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Journal of Construction in Developing Countries, Vol. 16(1), 69–89, 2011
© Penerbit Universiti Sains Malaysia, 2011
Selection of Project Managers in Construction Firms Using Analytic Hierarchy Process (AHP) and Fuzzy
Topsis: A Case Study
Fatemeh Torfi1 and *Abbas Rashidi2
Abstract: Selecting a project manager is a major decision for every construction company. Traditionally, a project manager is selected by interviewing
applicants and evaluating their capabilities by considering the special requirements of the project. The interviews are usually conducted by senior managers,
and the selection of the best candidate depends on their opinions. Thus, the results may not be completely reliable. Moreover, conducting interviews for a
large group of candidates is time-consuming. Thus, there is a need for computational models that can be used to select the most suitable applicant, given
the project specifications and the applicants’ details. In this paper, a case study is performed in which a Fuzzy Multiple Criteria Decision Making (FMCDM)
model is used to select the best candidate for the post of project manager in a large construction firm. First, with the opinions of the senior managers, all the
criteria and sub-criteria required for the selection are gathered, and the criteria priorities are qualitatively specified. Then, the applicants are ranked using the
Analytic Hierarchy Process (AHP), approximate weights of the criteria, and fuzzy technique for order performance by similarity to ideal solution (TOPSIS). The
results of the case study are shown to be satisfactory.
Keywords: Construction Firms, Fuzzy TOPSIS, Criteria, AHP, Project Manager
INTRODUCTION
Project managers play a significant role in determining the
quality, cost, and duration of construction projects. The
project manager makes most of the major decisions. Thus,
selecting the most suitable applicant is important.
1PhD Candidate, Department of Industrial Engineering,
Mazandaran University of Science and Technology, Babol, IRAN
2Lecturer, Islamic Azad University, Semnan Branch, IRAN
*Corresponding email: rashidi@gatech.edu
Traditionally, a manager is selected by interviewing
applicants and considering their qualifications and the
project requirements. The interviews are usually conducted
by senior managers. In every human decision, there is the
possibility of an error in judgment, so the results may not be
dependable. Thus, there is a need for a method that can
select the most suitable applicant for the post of project
manager, given his/her capabilities and the senior
managers’ opinions. In this paper, the Analytic Hierarchy
Process (AHP) and Fuzzy TOPSIS (FTOPSIS) are used to
Fatemeh Torfi and Abbas Rashidi
70/PENERBIT UNIVERSITI SAINS MALAYSIA
conduct a case study of the project manager selection
procedure in a major Iranian construction company, the
Polband Construction Company. The Fuzzy Multiple Criteria
Decision Making (FMCDM) model presented here consists
of the following steps:
Step 1: Determine all criteria and sub-criteria used by the
senior managers of the company to select the
project manager.
Step 2: Determine the approximate weight for each criteria
with the AHP and by considering the senior
managers’ opinions.
Step 3: Gather applicants’ information, and rank them
using FTOPSIS.
A schematic of the project manager evaluation and
selection procedure is presented in Figure 1.
To evaluate the method and test its validity, its results
were compared to those obtained by solving the problem
using Data Envelopment Analysis (DEA), a valuable
analytical research instrument, and a practical decision
support tool, which is briefly discussed in the Model
Assessment’s chapter.
Figure 1. Evaluation and Selection Procedure
In recent years, many studies have examined the
application of MCDM modelling methods in decision-
making processes, particularly in the construction industry.
Obviously, these models cannot fully replace human
decision making or management and control of a project.
However, they can certainly be used as aids in the
workplace.
LITERATURE REVIEW
MCDM involves finding the best opinion from all feasible
alternatives in the presence of multiple, usually conflicting,
decision criteria. Priority-based, outranking, distance-
Selection of Project Managers in Construction Firms
PENERBIT UNIVERSITI SAINS MALAYSIAI71
based, and mixed methods are the primary approaches
(Pomerol and Romero, 2000).
