weights of the candidates obtained from ANP and
AHP are compared. Table 4 presents the local relative
weights of the three candidates based on the results
from ANP, as well as the local relative weights from
AHP. In the demonstrated example, candidate Ashould be chosen because it has the largest relative
weights (= 0.473, from ANP in Table 4). However, if
the decision model does not specify the interdepen-
dent relationships (i.e. only AHP model), candidate
B should have been selected since it had the largest
relative weights (= 0.448, from AHP in Table 4).
Candidate A was even the worst among all candi-
dates. It is because the ANP decision model has taken
into account the interdependencies among selection
criteria that exert extra influences on the model.
AHP has its limitation because it can only be applied in
simple hierarchical structures, while ANP provides pow-
erful capability in solving nowadays construction manage-
ment issues that involve more complicated decision
problems. It is not to say that results from AHP would be
different from those of ANP. It depends on the subjective
and/or objective ratings given to the judgment matrices.
However, when there are interdependent influences, ANP
is a viable method for prioritization. In this study, the
ANP method is applied in contractor selection, and ANP
enhances the increasingly popular multi-criteria decision-
making (MCDM) approach to criteria prioritization.
When researchers and practitioners have realized that
lowest-price is not the promising approach to attain the
overall lowest project cost upon project completion,
multi-criteria selection becomes more popular (Wong
et al., 2001). There are various methods used for multi-
criteria contractor evaluation. Multivariate statistical ana-
lytic methods are more quantitative in nature. Wong et al.
(2001) refer to them as the objective tender evaluationmethods. Yet, these methods need a sufficiently large
amount of respondents in order to ensure the objective
quality. Although researchers tend to believe the need for
identifying a set of general selection criteria using empiri-
cal surveys (Holt et al., 1995; Fong and Choi, 2000; Wong
et al., 2001), assigning weights to these general criteria is
however the internal business decisions made by indi-
vidual clients. In other words, the clients evaluate contrac-
tors according to the requirements of individual projects.
Basically, there are two types of projects: public and pri-
vate. There may be necessary to develop individual sets of
criteria for these project types. For example, there is an
expanding view that long-term or strategic partneringbecomes more appropriate in private projects procure-
ment. Hence, the relationship between the client and
the bidding contractors may be an important selection
criterion. On the other hand, the competitive tendering
process is still the current practice for public projects
although some may argue that it is becoming less popular.
The private relationship criterion would be inappropri-
ate when selecting contractors in the process of public
tendering.
In normal practices of contractor selection, only a small
group of experts (mainly the top management of the
client) is responsible for evaluating the contractor candi-
dates. In such circumstances, using the MCDM approach
to contractor selection is more plausible (Mahdi et al.,
2002). ANP and AHP can help assign weights to selection
criteria so as to increase the accuracy of judgments made
by experts. They are not only the decision tools appropri-
ate for contractor evaluation at both the pre-qualification
and project-specific stages but can also act as the quantita-
tive tools for assigning weights to criteria in other methods
(e.g. MAA and MAUT). These decision tools set the new
horizon for contractor selection by raising key processes of
7/30/2019 Contractor Selection AHP
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1030 Cheng and Li
Table2
Supermatrix(major
components)
Go
al
Selectioncriteria
Selectionsub-criteria
F.C.
P.P.
P.E.
R.
T.P.
F.C.
P.P.
P.E.
R.
C.W.
C.R.S.P.
F.S.
F.R.C
.C.C.O.
D.
A.Q.S.C.T.C.
E.A.
P.R.
H.R.
Goal
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.000
.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
Selection
T.P.0.38
0.00
0.56
0.33
0.31
0.21
0.20
0.17
0.18
0.00
0.000
.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
criteria
F.C.0.28
0.14
0.00
0.37
0.32
0.24
0.26
0.17
0.14
0.00
0.000
.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
P.P.
0.13
0.20
0.06
0.00
0.20
0.21
0.18
0.17
0.17
0.00
0.000
.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
P.E.
