osInternational Journal of Civil Engineering and Technology (IJCIET)
Volume 10, Issue 04, April 2019, pp. 1798-1807, Article ID: IJCIET_10_04_188
Available online at http://www.iaeme.com/ijciet/issues.asp?JType=IJCIET&VType=10&IType=04
ISSN Print: 0976-6308 and ISSN Online: 0976-6316
© IAEME Publication
Scopus Indexed
AN INTEGRATED EVALUATION METHOD OF
CONSTRUCTION INVESTMENT PROJECTS
Nguyen V. Duc
Thuyloi University, 175 Tay Son, Dong Da, Hanoi, Vietnam
ABSTRACT
An integrated evaluation of investment construction project is a complex decision
process. Based on the study of AHP, the authors proposed an integrated evaluation
method of multiple construction projects simultaneously, therefore it helps the investor
to be able to select the construction project, which possesses the most advantages
among others, satisfies the determined objective. This method also allows expert groups
analyze and evaluate construction investment projects in a feasible manner. It is able
to "quantify” specific comparisons accurately into the master document, containing a
lot of reliable information. Therefore, the results would be more comprehensive and
avoid making unnecessary subjective decisions by investors.
Keyword head: AHP, Decisive selection, Construction investment, Expert reviews,
Criteria
Cite this Article: Nguyen V. Duc, an Integrated Evaluation Method of Construction
Investment Projects. International Journal of Civil Engineering and Technology,
10(04), 2019, pp. 1798-1807
http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=10&IType=04
1. INTRODUCTION
During the preparatory phase of investment, the projects of construction design or
transportation and/or residential area planning need to be evaluated properly and precisely.
There should be the assessment of either the project investment efficiency or the environmental
and social impact on the location, where people will settle in the future. This paper focus on an
integrated evaluation method, selection of design and/or planning projects serving for
construction investment, the opinions of internal expert group, which comply with objectives
or criteria of the investor and initial statement from the state competent authorities at the
preparatory phase of investment.
Applying an algorithm “Analytic Hierarchy Process” (AHP), the research in this paper
proposes a useful technique, which combines mathematics and psychology, supporting experts
to synthetic comments of projects scientifically and comprehensively. This also helps investors
and the state authorities have full information to make a decision on the construction project
that possesses the most advantages among others.
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2. BASIS OF DECISION MAKING METHODS
2.1. The Analytic Hierarchy Process
The Analytic Hierarchy Process (AHP), introduced by Thomas Saaty (1980), is an effective
tool for dealing with complex decision making, and may aid the decision maker to set priorities
and make the best decision. By reducing complex decisions to a series of pairwise comparisons,
and then synthesizing the results, the AHP helps to capture both subjective and objective
aspects of a decision. In addition, the AHP incorporates a useful technique for checking the
consistency of the decision maker’s evaluations, thus reducing the bias in the decision making
process (Saaty, 1980).
2.2. Determination of primary crucial criteria for construction investment
project
The investors should be aware of the State policies and laws, keep in touch with the relevant
authorities to clarify the issue of investment projects, including the ability of the market
demand. The criteria are usually given when considering construction/ planning investment
project include:
 Study on the need of investment projects and the scale of investment;
 Report on the survey and choose the form of the construction works;
 Technical and economic reports, the ability to raise funds, building plans for
compensation and site clearance;
 Evaluate the effectiveness of projects and determine the total investment;
 Overall aesthetic issue of the project conforming to the environmental landscape
and the possible impacts on the environment during construction, execution and
operation;
 Execution of works affecting on existing traffic and remedial measures;
 Design suitable for execution conditions of labor skills and equipment of the
contractor; availability of materials and equipment, good quality locally available
construction materials;
 Develop and compilation of the work of the construction project at each stage of
the management of construction investment to be feasible;
 Taking into account the overall construction time, tailored to the standards of safety,
easy application of advanced construction methods, ability to re-use of auxiliary
materials.
