International Journal of Computer Applications (0975 8887)

Volume 28 No.10, August 2011

Prequalification of Construction Contractor

using a FAHP

M. K. Trivedi M. K. Pandey S. S. Bhadoria

Department of Civil Department of Civil SGSITS
Engineering Engineering Indore, INDIA
MITS, Gwalior, INDIA ITM, Gwalior, INDIA

ABSTRACT Multicriteria decision making problem involve six components

Analytical hierarchy process (AHP) as multiple criteria decision are discussed in [3] an [4] as follows;
making tools can be used in the problems with spatial nature like A goal or a set of goals the decision makers want to
selection of construction contractor. In this study the application achieve.
of AHP and its weakness and strength and ultimately the fuzzy The decision maker or a group of decision maker involved
modified analytical hierarchy process (FAHP) is proposed after in the decision making process with their
the concept of fuzziness, uncertainty and vagueness. A preferences with respect to the evaluation criteria.
triangular fuzzy umber is considered to form a fuzzy comparison A set of evaluation criteria.
matrix for criteria and alternatives (contractors). Consequently a
A set of decision alternatives.
fuzzy score matrix is prepared to obtained crisp score
A set of uncontrollable, uncertain ( independent)
(defuzzified value), which ultimately gives overall ratting of the
variables or states of nature ( decision environment) and
alternatives (contractors). The construction industry is an
integral part of infrastructural development of country. The The set of outcomes or consequences associated with each
selection of appropriate construction contractor is the multi alternative attribute pair.
criteria decision making process. In the large project it is very 1.1 Analytical hierarchy process (AHP)
difficult for the decision makers to analyze the capabilities of Analytical hierarchy process is a multicriteria decision technique
contractors against vagueness, imprecision, inexact and that uses hierarchical structures to define a problem and then
qualitative criteria. These criteria can be best expressed in the develop priorities for the alternatives based on the judgment of
linguistic terms, which cab be translated into mathematical the user is given in [5].
measures by using multi criteria decision making techniques
In [6], the AHP procedure involves six steps.
(AHP and FSM). In this paper, we present an effort to provide
application of fuzzy analytical hierarchy process in the selection Define the unstructured problem
of contractor. To develop a fuzzy analytical hierarchy approach Developing the AHP hierarchy
to rank the suitable contractor for the housing project. Pair wise comparison
Estimate the relative weights
Keywords Check the consistency
AHP, FAHP, FSM, decision making. Obtain the overall ranking
1. INTRODUCTION The first step in the AHP method is to decompose the decision
In the present scenario of competition in the construction
problem into a hierarchy that consist of the most important
industry, the selection of appropriate construction contractor for
element of the decision problem in [7].
the project is very important for the success of project. Selection
of suitable contractor for any housing project is a complex and The relative importance of the decision elements is assessed
difficult decision making problem. indirectly from comparison judgments in the second step. The
decision maker is required to provide his / her performance by
The selection of construction contractor in general is two stage comparing all criteria, sub criteria and alternatives with respect
problem. First is prequalification stage and second is bid to upper level decision elements and construct a pair wise
evaluation stage. In the prequalification stage a large numbers of comparison matrix by using the relative scale measurements
contractors are invited and analyzed, based on predetermined as shown in Table 1.
criteria and a short listed contractors is drawn by the clients. In
the bid evaluation stage short listed contractors in the
prequalification stage are again invited and investigated to select
the appropriate contractor for the project. The contractors (1)
prequalification can be taken as external auditing of their
capabilities in [1].
Prequalification is the screening of contractors by clients In this matrix , , = weight of elements
(owners) based on a set of criteria is presented in [2]. .

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 International Journal of Computer Applications (0975 8887)
Volume 28 No.10, August 2011

Table 1. Scales of pair wise comparison vagueness or ambiguity presented in [9]. The conventional AHP
approach may not fully reflect a style of human thinking because
Preference in numeric Preferences in linguistic
the decision maker usually feel more confident to give interval
variables variables
judgments rather than expressing their judgments in the form of
1 Equal importance
single numeric values and so FAHP is capable of capturing a
3 Moderate importance
humans appraisal of ambiguity when complex multi criteria
5 Strong importance
decision making problems are considered in [10]. This ability
7 Very strong importance
comes to exist when the crisp judgment transformed into fuzzy
9 Extreme importance
judgments. In modeling, a real life problems, trapezoidal and
2,4,6,8 Intermediate values between
triangular fuzzy numbers are used in [11] and [12].
adjacent scale values.
In the proposed work triangular fuzzy number is used. A
1.2 Estimation of Relative Weights triangular fuzzy number is defined by three real numbers
Some methods like eigenvector method and lease square method and the membership function for triangular fuzzy
are used to compute the relative weights of elements in each pair number is defined as;
wise comparison matrix.