One of the most widely used MCDM approaches is
the AHP (Saaty, 1986), which finds the relative weights of
the factors and the total value of each alternative based
on these weights. The AHP has widely been used in multi-
criteria decision-making and has been successfully applied
to many practical problems (Saaty, 2003). In spite of its
popularity, it is often criticised because of its inability to
handle uncertain decision-making problems (Cheng, 1999).
TOPSIS, another MCDM method, is based on choosing the
alternative that has the shortest distance from the positive-
ideal alternative and the longest distance from the
negative-ideal alternative (Hwang and Yoon, 1981).
In primitive forms of the AHP and TOPSIS, experts’
weightings of the criteria, sub-criteria, and alternatives are
represented as exact numbers. However, in many practical
cases, the experts are reluctant or unable to make
numerical comparisons. FMCDM is a powerful tool for
decision-making in a fuzzy environment. Classical decision-
making methods work only with exact data; there is no
place for fuzzy or vague data. However, humans can
perform qualitative data processing, which helps them to
make decisions in a fuzzy environment. TOPSIS and fuzzy
TOPSIS (FTOPSIS) have been applied in different situations
and are commonly used to solve Multiple-Attribute
Decision-Making (MADM) (Yang and Chou, 2005; Yoon
and Hwang, 1995).
Salehi (2009) used FTOPSIS for project evaluation.
Cheng et al. (2009) discussed an application of fuzzy
Delphi and fuzzy AHP to the evaluation of wafer suppliers in
the semiconductor industry. Srdjevic (2007) linked the AHP
and social-choice methods to support group decision-
making in water management. Chu et al. (1996) used a
heuristic method based on fuzzy logic for ranking projects.
The AHP has been used by many authors for decision
making in project selection (Wei et al., 2005; Dey, 2006; Lien
and Chan, 2006). Aiello et al. (2008) focused on a clean
agent selection approached with FTOPSIS. Dagdeviren et
al. (2009) developed an evaluation model based on the
AHP and TOPSIS to help managers in the defence industry
select the optimal weapon in a fuzzy environment. Torfi et
al. (2010) proposed an FMCDM approach to evaluate
alternative options with respect to a user’s preferences.
Two fuzzy procedures are proposed for solving the MCDM
problem: the fuzzy AHP (FAHP) is applied to determine the
relative weights of the evaluation criteria, and FTOPSIS is
applied to rank the alternatives.
Our proposed method consists of two steps: first, the
AHP is applied to determine the relative weights of the
evaluation criteria, and second, FTOPSIS is applied to rank
the alternatives. We chose the AHP and FTOPSIS for their
Fatemeh Torfi and Abbas Rashidi
72/PENERBIT UNIVERSITI SAINS MALAYSIA
simplicity, popularity, and accuracy. The underlying
concepts are easily understood, so they can easily be
implemented in a construction company. Moreover, the
computational overhead is relatively low, yet the results are
precise. If the numbers of criteria and candidates increase,
this will become important. We chose not to use fuzzy
expert systems because they need considerable historical
data to train the initial system. In our case study, insufficient
historical data were available.
AHP AND FTOPSIS METHOD
AHP
The AHP is a powerful decision-making method for
determining priorities given different criteria. It
encompasses six basic steps (Isiklar and Buyukozkan, 2006):
Step 1. The AHP uses several small subproblems to represent
a complex decision problem. Thus, we first
decompose the decision problem into a hierarchy
with a goal at the top, criteria and sub-criteria at
various levels, and decision alternatives at the
bottom (see Figure 3).
Step 2. The comparison matrix D gives pairwise
comparisons of the elements of the hierarchy. The
aim is to set their priorities with respect to each of
the elements one level higher.
11 12 1
21 22 2
12
n
n
mm mn
xx x
xx x
D
xx x
(1)
The elements
ij
x
can be interpreted as the degree
of preference for the ith criterion over the jth criterion.