2.3. Determination of the most feasible options
Chief Officer of construction project is responsible for consulting to the investors, based on the
analysis of the information on construction site inspection and plans, the natural characteristics,
social and general landscape, he needs to determine the most feasible technical options for the
project.
When initiating the construction project, most of the time there will be many technical
options to meet the general characteristics and satisfying the primary criteria. The responsibility
of the expert group is to evaluate properly the advantages and disadvantages of every option
and the experts should recommend the investor the most optimal option that possesses the most
advantages among others.
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2.4. Integrated evaluation method of construction investment project
2.4.1. Determination of the weight vector of criteria
In order to compute the weights for the different criteria, the AHP starts creating a pairwise
comparison matrix A. The matrix A is a n×n real matrix, where n is the number of evaluation
criteria considered. Each entry ajk of the matrix A represents the importance of the jth criterion
relative to the kth criterion. If ajk > 1, then the jth criterion is more important than the kth
criterion, while if ajk < 1, then the jth criterion is less important than the kth criterion. If two
criteria have the same importance, then the entry ajk is 1. The entries ajk and akj satisfy the
following constraint [Saaty, 1980]:
ajk * akj = 1
(1)
Obviously, ajj = 1 for all j . The relative importance between two criteria is measured
according to a numerical scale from 1 to 9, as shown in Table 1, where it is assumed that the
jth criterion is qually or more important than the kth criterion. The phrases in the
“Interpretation” column of Table 1 are only suggestive, and may be used to translate the
decision maker’s qualitative evaluations of the relative importance between two criteria into
numbers. It is also possible to assign intermediate values which do not correspond to a precise
interpretation. The values in the matrix A are by construction pairwise consistent. On the other
hand, the ratings may in general show slight inconsistencies. However these do not cause
serious difficulties for the AHP.
Table 1 Table of relative scores.
Value of ajk
1
3
5
7
9
Interpretation
j and k are equally important
j is slightly more important than k
j is more important than k
j is strongly more important than k
j is absolutely more important than k
Process weight vector calculation method is standardized matrix follow the algorithm
(Aczel and Saaty, 1983):
 Count the total value of each column of the matrix of pairwise comparison A.
 Divide each component in the pairwise comparison matrix A corresponding to the
total column (results comparing normalized matrix).
 Count each row of the matrix standardized.
 Divide total sum of each row for the sum of all rows corresponding weight vector
w for the criteria.
2.4.2. Check the consistency of pairwise comparison matrices
When many pair, some conflicts may arise. An example is as follows: suppose three criteria
are considered, the criterion 1 is slightly more important criterion than 2, while criterion 2 is
slightly more important than the criteria 3. An apparent contradiction found birth if experts
estimate that 3 is equal to or criteria more important criterion 1. On the other hand, a small
conflict arises if an assessment criterion 1 is also slightly more important evaluation criteria 3.
A consistent 1 case will be an important criterion than 3 criteria.
AHP combines an effective technique to examine the appropriateness of the assessment
made by the decision-makers when building pairwise comparison matrices join the process,
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namely the matrix A. This technique is based on the calculation of a consistency ratio suitable
CR. Especially if CR ≤ 0.1 means that the conflict is acceptable, and reliable results can be
expected from the AHP; reverse the judgment is random, it should be adjusted [Saaty, 1980,
2008).
Scores are determined consistent CR:
CR =
CI
RI
(2)
Where, CI (Consistency Index) is consistent indicators, measuring the level of consistency
deflected. A perfect fit decisions should always get CI = 0, but small values of inconsistencies
can be tolerated. CI is determined by the formula:
CI =
λmax −n
𝑛−1
(3)
In it, λmax called the largest eigenvalues, obtained by the average value of a consistent
vector; and n is the number of the criteria.
RI (Random Index) is a random index, ie the unified index when the elements of A is
completely random. The value of RI for minor problems (n ≤ 10) are shown in Table 2.