Determination of the consistency:

The consistency is determined by using the eigenvalue .
calculate the consistency index, CI as follows

(2)

The consistency ratio is calculated as

1.0
(3)
1.0
Where will be taken from the Table 2 on the basis of size of a b c
matrix. If the value of is less than 0.10, the judgments are
consistent, if it is more, the judgments are inconsistent then the
judgments should be reviewed to obtain consistence matrix. Fig 1: Fuzzy Triangular Number and Membership Function

Table 2. Random Inconsistency Indices In the next step of decision making process, weights of all
criteria and scores of alternatives are to be calculated from fuzzy
Size of 1 2 3 4 5 6 pair wise comparison matrices of the type (1) as depicted in
Matrix Fig. 2.
0 0 0.58 0.9 1.12 1.24
1.5 Determination of weights for
criteria
1.3 Determine the overall rating The fuzzy comparison judgments given by the experts to each of
In the last step the relative weights of decision elements are the decision criteria and the average fuzzy scores, defuzzified
aggregated to obtain an overall rating for the alternatives as values and normalized weights of criteria are obtained and same
follows: are given in the Table 3.

(4) Case study: Six criteria are chosen for evaluation of alternative
construction contractors, namely post experience, financial
Where = Total weight of alternative turnover, past performance, man power resource, plant and
= Weight of alternatives associated to criteria . equipment resource and similar projects in hand. Five alternative
construction contractors are indentified as potential construction
= Number of criteria
contractions. The goal is to select an appropriate contractor for
= Number of alternatives.
the specific project, satisfying all criteria in the best way.
The proposed methodology is the modification of AHP method,
1.4 Fuzzy Analytical Hierarchy Process
( FAHP): the first step in applying the fuzzy AHP is to construct a
In spite of popularity of AHP, this method is often criticized for hierarchy of alternative contractors and criteria as shown in
its inability to adequately handle inherent uncertainty and Fig 2.
imprecision associated with the mapping of the decision makers
perception to exact numbers in [8]. Since fuzziness and
vagueness are common characteristics in most of the decision
making problems, a fuzzy AHP method can able to tolerate

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 International Journal of Computer Applications (0975 8887)
Volume 28 No.10, August 2011

Prequalification of Contractor
1.6 Determination of weights for
alternatives
Fuzzy pairwise matrix for past experience, financial turnover,
past performance, man power resources, plant and equipment
resources and similar projects in hand are prepared on the basis
Exp. F.T.
P.P.
M.P.R. P.E.R. P.I.H. of fuzzy comparision judgements given by the experts to the
alternatives (contractors) and the average fuzzy scores,
defuzzified values and normalized. weights of alternatives are
obtained as shown in Table 4, 5, 6, 7, 8, 9.

1.7 Decision Matrix for Contractor Pre-

qualification
The weights of criteria and the weights of each alternatives
relative to each criteria are combined in order to determine
the overall ranking of the contractors, using equation 4. The
results are shown in Table 10.

A B C D E

Fig 2: Hierarchical structure of decision problem

Table 3. Fuzzy Pairwise Comparison Matrix for the Criteria

Criteria Exp. F.T P.P M.P.R P.E.R P.I.H

Exp. (1,1,1) (1,2,3) (3,4,5) (4,5,6) (5,6,7) (4,5,6)

F.T (1,1,1) (2,3,4) (6,7,8) (6,7,8) (4,5,6)
(1/3 , 1/2 , 1)
P.P (1,1,1) (2,3,4) (2,3,4) (3,4,5)
(1/5 , 1/4 , 1/3) (1/4 , 1/3 , 1/2)
M.P.R (1,1,1) (1,2,3)
(1/6 , 1/5 , 1/4) (1/8 , 1/7 , 1/6) (1/4 , 1/3 , 1/2) (1/4 , 1/3 , 1/2)
P.E.R (1,1,1)
(1/7 , 1/6 , 1/5) (1/8 , 1/7 , 1/6) (1/4 , 1/3 , 1/2) (1/3 , 1/2 , 1) (1/4 , 1/3 , 1/2)
P.I.H (2,3,4) (2,3,4) (1,1,1)
(1/6 , 1/5 , 1/4) (1/6 , 1/5 , 1/4) (1/5 , 1/4 , 1/3)

Criteria Average fuzzy scores Defuzzified values Normalized

weight
Exp. 3.000 3.833 4.666 3.833 0.317
F.T 3.222 3.916 4.666 3.930 0.325
P.P 1.048 1.930 2.472 1.935 .160
M.P.R 0.465 0.668 0.902 0.675 0.055
P.E.R 0.350 0.412 0.561 0.433 0.035
P.I.H 0.922 1.275 1.638 1.277 0.105