0.08
0.11
0.06
0.06
0.00
0.18
0.18
0.09
0.16
0.00
0.000
.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
R.
0.04
0.20
0.06
0.06
0.04
0.00
0.07
0.17
0.23
0.00
0.000
.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
C.W.0.03
0.11
0.06
0.06
0.04
0.09
0.00
0.17
0.03
0.00
0.000
.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
C.R.0.04
0.11
0.06
0.06
0.06
0.04
0.03
0.00
0.10
0.00
0.000
.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
S.P.
0.02
0.11
0.12
0.06
0.03
0.04
0.07
0.04
0.00
0.00
0.000
.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
Selection
F.C.F.S.
0.00
0.00
0.90
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.000
.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
sub-criteria
F.R.0.00
0.00
0.10
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.000
.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
P.P.C.C.0.00
0.00
0.00
0.71
0.00
0.00
0.00
0.00
0.00
0.00
0.000
.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
C.O.0.00
0.00
0.00
0.11
0.00
0.00
0.00
0.00
0.00
0.00
0.000
.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
D.
0.00
0.00
0.00
0.11
0.00
0.00
0.00
0.00
0.00
0.00
0.000
.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
A.Q.0.00
0.00
0.00
0.07
0.00
0.00
0.00
0.00
0.00
0.00
0.000
.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
P.E.S.C.0.00
0.00
0.00
0.00
0.48
0.00
0.00
0.00
0.00
0.00
0.000
.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
T.C.0.00
0.00
0.00
0.00
0.41
0.00
0.00
0.00
0.00
0.00
0.000
.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
E.A.0.00
0.00
0.00
0.00
0.11
0.00
0.00
0.00
0.00
0.00
0.000
.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
R.
P.R.0.00
0.00
0.00
0.00
0.00
0.50
0.00
0.00
0.00
0.00
0.000
.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
H.R.0.00
0.00
0.00
0.00
0.00
0.50
0.00
0.00
0.00
0.00
0.000
.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
Contractor
A
0.00
0.07
0.00
0.00
0.00
0.00
0.47
0.81
0.18
0.20
0.750
.18
0.80
0.69
0.77
0.73
0.40
0.12
0.75
0.69
candidates
B
0.00
0.65
0.00
0.00
0.00
0.00
0.08
0.07
0.59
0.40
0.060
.59
0.12
0.22
0.07
0.08
0.20
0.42
0.18
0.09
C
0.00
0.28
0.00
0.00
0.00
0.00
0.45
0.12
0.23
0.40
0.190
.23
0.08
0.09
0.16
0.19
0.40
0.46
0.07
0.22
Note:Allfiguresareroundedtotw
odecimalplaces.
7/30/2019 Contractor Selection AHP
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1031Contractor selection using analytic network process
Table3
Thelimitmatrix(lo
calprioritiesformajorcomponents)
G
oal
Selectioncrite
ria
Selectionsub-criteria
F.C.
P.P.
P.E.
R.
T.P.
F.C.
P.P.
P.E.
R.
C.W.
C.R.S.P.
F.S.F.R.C.C.C.O.
D.
A.Q.
S.C.
T.C.
E.A.
P.R.H.R.
Selection
T.P.0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.250.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
criteria
F.C.0.19
0.19
0.19
0.19
0.19
0.19
0.19
0.19
0.19
0.19
0.190.19
0.19
0.19
0.19
0.19
0.19
0.19
0.19
0.19
P.P.0.14
0.14
0.14
0.14
0.14
0.14
0.14
0.14
0.14
0.14
0.140.14
0.14
0.14
0.14
0.14
0.14
0.14
0.14
0.14
P.E.0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.100.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
R.