Table 2 Value of the random index (RI) for minor problems (Saaty, 1980)
n
RI
2
0
3
0,58
4
0,90
5
1,12
6
1,24
7
1,32
8
1,41
9
1,45
10
1,51
Process consistency check is performed as follows [Saaty, 1980, Nguyen et al., 2016, Ngo
et al., 2016]:
- Step 1: Calculate the total weight vector W: A's comparison matrix with weight vector w.
- Step 2: Calculate the vector consistent Wconsistency: Divide the total weight vector W for
the weight vector w.
- Step 3: Calculate the largest eigenvalues λmax is the average value of a consistent vector,
i.e. the vector sum of the column divided by n consistent.
- Step 4: Calculate the consistency index CI formula (3).
- Step 5: Calculate the consistency ratio CR by the formula (2), in which a random index
RI with n ≤ 10 receives from Table 2.
Weight vector w is approved only when satisfying the conditions CR <0.1.
2.4.3. Determination of synthesized comparative matrix
The AHP algorithm also allows many experts to participate making decision. Then each expert
will establish a pairwise comparison matrix A. The pairwise comparison matrices have a
consistent assembled into comparison matrix synthesis Aij (Aczel and Saaty, 1983):
1
aij = [∏𝑙𝑘=1 𝑎𝑖𝑗𝑘 ] 𝑙
(4)
In formula, each entry aij of the matrix Aij is the average multiplied of the elements of the
pairwise comparison matrix A with l experts’ opinion. Take into calculating, we get vector
weight for the criteria w is the evaluation results of l expert.
2.4.4. Determination of matrix of option scores
When there is the large optional plan, the assessment for each criterion will encounter
inconsistency. Decision makers need to compute the matrix of option scores.
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The matrix of option scores is a n×m real matrix S. Each entry sij of S represents the same
score of the ith option with respect to the jth criterion. In order to derive such scores, a pairwise
comparison matrix B(j) is first built for each of the m criteria, j=1,...,m. The matrix B(j) is a n×n
(𝑗)
real matrix, where n is the number of options evaluated. Each entry 𝑏𝑖ℎ of the matrix B(j)
represents the evaluation of the ith option compared to the hth option with respect to the jth
criterion.
The S matrix obtained as follows (Saaty, 2008):
S = [ s(1) … s(m) ]
(5)
(j)
That mean jth column of S matrix corresponds to s .
2.4.5. Determination of vector scores global for the options
Vector v global scores received by multiplied S and w [2], ie:
v=S*w
(6)
Based on vector scores global, it gives the order of the preferred embodiments to compare
the overall assessment of the technical options for the construction project.
3. EXAMPLES OF APPLICATION
An example herein is aimed to clarify the integrated evaluation method of construction
investment projects described in this paper. BH City is studying on design and construction of
complete intersections at crossroad area between the DK street and the NAQ street. Currently,
there are frequent traffic jams during peak hours at this crossroad area. This place is also the
main gateway (along DK) that workers from the TD ward and some from the TP, TH, HN
wards go to work at the industrial parks such as Am, BH2, Lot. Both roundabout measures and
traffic lights are used regulate the vehicles at this crossroad area.
3.1. Determination of primary crucial criteria for construction investment
project
The investor's criteria set out for construction investment projects: Table 3.
Table 3 Criteria of the project.
Criteria
Results of the project proposals and scales to ensure traffic safety at
municipal level, local flooding. Vision 2035.
Report on economic and technical feasibility, building plans for
compensation and site clearance in a transparent way. Fund: Provincial
budget (including compensation and site clearance).
Evaluate the effectiveness of investment and determine the total investment.
The report surveys the actual limited total investment incurred.
Selecting appropriate form of investment disbursement schedule of the
province.
The overall aesthetic of the modern project, conforming to the city
landscape. Ensure allowable dust and noise limitation in the construction
process.
Not affect the architectural and existing underground works, ensure smooth
streaming traffic safety and corrective measures in case of jam incidents.
