Multiple criteria selection of pile-column construction technology.
Zavadskas, Edmundas Kazimieras ; Susinskas, Saulius ; Daniunas, Alfonsas 等
1. Introduction
In construction, piles can be used in various ways. In urban areas,
many high-rise buildings and viaducts are founded on a pile foundation.
Construction technologies are highly dependent on in-situ conditions,
e.g. soil conditions are particularly important for a foundation. The
way the designed and actual founding depths of foundations correspond to
variability of geological conditions has long been a concern (Zhang et
al. 2011b). Tomlinson and Woodward (2008) presented a lot of pile design
examples. Sivilevicius et al. (2012) presented results of an
experimental study on technological indicators of pile-columns at a
construction site. Based on in-situ investigation of natural soil
conditions, regression equations have been determined, which can be very
useful when planning similar works at a construction site. Besides, they
allow determining duration and energy consumption of construction works.
Zhang and Dasaka (2010) evaluated the spatial variability
characteristics at a weathered soil site. Susinskas et al. (2011)
presented the process for selection of the most fitting and effective
pile-column instalment alternative. The model is based on ARAS method
and AHP technique. Zhang et al. (2011a) proposed a two-stage analysis
method to study the behaviour of pile groups with rigid elevated caps. A
single pile foundation utilizes a single, generally a large-diameter
structural element to support all of the loads (weight, wind, etc.) of a
large above-surface structure. Yoon et al. (2011) presented the
evaluation results of the load test on columns and the rationale used
for the selection of the resistance factor. Zhao et al. (2009) presented
the model for stability analysis of high pile-column bridge pier. Zhang
et al. (2011b) analysed excavation-induced responses of loaded pile
foundations considering the uploading effect. Zhao et al. (2007)
revisited the stability analysis regarding the pile-columns of a bridge
pier.
Sustainable development aims to reconcile economic growth, social
progress and frugal use of natural resources, to maintain ecological
balance and to ensure favourable living conditions for current and
future generations (Raslanas et al. 2011). Selection of an investment
strategy and related decision making relies heavily on personal
experience and behaviour (Wu et al. 2012; Saparauskas et al. 2011;
Banaitiene et al. 2011). Multiple criteria decision making is an
important part of modern decision science (Zavadskas, Turskis 2011;
Zavadskas et al. 2008). How to select an effective algorithm for a
multiclass classification task is an important yet difficult issue (Peng
et al. 2011). Most of the real-world multiple criteria decision-making
problems contain a mixture of quantitative and qualitative criteria
(Nieto-Morote, Ruz-Vila 2011; Kaklauskas et al. 2011; Merigo,
Gil-Laufente 2011). The typical MCDM problem is concerned with the task
of ranking. In order to evaluate the overall efficiency of technological
alternatives, typically it is necessary: a) to identify the system for
evaluation of criteria that relates the system capabilities to goals; b)
to develop alternative systems for attaining the goals (generating
alternatives); c) to assess a finite number of decision alternatives,
each of which is described in terms of different decision criteria which
are taken into account simultaneously; d) to apply a normative multiple
criteria analysis method; e) to accept one alternative as the most
preferable; f) to gather new information and go into the next iteration
of multiple criteria optimization if the final solution is not accepted.
At the beginning of his book, Zeleny (1982) stated that "It
has become more and more difficult to see the world around us in a
unidimensional way and to use only a single criterion when judging what
we see". In reality, the modelling of engineering problems is based
on a different kind of logic taking into consideration the existence of
multiple criteria, the conflicting aims of decision maker, the complex,
subjective and different nature of the evaluation process, and the
participation of several decision makers. The use of the new and
modernisation of the existing technologies as well as the selection of
the most suitable alternative among those feasible with the help of
different models are challenging tasks for the modern civil engineering
(Prentkovskis et al. 2012; Krayushkina et al. 2012). Estimation and
modelling of problems depends the recent advances achieved in different
fields (Dzemyda, Sakalauskas 2011). Selection of the right construction
technology plays a vital role in the overall performance of a project,
thus posing the most crucial challenge for any contractor. Numerous and
often conflicting objectives and alternatives, such as tender price,
completion date, and experience, need to be considered. Recently, to
assist contractors and stakeholders in decision-making, there has been a
trend to move away from the "lowest-price wins" principle and
subjective judgement to the multiple criteria selection approach in the
selection of alternatives (San Cristobal 2012).
[TABLE 1 OMITTED]
2. Case study
Projects with pile-columns are complex systems that are rather
difficult to select in practice. For this reason, a decision-maker
should possess a large amount of multidisciplinary knowledge and be
familiar with multidisciplinary techniques of operations research. The
case study presents the process of selecting the pile-column alternative
for a building that stands on the aquiferous soil. The aim of the study
is to design and install the most effective pile-columns. The study
shows how a decision-maker can find the most reasonable alternative with
the help of a certain dataset. Taking into account the aforementioned
suggestions and references of experts as well as the aim to install the
most effective pile-columns, the five following alternatives were
considered (Table 1).