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 International Journal of Computer Applications (0975 8887)
Volume 28 No.10, August 2011

Table 4. Fuzzy Pairwise Comparison Matrix for Experience

Alternative A B C D E
A (1,1,1) (2,3,4) (4,5,4) (2,3,4)
(1/6 , 1/5 , 1/4)
B (1,1,1) (1,2,3,) (3,4,5)
(1/4 , 1/3 , 1/2) (1/5 , 1/4 , 1/3)
C (1,1,1) (1,2,3)
(1/6 , 1/5 , 1/4) (1/3 , 1/2 , 1) (1/6 , 1/5 , 1/4)
D (1,1,1) (6,7,8)
(4,5,6) (3,4,5) (4,5,6)
E (1,1,1)
(1/4 , 1/3 , 1/2) (1/5 , 1/4 , 1/3) (1/3 , 1/2 , 1) (1/8 , 1/7 , 1/6)

Alternative Average fuzzy scores Defuzzified values Normalized weight

A 1.833 2.440 3.050 2.440 0.256
B 1.090 1.516 1.966 1.522 0.160
C 0.533 0.580 1.100 0.698 0.073
D 3.600 4.400 5.200 4.400 0.461
E 0.381 0.445 0.600 0.467 0.049

Table 5. Fuzzy Pairwise Comparison Matrix for Turnover

Alternative A B C D E
A
(1,1,1) (2,3,4) (3,4,5) (1/5 , 1/4 , 1/3) (3,4,5)
B
(1/4 , 1/3 , 1/2) (1,1,1) (1,2,3) (1/5 , 1/4 , 1/3) (4,5,6)
C
(1/5 , 1/4 , 1/3) (1/3 , 1/2 , 1) (1,1,1) (1/5 , 1/4 , 1/3) (2,3,4)
D
(3,4,5) (3,4,5) (3,4,5) (1,1,1) (4,5,6)
E
(1/5 , 1/4 , 1/3) (1/6 , 1/5 , 1/4) (1/3 , 1/2 , 1) (1/6 , 1/5 , 1/4) (1,1,1)

Alternatives Average Fuzzy Scores Defuzzified Values Normalized Weights

A 1.840 2.450 3.066 2.451 0.266
B 1.290 1.716 2.166 1.722 0.187
C 0.746 1.000 1.333 1.019 1.110
D 2.800 3.600 4.400 3.600 0.391
E 0.356 0.396 0.466 0.4103 0.0493

Table 6. Fuzzy Pairwise Comparison Matrix for Experience

Alternative A B C D E
A (1,1,1) (2,3,4) (4,5,6)
(1/5 , 1/4 , 1/3) (1/4 , 1/3 , 1/2)
B (1,1,1) (5,4,3)
(1/4 , 1/3 , 1/2) (1/4 , 1/3 , 1/2) (1/5 , 1/4 , 1/3)
C (5,4,3) (2,3,4) (1,1,1) (1,2,3) (4,5,6)
D (2,3,4) (3,4,5) (1,1,1) (4,5,6)
(1/3 , 1/2 , 1)
E (1,1,1)
(1/6 , 1/5 , 1/4) (1/5 , 1/4 , 1/3) (1/6 , 1/5 , 1/4) (1/6 , 1/5 , 1/4)

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 International Journal of Computer Applications (0975 8887)
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Alternative Average fuzzy scores Defuzzified values Normalized weight

A 1.490 1.916 2.366 1.922 0.201
B 1.340 1.183 1.066 1.193 0.125
C 2.600 3.000 3.400 3.000 0.314
D 2.066 2.700 3.400 2.716 0.286
E 1.700 0.370 0.416 0.714 0.074

Table 7. Fuzzy Pairwise Comparison Matrix for Turnover

Alternative A B C D E
A (1,1,1) (3,4,5)
(1/4 , 1/3 , 1/2) (1/3 , 1/2 , 1) (1/5 , 1/4 , 1/3)
B (2,3,4) (1,1,1) (1,2,3) (3,4,5)
(1/5 , 1/4 , 1/3)
C (1,2,3) (1,1,1) (1,2,3) (3,4,5)
(1/3 , 1/2 , 1)
D (3,4,5) (1,2,3) (1,1,1) (4,5,6)
(1/3 , 1/2 , 1)
E (1,1,1)
(1/5 , 1/4 , 1/3) (1/5 , 1/4 , 1/3) (1/4 , 1/3 , 1/2) (1/6 , 1/5 , 1/4)