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Notes abbreviated
Criteria 1
Criteria 2
Criteria 3
Criteria 4
Criteria 5
Criteria 6
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Design suitable for execution conditions of labor skills and equipment of the
contractor; availability of materials and equipment, good quality locally
available construction materials;
Develop and compilation of the work of the construction project at each
stage of the management of construction investment to be feasible
Shortest total construction time, construction design in accordance with the
standards of the current occupational safety.
Advanced construction solutions and reuse of secondary raw materials
Criteria 7
Criteria 8
Criteria 9
Criteria 10
3.2. Determination of the most feasible options
Based on survey report on natural conditions, social conditions, traffic characteristics and local
construction, the design team came up with three plans to opt for (see Table 4). Note that the
proposed options were made to meet 10 criteria, but to varying degrees.
Table 4 Technical options.
No.
1
2
3
The most feasible options
The design proposal for intersection with the overpass along main
branch
The design proposal for a same-level intersection
The design proposal for intersection with the tunnel along
auxiliary branch
Notes abbreviated
Op1
Op2
Op3
3.3. Determination of the weight vector of criteria
3.3.1. Check the consistency of pairwise comparison matrices
The investors invite 08 leading experts from universities, research institutes, design offices and
construction companies, who are aware of the characteristics of the local construction. Experts
are given a preprinted cards and they need to make a pair-wise comparisons and mark points
in accordance with Table 1, taking into account that the numbers 2, 4, 6, 8 are intermediate
between points 1, 3, 5, 7, 9 . The pair-wise evaluation of the experts is then listed in Table 5.
Thus, the test results of the consistency of pairwise comparison matrices of experts are also in
this Table. If the ratio CR is smaller than 10%, the recorded pairwise comparison of experts
will be consistent.
Table 5 Results of pairwise comparison of experts and check the consistency of pair-wise comparison
matrices
Pairwise comparison
j
K
Criteria 2
Criteria 3
Criteria 4
Criteria 5
Criteria 1
Criteria 6
Criteria 7
Criteria 8
Criteria 9
Criteria 10
1
1
2
3
3
4
4
4
7
9
Results of pairwise comparison of k-th expert
2
3
4
5
6
7
1
2
1/2
1
1
1/2
2
2
1
2
2
1
1
2
2
3
3
3
3
1/2
2
3
3
5
2
2
3
4
4
6
4
3
3
3
3
5
4
3
4
5
5
7
4
3
4
7
7
7
5
7
5
8
8
9
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1/2
1
3
4
6
5
6
6
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Criteria 3
Criteria 4
Criteria 5
Criteria 6
Criteria 2
Criteria 7
Criteria 8
Criteria 9
Criteria 10
Criteria 4
Criteria 5
Criteria 6
Criteria 3
Criteria 7
Criteria 8
Criteria 9
Criteria 10
Criteria 5
Criteria 6
Criteria 7
Criteria 4
Criteria 8
Criteria 9
Criteria 10
Criteria 6
Criteria 7
Criteria 5
Criteria 8
Criteria 9
Criteria 10
Criteria 7
Criteria 8
Criteria 6
Criteria 9
Criteria 10
Criteria 8
Criteria 7
Criteria 9
Criteria 10
Criteria 9
Criteria 8
Criteria 10
Criteria 9
Criteria 10
Consistency ratio CR (%)
1/2
2
3
3
3
3
6
8
1
2
2
2
5
5
7
1/2
2
2
3
5
6
1
2
3
4
5
1
3
3
4
1/3
2
3
1
2
1
4.49
1
1
2
2
3
3
4
5
1
1/2
2
3
3
4
5
1
1
2
3
3
6
1
2
2
3
5
1
2
4
6
2
5
6
3
5
5
5.30
3/2
1
2
2
3
3
4
6
1/2
1/2
2
3
3
3
6
1
1
2
3
3
6
1
2
2
3
5
1
2
4
5
5
5
6
6
5
3
7.63
1
1
2
3
3
4
5
6
1
2
3
4
5
5
6
2
3
3
4
5
6
1
2
3
3
5
2
3
4
6
3
5
6
5
7
5
7.43
1/2
2
3
3
3
5
6
8
1
2
2
2
4
5
7
1
2
2
3
5
6
1
1
3
4
5
1/2
3
3
4
1
2
3
1
3
1
2.84
1/2
1
3
3
3
5
6
9
1/3
2
2
2
4
5
7
1
1
2
3
3
6
1/2
1
2
4
5
1/2
1/2
2
4
1
2
2
1
3
1
5.87
1/2
1
3
3
3
5
6
8
1
2
2
4
4
5
7
1
1
2
3
5
9
1/2
1
3
4
5
1/2
3
3
4
1
1
2
1
3
1
5.43
1/2
1
3
3
3
7
6
7
1/3
2
2
4
5
5
6
1/3
1
2
3
5
6
1/2
1
3
4
5
1/2
2
3
4
2
1
4
1/2
3
1
9.19
3.3.2. Determination of synthesized comparative matrix Aij
The elements aij of the synthesized comparative matrix Aij (size 10x10) established by the
formula (4) and is rewritten as follows:
1
aij = [∏8𝑘=1 𝑎𝑖𝑗𝑘 ]8
(7)
The result of the synthesized comparative matrix Aij is included in Table 6.