0.11
0.11
0.11
0.11
0.11
0.11
0.11
0.11
0.11
0.11
0.110.11
0.11
0.11
0.11
0.11
0.11
0.11
0.11
0.11
C.W.0.07
0.07
0.07
0.07
0.07
0.07
0.07
0.07
0.07
0.07
0.070.07
0.07
0.07
0.07
0.07
0.07
0.07
0.07
0.07
C.R.0.07
0.07
0.07
0.07
0.07
0.07
0.07
0.07
0.07
0.07
0.070.07
0.07
0.07
0.07
0.07
0.07
0.07
0.07
0.07
S.P.0.07
0.07
0.07
0.07
0.07
0.07
0.07
0.07
0.07
0.07
0.070.07
0.07
0.07
0.07
0.07
0.07
0.07
0.07
0.07
Selection
F.C.F.S.0.90
0.90
0.90
0.90
0.90
0.90
0.90
0.90
0.90
0.90
0.900.90
0.90
0.90
0.90
0.90
0.90
0.90
0.90
0.05
sub-criteria
F.R.0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.100.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.01
P.P.C.C.0.71
0.71
0.71
0.71
0.71
0.71
0.71
0.71
0.71
0.71
0.710.71
0.71
0.71
0.71
0.71
0.71
0.71
0.71
0.03
C.O.0.11
0.11
0.11
0.11
0.11
0.11
0.11
0.11
0.11
0.11
0.110.11
0.11
0.11
0.11
0.11
0.11
0.11
0.11
0.01
D.
0.11
0.11
0.11
0.11
0.11
0.11
0.11
0.11
0.11
0.11
0.110.11
0.11
0.11
0.11
0.11
0.11
0.11
0.11
0.01
A.Q.0.07
0.07
0.07
0.07
0.07
0.07
0.07
0.07
0.07
0.07
0.070.07
0.07
0.07
0.07
0.07
0.07
0.07
0.07
0.00
P.E.S.C.0.48
0.48
0.48
0.48
0.48
0.48
0.48
0.48
0.48
0.48
0.480.48
0.48
0.48
0.48
0.48
0.48
0.48
0.48
0.02
T.C.0.41
0.41
0.41
0.41
0.41
0.41
0.41
0.41
0.41
0.41
0.410.41
0.41
0.41
0.41
0.41
0.41
0.41
0.41
0.01
E.A.0.11
0.11
0.11
0.11
0.11
0.11
0.11
0.11
0.11
0.11
0.110.11
0.11
0.11
0.11
0.11
0.11
0.11
0.11
0.00
R.
P.R.0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.500.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.02
H.R.0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.500.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.02
Contractor
A
0.47
0.47
0.47
0.47
0.47
0.47
0.47
0.47
0.47
0.47
0.470.47
0.47
0.47
0.47
0.47
0.47
0.47
0.47
0.47
candidates
B
0.27
0.27
0.27
0.27
0.27
0.27
0.27
0.27
0.27
0.27
0.270.27
0.27
0.27
0.27
0.27
0.27
0.27
0.27
0.27
C
0.26
0.26
0.26
0.26
0.26
0.26
0.26
0.26
0.26
0.26
0.260.26
0.26
0.26
0.26
0.26
0.26
0.26
0.26
0.26
Notes:(1)Eachcolumnisthesam
e.(2)Allfiguresareroundedtotwodecimalplaces.
7/30/2019 Contractor Selection AHP
12/12
1032 Cheng and Li
decomposing a complex problem to a manageable
network or hierarchical structure, eliciting accurate
rating by employing pair-wise comparison and consis-
tency measure, and obtaining overall priority vector by
dependent and/or interdependent matrix computations.
Conclusions
ANP extends the function of AHP and is a viable
method for multi-criteria decision problems that involve
interdependent relationships. In order to highlight the
possible difference between the use of AHP and ANP,the results obtained from both supermatrix and limit
matrix are compared. The mathematics performed in
this research may not be familiar to every reader. Yet,
Saaty is now developing a software tool for conducting
ANP. Once the software tool is available for sale, a
much faster growing use of ANP can be anticipated.
Acknowledgement
This paper was financially supported by The Hong
Kong Polytechnic University under grant number
G-YW72.
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Table 4 Comparing the results from ANP and AHP
Candidate ANP AHP
A 0.473 0.262
B 0.271 0.448
C 0.255 0.290