Alternatives Average Fuzzy Scores Defuzzified Values Normalized Weights

A 0.956 1.216 1.566 1.238 0.154
B 1.600 2.400 3.200 2.400 0.300
C 0.933 1.400 2.000 1.433 0.180
D 1.866 2.500 3.200 2.516 0.314
E 0.363 0.406 0.483 0.414 0.051

Table 8. Fuzzy Pairwise Comparison Matrix for Plant and Equipment Resources
Alternative A B C D E
A (1,1,1) (2,3,4) (4,5,6)
(1/4 , 1/3 , 1/2) (1/5 , 1/4 , 1/3)
B (1,1,1) (5,6,7)
(1/4 , 1/3 , 1/2) (1/4 , 1/3 , 1/2) (1/6 , 1/5 , 1/4)
C (2,3,4) (2,3,4) (1,1,1) (8,9,10)
(1/5 , 1/4 , 1/3)
D (3,4,5) (4,5,6) (3,4,5) (1,1,1) (8,9,10)
E (10,9,8) (1,1,1)
(1/6 , 1/5 , 1/4) (1/7 , 1/6 , 1/5) (1/10 , 1/9 , 1/8)

Alternatives Average Fuzzy Scores Defuzzified Values Normalized Weights

A 1.490 1.916 2.366 1.922 0.164
B 1.333 1.573 1.850 1.582 0.135
C 2.460 3.250 3.866 3.251 0.278
D 3.800 4.600 5.400 4.600 0.394
E 0.302 0.317 0.340 0.391 0.027

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 International Journal of Computer Applications (0975 8887)
Volume 28 No.10, August 2011

Table 9. Fuzzy Pairwise Comparison Matrix for Projects in Hand

Alternative A B C D E
A (1,1,1) (3,4,5) (1,2,3) (1,2,3) (2,3,4)
B (1,1,1) (1,2,3)
(1/5 , 1/4 , 1/3) (1/4 , 1/3 , 1/2) (1/5 , 1/4 , 1/3)
C (2,3,4) (1,1,1) (2,3,4)
(1/3 , 1/2 , 1) (1/5 , 1/4 , 1/3)
D (3,4,5) (3,4,5) (1,1,1) (4,5,6)
(1/3 , 1/2 , 1)
E (1,1,1)
(1/4 , 1/3 , 1/2) (1/3 , 1/2 , 1) (1/4 , 1/3 , 1/2) (1/6 , 1/5 , 1/4)

Alternatives Average Fuzzy Scores Defuzzified Values Normalized Weights

A 1.600 2.400 3.200 2.400 0.296
B 0.530 0.766 1.033 0.773 0.095
C 1.066 1.550 2.066 1.558 0.191
D 2.266 2.900 3.600 2.916 0.358
E 0.400 0.473 0.650 0.500 0.061

Table 10. Decision Matrix for Contractor Pre-qualification

Alternative
Exp. F.T. P.P. M.P.R. P.E.R. P.I.H. Overall Order of
(0.317) (0.325) (0.160) (0.055) (0.035) (0.105) Priority Ranking
Vectors
A
0.256 0.266 0.201 0.154 0.164 0.294 0.245 2
B
0.160 0.187 0.125 0.300 0.135 0.950 0.162 3
C
0.073 0.110 0.314 0.180 0.278 0.191 0.148 4
D
0.610 0.391 0.284 0.314 0.394 0.358 0.387 1
E
0.049 0.043 0.074 0.051 0.027 0.061 0.051 5

judgments in the form of single numeric values (crisp value)

2. RESULTS AND DISCUSSION therefore FAHP is capable of capturing a humans appraised of
From the various calculation done using the fuzzy analytical
ambiguity when complex multicriteria decision making
hierarchy process, for prequalification, the order of ranking of
problems are considered. This ability comes to exist when the
contractors are as . The result shows that
crisp judgments transformed into fuzzy judgment. Results are
is the best qualified construction contractor to perform the
shown that efficacy of proposed approach using FAHP. In
project. Since, fuzziness and vagueness are common
future, we will enhance our proposed model by more
characteristics in most of the decision making problems, a fuzzy
construction constraints and environmental scenarios.
AHP can able to tolerate vagueness and ambiguity. The
conventional AHP may not fully reflect a style of human 4. ACKNOWLEDGMENTS
thinking because the decision maker usually feel more confident Our special thanks to Mr. Brijesh Kumar Chaurasia and
to give internal judgments (Fuzzy judgment) rather then a single contractors, who have contributed towards development of this
numeric values (Crisp Judgment). research work.
3. CONCLUSION
The conventional AHP approach may not fully reflect a style of
human thinking because the decision maker usually feel more
confident to give interval judgments rather than expressing their

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 International Journal of Computer Applications (0975 8887)
Volume 28 No.10, August 2011

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