Criteria can be weighted more reliably when the weighting
is based on pairwise comparisons because it is easier to
compare two attributes than to make an overall weight
assignment. Before calculating the vector of the priorities,
we normalise the comparison matrix to the [0, 1] range:
1
ij
ij n
ij
i
x
r
x
(2)
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PENERBIT UNIVERSITI SAINS MALAYSIAI73
11 12 1
21 22 2
12
n
n
nn nn
rr r
rr r
R
rr r
(3)
The comparison matrix involves the pair-wise
comparison of elements of the constructed hierarchy. The
aim is to set their relative priorities with respect to each of
the elements at the next higher level.
Step 3. The AHP also calculates an inconsistency index (or
consistency ratio) to reflect the consistency of the
decision maker’s judgments during the evaluation
phase. The inconsistency index for both the
decision matrix and in the pair-wise comparison
matrix can be calculated via (Aguaron et al.,
2003):
max
.1n
II n
(4)
where I.I is the inconsistency index, n is the size of the
comparison matrix, and λmax is the largest eigenvalue,
which is calculated as:
max 1
1(./)
n
iDR R
n
(5)
The closer the inconsistency index is to zero, the
greater is the consistency. The relevant index should be
lower than 0.10 for the AHP results to be acceptable. If this
is not the case, the decision-maker should redo the
assessments and comparisons.
Step 4. Before calculating the vector of the priorities, the
comparison matrix R must be normalised using Eq.
(2).
Step 5. To find the weights of the criteria, the average of
the elements of each row is calculated from the
matrix R.
FUZZY SET THEORY
We briefly review fuzzy theory.
Definition 3.2.1. A fuzzy set a
in a universe of
discourse X is characterised by a membership function
a
x
, which associates with each element x in X a real
Fatemeh Torfi and Abbas Rashidi
74/PENERBIT UNIVERSITI SAINS MALAYSIA
number in the interval [0, 1]. The function value
a
x
is
termed the grade of membership of x in a
(Zadeh, 1965).
The present study uses triangular fuzzy numbers. A triangular
fuzzy number a
can be defined by a triplet (a1, a2, a3). Its
conceptual schema and mathematical form are given by
(Kaufmann and Gupta, 1985):
1
112
21
323
32
3
0
1
a
xa
xa axa
aa
xax axa
aa
xa
(6)
Definition 3.2.2. Let
123 123
,, and ,,aaaa bbbb
be
two triangular fuzzy numbers. Then, a vertex method is
defined to calculate the distance between them, as shown
in Eq. (7):
222
11 22 33
1
,3
dab a b a b a b
(7)
Property 3.2.1. Assuming that both
123
,,aaaa
and
123
,,bbbb
are real numbers, the distance
measurement
,dab
is identical to the Euclidean
distance (Chen, 2000).
Property 3.2.2. Let
a,b,and c , be three triangular
fuzzy numbers. Then a
is closer to b
than to c
if, and only if,
,,dab dac
(Chen, 2000).
The basic operations on fuzzy triangular numbers are
as follows (Yang and Hung, 2007).
For multiplication:
112 23 3
,,ab a ba ba b
(8)
For addition:
11223 3
,,ab a ba ba b
(9)
Selection of Project Managers in Construction Firms
PENERBIT UNIVERSITI SAINS MALAYSIAI75
FUZZY MEMBERSHIP FUNCTION
Experts usually use a linguistic variable to evaluate the
importance of the criteria and the rating of alternatives.
The example in the present study has precise values for the
performance ratings and the criteria weights. To illustrate
the idea of fuzzy MACD, we deliberately transform the
precise values to five levels of fuzzy linguistic variables: Very
Low (VL), Low (L), Medium (M), High (H) and Very High
(VH). The purpose of the transformation process is twofold:
(1) to illustrate the proposed fuzzy MACD method and (2)
to benchmark the empirical results against precise-value
methods.