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Table 6. The result of computing the synthesized comparative matrix Aij
Criteria
1st
2nd
3rd
4th
5th
6th
7th
8th
9th
10th
Total
column
1st
1.00
1.19
0.65
0.42
0.40
0.28
0.27
0.22
0.19
0.14
2nd
0.84
1.00
1.47
0.84
0.39
0.37
0.33
0.24
0.19
0.14
3rd
1.54
0.68
1.00
1.44
0.71
0.48
0.35
0.25
0.22
0.16
4th
2.36
1.19
0.70
1.00
1.15
0.73
0.48
0.32
0.24
0.16
5th
2.52
2.58
1.41
0.87
1.00
1.30
0.71
0.39
0.28
0.20
6th
3.59
2.71
2.10
1.36
0.77
1.00
1.30
0.49
0.31
0.22
7th
3.66
3.00
2.87
2.10
1.41
0.77
1.00
0.69
0.42
0.27
8th
4.60
4.19
4.05
3.11
2.58
2.06
1.45
1.00
0.62
0.28
9th
5.37
5.30
4.56
4.13
3.59
3.18
2.37
1.61
1.00
0.58
10th
7.31
7.01
6.33
6.31
5.00
4.55
3.64
3.60
1.72
1.00
4.75
5.81
6.81
8.33
11.25
13.86
16.21
23.94
31.69
46.48
3.3.3. Determination of the weight vector of criteria
The weight vector of criteria w is determined as follows:
 Determination of synthesized standardized matrix from synthesized comparative
matrix Aij: Divide the element aij into the corresponding total column. The results
is included into Table 7
 The obtained weight vector w after dividing the total row of synthesized
standardized matrix by total rows of the matrix.
Table 7 Results of computing synthesized standardized matrix
Criteria
1st
2nd
3rd
4th
5th
6th
7th
8th
9th
10th
1st
2nd
3rd
4th
5th
6th
7th
8th
9th
10th
Sum
rows
0.21
0.25
0.14
0.09
0.08
0.06
0.06
0.05
0.04
0.03
0.14
0.17
0.25
0.14
0.07
0.06
0.06
0.04
0.03
0.02
0.23
0.10
0.15
0.21
0.10
0.07
0.05
0.04
0.03
0.02
0.28
0.14
0.08
0.12
0.14
0.09
0.06
0.04
0.03
0.02
0.22
0.23
0.13
0.08
0.09
0.12
0.06
0.03
0.02
0.02
0.26
0.20
0.15
0.10
0.06
0.07
0.09
0.04
0.02
0.02
0.23
0.19
0.18
0.13
0.09
0.05
0.06
0.04
0.03
0.02
0.19
0.17
0.17
0.13
0.11
0.09
0.06
0.04
0.03
0.01
0.17
0.17
0.14
0.13
0.11
0.10
0.07
0.05
0.03
0.02
0.16
0.15
0.14
0.14
0.11
0.10
0.08
0.08
0.04
0.02
Total
row
2.09
1.77
1.52
1.27
0.95
0.80
0.66
0.44
0.30
0.20
10.00
Weight Vector of criteria: w = [0.21 0.18 0.15 0.13 0.10 0.08 0.07 0.04 0.03 0.02]T.