The construction technology of alternatives is described by six
criteria. The set of criteria was determined by qualified civil
engineers and shown in Table 2. The selection is based on a set of
criteria: labour expenditures ([x.sub.1] > hours), cost of instalment
([x.sub.2], [epsilon]), consumption of concrete ([x.sub.3], [m.sup.3]),
consumption of steel ([x.sub.4], kg), machinery expenditures ([x.sub.5],
hours), and consumption of energy ([x.sub.6], GJ). The criteria set for
evaluation is selected considering the factors that influence the
efficiency of the construction process. Significance of criteria
significances (weights) was determined with the help of the expert
judgement method and the analytic hierarchy process (AHP) method.
Integrated criteria weights were applied in the solution process.
2.1. Determining criteria weights
One of the major tasks is to determine the weights of the criteria.
The weights demonstrate which criterion is the most important in
comparison to the other criteria (Kersuliene et al. 2010). The expert
judgment method was applied (Kendall 1970) at the first stage of
criteria weight determination. Zavadskas et al. (2010a) provided a
detailed presentation of the algorithm and discussed peculiarities of
weight determination. The weights [p.sub.j] of attributes presented in
Table 1 were determined by application of the expert judgment method
proposed by Kendall. This expert judgment method was implemented at the
following stages: a) calculation of values t; b) calculation of weights
w; c) calculation of values S; d) calculation of values [T.sub.k]; e)
calculation of concordance value W; f) calculation of values [chi
square]; g) testing the statement [chi square] > [[chi
square].sub.tbl].
The values [t.sub.jk] for statistical processing were obtained by
interviewing the respondents.
Kendall (1970) has demonstrated that, when n > 7, the value
[[chi square].sub.[alpha],x,v] = W * r * (n - 1) has a distribution with
degrees of freedom v = n - 1, where n is the number of attributes
considered and r - the number of experts. If the calculated value [chi
square] is larger than the critical tabular value [[chi square].sub.tbi]
for the pre-selected level of significance [alpha], then the hypothesis
about the agreement of independent expert judgments is not rejected. In
the case study, the number of experts r = 26, the degrees of freedom v =
n - 1 = 5 and the pre-selected level of significance is [alpha] = 0.05.
The calculated concordance coefficient based on the weights of
attributes is W = 0.558. The tabular value [[chi square].sub.tbl] =
15.08 ([alpha] = 0.05) (Fisher, Yates 1963).
Since [[chi square].sub.tbl] = 15.08 > [[chi
square].sub.[alpha],v] = 72.55 then the assumption is made that the
coefficient of concordance is significant and expert rankings are in
concordance with 95% probability.
During the next step, experts applied the WEAR software (which
contains the AHP method) to determine criteria weights (Zavadskas et al.
2012) (see Table 3).
In decision analysis, the analytical hierarchy process (AHP) and
the analytical network process (ANP) are widely used to assess the key
factors and analyse the impacts and preferences of decision alternatives
(Ergu et al. 2011a, b).
The recent developments of decision making models based on the AHP
(Saaty 1980; Saaty, Zoffer 2011; Vaidogas, Sakenaite 2011) methods are
listed below: Medineckiene et al. (2010) applied the AHP in sustainable
construction; Maskeliunaite et al. (2009), Sivilevicius and
Maskeliunaite (2010), and Sivilevicius (2011a) applied the AHP in
modelling of transport systems; and Sivilevicius (2011b) used the AHP to
determine the quality of technology.
Integrated criteria weights were calculated during the third stage
of criteria weight determination (Table 4).
2.2. Problem solving
Three different multiple criteria decision making methods --TOPSIS,
COPRAS and ARAS--were selected to solve the investigated problem An
Additive Ratio Assessment (ARAS) method (Zavadskas, Turskis 2010;
Turskis, Zavadskas 2010a) is based on the argument that complicated
phenomena could to be understood by using simple relative comparisons.
It is argued that the ratio of the sum of normalised and weighted values
of criteria, which describe an alternative under consideration, to the
sum of the values of normalised and weighted criteria, which describes
the optimal alternative, is the degree of optimality, which is reached
by the alternative under comparison.
The recent developments of decision making models based on the ARAS
method are listed below: Kersuliene and Turskis (2011) presented an
integrated fuzzy multiple criteria decision making model for the
selection of an architect; Turskis and Zavadskas (2010b) performed
multiple criteria analysis in order to select the location for a
logistics centres; and Zavadskas et al. (2010b) analysed foundation
alternatives.
[TABLE 5 OMITTED]
The method of complex proportional assessment COPRAS (Zavadskas,
Kaklauskas 1996) assumes direct and proportional dependence of
significance and utility degree of investigated alternatives on a system
of criteria adequately describing the alternatives, and on values and
weights of the criteria. This method was used to solve various problems
in construction.