Triangular and trapezoidal fuzzy numbers are often
adopted due to their simplicity in modelling and easy
interpretation. Both triangular and trapezoidal fuzzy
numbers are applicable to the present study. We assume
that triangular fuzzy numbers can adequately represent
the five-level fuzzy linguistic variables, and we use them for
our analysis (see Table 1).
Each rank is assigned an evenly spread membership
function that has an interval of 0.30 or 0.25. A
transformation table can then be found, as shown in Table
1. For example, the fuzzy variable VL has an associated
triangular fuzzy number with a minimum of 0.00, mode of
0.10, and maximum of 0.25. The same transformation is
then applied to the other fuzzy variables. Figure 2 illustrates
the fuzzy membership function (Yang and Hung, 2007).
Table 1. Transformation for Fuzzy Membership Functions
Membership function Sub -Criteria grade Rank
(0.00,0.10,0.25) 1 Very low (VL)
(0.15,0.30,0.45) 2 Low (L)
(0.35,0.50,0.65) 3 Medium (M)
(0.55,0.70,0.85) 4 High (H)
(0.75,0.90,1.00) 5 Very high (VH)
Figure 2. Fuzzy Triangular Membership Functions
PRINCIPLES OF TOPSIS
TOPSIS is based on choosing the alternative with the
shortest distance from the positive-ideal solution and the
Fatemeh Torfi and Abbas Rashidi
76/PENERBIT UNIVERSITI SAINS MALAYSIA
longest distance from the negative-ideal solution; see
Hwang and Yoon (1981).
FTOPSIS MODEL
It is often difficult for a decision-maker to assign a precise
performance rating to an alternative for the criteria under
consideration. A fuzzy approach assigns the relative
importance of the criteria using fuzzy numbers instead of
precise numbers. This section extends TOPSIS to the fuzzy
environment. A fuzzy MCDM can be concisely expressed as
a matrix:
123
1111213 1
2212223 2
3313233 3
123
n
n
n
n
mmmm mn
CCC C
A
xxx x
A
xxx x
A
xxx x
A
xxx x
(10)
12
, ,..., n
Www w
(11)
where , 1,2,..., ; 1,2,...,
ij
x
imjn
and , 1,2,...,
j
wj n
are
linguistic triangular fuzzy numbers:
,,
ij ij ij ij
x
abc
and
123
,, .
jjjj
wabc
Note that ij
x
is the performance rating
of the ith alternative, Ai, with respect to the jth criteria, and
j
w
represents the weight of the jth criteria, Cj. The
normalised fuzzy decision matrix is:
ij mn
Rr
(12)
The weighted fuzzy normalised decision matrix is:
mnnm
n
n
vvv
vvv
vvv
V
~~~
~~~
~
~
~
21
22221
11211
111 212 1
121 222 2
11 2 2
.
nn
nn
mm nmn
wr wr wr
wr wr wr
wr wr wr
(13)
The benefit of using a fuzzy approach is that the relative
importance of criteria can be assigned to fuzzy numbers
instead of precise numbers. This section discusses the
extension of TOPSIS to the fuzzy environment. TOPSIS is
particularly suitable for solving the group decision-maker
Selection of Project Managers in Construction Firms
PENERBIT UNIVERSITI SAINS MALAYSIAI77
problem in a fuzzy environment. The proposed FTOPSIS
procedure is as follows:
Step 1: Choose the linguistic ratings
ij
x
i=1, 2, …, m; j=1, 2,
…, n for the alternatives with respect to the criteria
and the appropriate linguistic variables
( , 1,2,..., )
j
wj n
for the weights of the criteria. The
fuzzy linguistic rating
ij
x
preserves the property
that the normalised triangular fuzzy numbers are in
the range [0, 1]; there is no need for a normalisation
procedure. The D
defined by Eq. (10) is equivalent
to the
R
defined by Eq. (12).
Step 2. Construct the weighted normalised fuzzy decision
matrix. The weighted normalised value
V
is
calculated by Eq. (13).