3.4. Determination of matrix of option scores
3.4.1. Check the consistency of pairwise comparison matrices
The experts carry out pairwise comparison of one of 3 options for every criteria, mark points
in accordance with Table 1. The results of pairwise comparison of options pair of experts on
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each of the criteria will be used for determining the matrix B(j) and check the consistency of
the pairwise comparison matrix included in Table 7. The consistency ratio CR is acceptable
here.
Table 7 The results of pairwise comparison of options pair of experts on each of the criteria and
check the consistency of the pairwise comparison matrix
Pairwise comparison
i
h
Op 2
Op 1
Op 3
Op 2
Op 3
Consistency ratio CR (%)
1
2
5
1
8.20
Results of pairwise comparison of experts for n-th criteria
2
3
4
5
6
7
8
9
2
1
3
2
1/2
1/4
6
1/4
7
5
5
3
2
1/2
5
1/3
2
2
2
3
7
5
1/3
2
3.02 8.16 0.32 4.64 3.02 8.24 8.26 1.58
10
3
4
3
6.39
3.4.2. Determination of matrix of option scores
Matrix of option scores S is determined by using the formula (5) the size 3x10, which are the
number of options and the number of criteria, including the scores optional vector s(j) in 3D
column similar to the weight vector of criteria w. Table 8 shows the results of calculation of
the matrix S.
Table 8 Results of computing matrix of option scores S.
Criteria
Option
1
2
3
Total
column
1
2
3
4
5
6
7
8
9
10
0.60
0.23
0.17
0.63
0.26
0.11
0.49
0.37
0.14
0.65
0.23
0.12
0.52
0.33
0.14
0.26
0.63
0.11
0.13
0.68
0.19
0.71
0.09
0.20
0.12
0.56
0.32
0.61
0.27
0.12
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
3.5. Determination of vector scores global for the options
From the formula (6), the result of computing vector scores global v is:
v = S * w = [0.52 0.33 0.15]T.
(8)
Taking into consideration, the total value of vector v is equal to 1. During the selection
process, the investors should opt for the option with the highest global scores in accordance
with the criteria, which have been indicated initially. The priority order of construction
investment options in this example is 1-2-3; it means that the most feasible option is the design
proposal for intersection with the overpass along main branch
4. CONCLUSIONS
Several conclusion can be withdrawn:
 Each construction investment option has advantages and disadvantages. This
method proposed in this paper is able to “quantify” the advantages and
disadvantages by means of global scores, which help decision makers to avoid
subjective mistakes.
 The proposed method also allows groups of experts to involve into assessing many
construction investment projects; therefore the results would be more
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comprehensive. All the comments of the experts through comparative scores will
be processed appropriately and fairly.
 The proposed method helps the investor to turn the difficult issues of the
construction investment project into the simplified issue thanks to the support of the
expert team.
REFERENCES
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Aczél J. and Saaty T. L. (1983). Procedures for Synthesizing Ratio Judgements”. Journal
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Ngo, C. P., Nguyen, T. S. H, Bui, X. C. (2016). Development method of weight values for
fast bridge construction process. Vietnam Bridge Transportation No 6, pp. 11-15.
Nguyen, T. S. H. and Nguyen, T. C. (2016). Applied methodology Analytic Hierarchy
Process (AHP) to make decision to choose a phased investment in equipment of
construction companies”. Proceeding of AMTAE2016, pp. 307-312.
Saaty, T.L. (1980). The Analytic Hierarchy Process. NY: McGraw-Hill
Saaty, T. L. (2008). Decision making with the analytic hierarchy process. International
Journal of Services, Sciences, Vol. 1, No. 1, p. 83 – 98.
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