Step 3. Identify the positive-ideal (A*) and negative-ideal
(A-) solutions. The fuzzy positive-ideal solution (FPIS,
A*) and the fuzzy negative-ideal solution (FNIS, A-)
are:
12
, ,..., max 1,..., , 1,2,..., .
niij
A
vv v vi m j n
(14)
12
, ,..., min 1,..., , 1,2,..., .
niij
Avvv vi mj n
(15)
Step 4. Calculate the separation measures. The distance of
each alternative from A* and A- can be calculated
with:
1, , 1,2,...,
n
iijj
j
ddvvi m
(16)
1, , 1,2,...,
n
iijj
j
ddvvi m
(17)
Step 5. Calculate the similarities to the ideal solution via:
i
iii
d
CC dd
(18)
Step 6. Rank the preference order. Choose an alternative
with maximum i
CC
or rank the alternatives
according to i
CC
in descending order.
Fatemeh Torfi and Abbas Rashidi
78/PENERBIT UNIVERSITI SAINS MALAYSIA
Table 2. Criteria and Sub-Criteria Used for Project Manager Selection in Polband Construction Company
No. Sub-Criteria Possible-Option
1.
Technical and
professional records
Total Job experience 0–30 years
2. Management experience 0–30 years
3. Work experi ence in the company 0–30 years
4. Work experience in similar projects 0–30 years
5. Work experience under projects owner's organisation 0–30 years
6. Work experience in similar projects 0–30 years
7. Having a share or being a member of managing board of the company Yes - No
8. Quality assessment of pervious projects 0–100 points
9.
Educational
background
Major Mechanical Engineering – Civil Engineering –Chemical Engineering-
Electrical Engineering – Others
10. Degree BS-MS-PhD
11. Quality of the university where the application is graduated 0–100 points
12. Specialisation Design-Construction-Supervision-Managemant-others
13. Continual Professional Development 0–200 hours
14. Language ability (English) 0–100 points
15,
Demographic
features
Gender Male-Female
16. Age 18–80 years
17. Physical and mental health Health-Unhealthy
18, Appearance 0–100 points
19.
General
management
abilities
Abilities in human resource management (Number of employees working
under his supervision)
0–500 persons
20. Abilities in Communicating effectively with project owner 0–100 points
21. Decision-making ability under critical circumstances 0–100 points
22. Accountability in task performing 0–100 points
23. Ability in project conditions assessment and in offrering predictions 0–100 points
Selection of Project Managers in Construction Firms
PENERBIT UNIVERSITI SAINS MALAYSIAI79
DETERMINING CRITERIA FOR PROJECT MANAGER SELECTION
Determining the criteria for the project manager selection
is the first step in developing the selection model. In
general, any construction company has its own criteria for
selecting a project manager. Expert researchers also have
differing point of views on the main criteria for selecting a
project manager (El-Saba, 2001). For example, Perini
stresses the following points as the main requirements (Liao,
2007):
a) Possesses superior technical skills
b) Builds and maintains effective team dynamics
c) Communicates effectively
d) Works hard
e) Focuses on client needs
f) Makes safety a top priority
g) Remains calm under pressure
h) Always asks the right questions
i) Takes responsibility and appropriate risks to
achieve excellence
j) Above all, leads by example.
Meredith et al. (1995) divided the main skills of project
managers into six groups: team skills, organisational skills,
communication skills, technical skills, coping skills, and
leadership and building skills. Godwin, however, claimed
that conceptual skills, technical skills, negotiation skills and
human skills are the four essential requirements (Goodwin,
1995), whereas Kats considered human skills, technical skills
and conceptual skills to be essential (Pheng and Chuan,
2006). Despite some differences in the researchers’
opinions, there are many common selection criteria for
project managers in construction companies.
In this study, we use the opinions of the senior
managers of the Polband Construction Company in
addition to those of other construction industry experts. This
gives four main criteria and twenty-three sub-criteria for
project manager selection, as shown in Table 2.
DETERMINING RELATIVE WEIGHT OF CRITERIA USING AHP
An overview of the project manager selection procedure
for the Polband Construction Company case study is
shown in Figure 3. There are four levels. On the first level, the
goal is to select a project manager. The second level
contains the four main criteria, and the third level contains
the twenty-three sub-criteria. The fourth level contains the
ten applicants. As mentioned earlier, the first step in the
AHP is to compare pairs of criteria and sub-criteria to
determine their relative weights.
Fatemeh Torfi and Abbas Rashidi
80/PENERBIT UNIVERSITI SAINS MALAYSIA
Figure 3. Hierarchical Structure of Project Manager Selection Procedure
Table 3. Pair-wise Comparison Matrix of the Criteria
No. C1 C2 C3 C4
C1 1 2 3 3
C2 1/2 1 2 2
C3 1/3 1/2 1 1
C4 1/3 1/2 1 1
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Table 4. Pair-wise Comparison Matrix of Subcriteria
Fatemeh Torfi and Abbas Rashidi
82/PENERBIT UNIVERSITI SAINS MALAYSIA
We asked the senior managers of Polband Construction
Company to rank the importance of each criteria and sub-
criteria. The results are given in Tables 3, 4, and 5. In the opinion
Table 5. Calculations of Relative Weights of Criteria
and Subcriteria Using AHP
of the senior managers, the first criteria C1 is much more
important than the second one C2. Thus, the preference of
C1 over C2 is 2 (second row, third column), and
consequently, the preference of C2 over C1 is 1/2 (third
row, second column). On the other hand, C2 is more
important than C3. Thus, the preference of C2 over C3 is 2
(third row, fourth column) and consequently, the
preference of C3 over C2 is ½ (fourth row, third column).
The weight of each criterion and each sub-criterion is
based on these pair-wise comparisons. A summary of the
calculations is shown in Table 5.
RANKING APPLICANTS USING FTOPSIS
The first step when ranking applicants is to form the
decision-making matrix, given an applicant’s status for
every criterion. This leads to the decision-making matrix
shown in Table 6.
To transform the performance ratings to fuzzy
linguistic variables, as discussed in page 108, the
performance ratings in Table 6 are normalised into the [0,
1] range via:
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PENERBIT UNIVERSITI SAINS MALAYSIAI83
(1) If a larger rating is better:
min{ } .
max{ } min{ }
ij ij
ij ij ij
xx
rxx
(19)
(2) If a smaller rating is better:
max{ } .
max{ } min{ }
ij ij
ij ij ij
xx
rxx
(20)
For the present study, C1 and C3 are better when
they are smaller; the others are better when they are
larger. The decision matrix of Table 6 can then be
transformed into Table 7. The next step uses the fuzzy
membership function discussed in page 75 to transform
Table 7 into Table 8.
Table 6. Decision Matrix
C4 C3 C2 C1 No.
8.0000 0.0119 3.7500 185.9500 A1
9.0000 0.0596 7.8500 206.3800 A2
8.0000 0.0714 7.7100 211.4600 A3
8.0000 0.0357 14.0000 228.0000 A4
8.0000 0.0476 6.2500 185.8500 A5
9.0000 0.0595 7.8500 183.1800 A6
5.0000 0.0714 2.0000 225.2600 A7
10.0000 0.0952 13.3000 202.8200 A8
8.0000 0.0476 7.7100 216.3800 A9
9.0000 0.0595 10.1600 185.7500 A10
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Table 7. Normalised Decision Matrix for FTOPSIS Analysis
C4 C3 C2 C1 No.
0.6 1 0.145833 0.938197 A1
0.8 0.427371 0.4875 0.482374 A2
0.6 0.285714 0.475833 0.369032 A3
0.6 0.714286 1 0 A4
0.6 0.571429 0.354167 0.940428 A5
0.8 0.428571 0.4875 0.940428 A6
0 0.285714 0 0.061133 A7
1 0 0.941667 0.561803 A8
0.6 0.571429 0.475833 0.259259 A9
0.8 0.428571 0.68 0.94266 A10
0.153 0.153 0.232 0.463 W
The fuzzy linguistic variable is then transformed into a
fuzzy triangular membership function, as shown in Table 9.
This is the first step of the FTOPSIS analysis. The fuzzy criteria
weight is also given in Table 9. The second step in the analysis
is to find the weighted fuzzy decision matrix. The fuzzy
multiplication equation, Eq. (3), leads to the fuzzy weighted
decision matrix given in Table 10. In Table 10, we know that
the elements ,,
ij
vij
are normalised positive triangular fuzzy
numbers in the closed interval [0, 1]. Thus, we can define the
fuzzy positive-ideal solution and the fuzzy negative-ideal
solution as
*1,1,1
j
v
and
*0,0, 0 ,
j
v
j = 1,2,…,n. This is the
third step of the FTOPSIS analysis. For the fourth step, the
distance of each alternative from A* and A- can be
calculated using Eqs. (16) and (17). The fifth step finds an
ideal solution using Eq. (18). The resulting FTOPSIS analyses are
summarised in Table 11.
Table 8. Decision Matrix Using Fuzzy Linguistic Variables
C4 C3 C2 C1 No.
M VH VL VH A1
H L M M A2
M L M L A3
M H VH VL A4
M M L VH A5
H L M VH A6
VL L VL VL A7
VH VL VH M A8
M H M L A9
H L H VH A10
L M H VH W
The results obtained from Table 11 give the following
preference order of the applicants:
A1> A5> A10> A6> A9>A4> A2> A8> A3> A7
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Table 9. Fuzzy Decision Matrix and Fuzzy Criteria Weights
DEA APPROACH
DEA is a linear-programming-based technique developed
by Charnes et al. (1978). DEA evaluates n Decision-Making
Units (DMUs). In this study, the 10 candidates are the DMUs.
Each DMU consumes varying amounts of m different inputs
to produce s different outputs. The relative efficiency of a
DMU is defined as the ratio of its total weighted output to its
total weighted input (Yang and Hung, 2007). As mentioned
in page 82, in this paper C1 and C3 could be considered
the inputs, and C2 and C4 could be considered the
outputs.
Table 10. Fuzzy Weighted Decision Matrix
Assume that there are 10 DMUs to be evaluated (10
candidates). Each DMU consumes various amounts of m =
2 (inputs) to produce s = 2 (outputs). Let:
DMUk = the kth DMU, k = 1,2,…,10;
Xik = the ith input for the kth DMU, i = 1,3 and k= 1,2,…,10;
Yrk = the rth output for the kth DMU, r = 2,4 and k = 1,2,…,10;
vi = the associated weight for the ith input i = 1,3;
ur = the associated weight for the rth output r = 2,4;
and hk = the efficiency score (hk
1).
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86/PENERBIT UNIVERSITI SAINS MALAYSIA
Then,
rrk
kiik
uY
hvX
(21)
This definition requires a set of factor weights ur and
vi, which are the decision variables. These weights can be
obtained using linear programming or another appropriate
method. In this paper, the relative weights of the criteria
have been calculated using the AHP. After the calculation
of hk for each applicant, the preference order is based on
their efficiency scores.
A more detailed discussion of DEA is not included
here, as it is outside the scope of this research. For more
information, see Yang and Kou (2003), Seiford (1996), or
Sinuany et al. (2000).
MODEL ASSESSMENT
To evaluate the proposed method and measure its validity,
the preferred order of the candidates was calculated with
DEA. The preference order of the top three applicants is
given in Table 12. Both DEA and our model give the same
top two choices.
It should be mentioned that, due to the MCDM nature of
the problem, an optimal solution may not exist. In the case
of an imprecise performance rating, FTOPSIS is
recommended. DEA is a viable approach, but it constrains
the number of decision-making units and is limited by the
discrepancy between the performance frontiers (Yang and
Hung, 2007). Therefore, the proposed method, a fuzzy
systematic evaluation of the problem, can reduce the risk
of a poor management decision and could be applied
with confidence to the selection of project managers for
the Polband Construction Company.
CONCLUSIONS AND FUTURE WORK
The selection of a project manager from a set of potential
candidates is an important, difficult, and time-consuming
task for the senior managers of any construction company.
This problem worsens as the number of candidates
increases. Moreover, there is a risk of human error in
judgment and decision making. On the other hand, not
interviewing all the candidates may mean missing some
qualified applicants. Therefore, there is a need for
computational models that can increase the accuracy of
decisions and reduce the time required for the decision-
making process.
Selection of Project Managers in Construction Firms
PENERBIT UNIVERSITI SAINS MALAYSIAI87
Table 11. FTOPSIS Analysis Results
i
CC
i
d
i
d
4
~
i
v
3
~
i
v
2
~
i
v
1
~
i
v
No.
0.456488 4.1964 4.9964 (0.12,0.25,0.42) (0.56,0.81,1.00) (0.00,0.01,0.06) (0.56,0.81,1.00) A1
0.184618 1.4693 6.4893 (0.19,0.35,0.55) (0.11,0.27,045) (0.00,0.05,0.16) (0.26,0.45,0.65) A2
0.10204 0.8564 7.5364 (0.12,0.25,0.42) (0.11,0.27,045) (0.00,0.05,0.16) (0.11,0.27,045) A3
0.194586 1.682 6.962 (0.12,0.25,0.42) (0.41,0.63,0.85) (0.00,0.09,0.25) (0.00,0.09,0.25) A4
0.343040 2.9286 5.6086 (0.12,0.25,0.42) (0.26,0.45,0.65) (0.00,0.03,0.11) (0.56,0.81,1.00) A5
0.309105 2.7464 6.1386 (0.19,0.35,0.55) (0.11,0.27,045) (0.00,0.05,0.16) (0.56,0.81,1.00) A6
0.045587 0.3899 8.1629 (0.00,0.05,0.16) (0.11,0.27,045) (0.00,0.01,0.06) (0.00,0.09,0.25) A7
0.154364 1.5264 8.3619 (0.26,0.45,0.65) (0.00,0.09,0.25) (0.00,0.09,0.25) (0.26,0.45,0.65) A8
0.245163 1.8564 5.7157 (0.12,0.25,0.42) (0.41,0.63,0.85) (0.00,0.05,0.16) (0.11,0.27,045) A9
0.329652 2.7673 5.6273 (0.19,0.35,0.55) (0.11,0.27,045) (0.00,0.07,0.21) (0.56,0.81,1.00) A10
(1,1,1) (1,1,1) (1,1,1) (1,1,1) A+
(0,0,0) (0,0,0) (0,0,0) (0,0,0) A-
(0.15,0.30,0.45) (0.35,0.50,0.65) (0.55,0.70,0.85) (0.75,0.90,1.00) W
Table 12. Comparison between Results Obtained
from DEA and FTOPSIS
DEA
AHP and
FTOPSIS
Preference Order
A1 A1 1
A5 A5 2
A8 A10 3
Fatemeh Torfi and Abbas Rashidi
88/PENERBIT UNIVERSITI SAINS MALAYSIA
In this paper, the authors propose a new method that
provides a simple approach to the assessment of different
candidates and helps the decision maker select the best
applicant as the project manager. The AHP is used to
determine the relative weights of the evaluation criteria,
and FTOPSIS is used to rank the candidates. The proposed
method is applied as a case study to a large Iranian
construction company, and the results are found to be
satisfactory. In the future, the authors intend to generalise
the proposed method for use in a wider range of
construction companies and to use other computational
techniques, such as fuzzy AHP, to obtain more precise
results. The development of a fuzzy expert system as a
decision support system to solve the problem of selecting
project managers in construction companies will be a
research opportunity in the future.
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