The recent developments of decision making models based on COPRAS
methods (Podvezko 2011) are listed below: Datta et al. (2009) solved the
problem of determining the compromise to selection of a supervisor;
Bindu Madhuri et al. (2010) presented the model for selection of
alternatives based on COPRAS-G and AHP methods; Uzsilaityte and
Martinaitis (2010) investigated and compared different alternatives for
the renovation of buildings taking into account energy, economic and
environmental criteria while evaluating impact of renovation measures
during their life cycle; Chatterjee et al. (2011) presented materials
selection model based on COPRAS and EVAMIX methods; Yazdani et al.
(2011) applied the COPRAS method to analyse critical infrastructures.
The TOPSIS (Technique for Order Preference by Similarity to Ideal
Solution) method determines a solution with the shortest distance from
the ideal solution and the farthest distance from the negative-ideal
solution (Hwang, Yoon 1981). Kalibatas et al. (2011) used it in order to
solve the problem of the assessment of dwelling-houses, determining the
ideal indoor environment. Rudzianskaite-Kvaraciejiene et al. (2010)
evaluated the effectiveness of road investment projects.
The description of the methods is presented in Table 5.
First of all, the initial decision making matrix was prepared. The
problem was solved by applying three different multiple criteria
decision making methods: TOPSIS, COPRAS and ARAS. The solution process
of the problem is presented in Table 6.
3. Conclusions
Overall, the main advantages that the MCDM provides in decision
making could be summarized in the following aspects: the possibility to
analyse complex problems; the possibility to aggregate both quantitative
and qualitative criteria in the evaluation process; good evidence of
decisions; the option for a decision-maker to participate actively in
the decision-making process; and the use of flexible scientific methods
in the decision making process.
According to the newly proposed model, the priorities of
alternatives can be determined according to the utility function value.
Consequently, it is convenient to evaluate and rank decision
alternatives when this model is used.
The degree of the alternative utility is determined by comparison
of the analysed variant with ideally the best one.
It can be stated that the ratio with an optimal alternative may be
used in cases when it is required to rank alternatives and find ways to
improve alternative projects.
Three MCDM methods were applied. Alternatives according to all
methods rank in the same way: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE
IN ASCII].
This means that the most preferable alternative is a4 that must be
selected and implemented.
The proposed model can be modified and applied to solve different
problems: to select, assess and rank constructions, technologies and
other alternatives.
doi: 10.3846/13923730.2012.744537
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Edmundas Kazimieras Zavadskas (1), Saulius Susinskas (2), Alfonsas
Daniunas (3), Zenonas Turskis (4), Henrikas Sivilevicius (5)
(1,3,4,5) Vilnius Gediminas Technical University, Sauletekio al.
11, 10223 Vilnius, Lithuania (2) Kaunas University of Technology
Panevezys Institute, S. Daukanto g. 12-138, 37164 Panevezys, Lithuania
E-mails: 1edmundas.zavadskas@vgtu.lt; (2) saulius.susinskas@ktu.lt; (3)
alfonsas.daniunas@vgtu.lt; (4) zenonas.turskis@vgtu.lt (corresponding
author); (5) henrikas.sivilevicius@vgtu.lt
Received 20 Dec. 2010; accepted 04 Nov. 2011
Dr Habil, Professor, Head of the Research Institute of Internet and
Intelligent Technologies and Head of the Department of Construction
Technology and Management of Vilnius Gediminas Technical University,
Lithuania. Research interests: building technology and management,
decision-making theory, automation in design and decision support
systems.
Saulius SUSINSKAS. Doctor, Associate Professor, Head of the
Department of Civil Engineering of Panevezys Institute Faculty of
Technologies, Kaunas University of Technology, Lithuania. Research
interests: civil engineering, construction materials and their strength
and durability, analysis of changes in substrate stiffness and its
effect on the behaviour of the building.
Alfonsas DANIUNAS. Doctor, Associate Professor at the Department of
Steel and Timber Structures of Vilnius Gediminas Technical University,
Lithuania. Research interests: analysis and optimization of elastic and
plastic steel structures, numerical methods, semi-rigid joints of steel
structures.
Doctor of Technical Science, Chief Research Fellow at Construction
Technology and Management Laboratory of Vilnius Gediminas Technical
University. Research interests: civil engineering, construction
technology and management, decision-making theory, computer-aided
automation in design, expert systems.
Dr Habil, Professor at the Department of Transport Technological
Equipment of Vilnius Gediminas Technical University, Lithuania. Research
interests: flexible pavement life-cycle, hot mix asphalt mixture
production technology, application of statistical and quality control
methods, recycling asphalt pavement technologies and design,
decision-making and expert systems theory.
Table 2. The Expert judgement method
Expert [x.sub.1] [x.sub.2] [x.sub.3]
[E.sub.1] 5 6 4
[E.sub.2] 1 5 6
[E.sub.3] 3 5 6
[E.sub.4] 5 4 6
[E.sub.5] 6 5 3
[E.sub.6] 3 4 6
[E.sub.7] 4 6 5
[E.sub.8] 1 3 5
[E.sub.9] 5 6 3
[E.sub.10] 6 5 3
[E.sub.11] 5 6 4
[E.sub.12] 5 6 3
[E.sub.13] 5 2 6
[E.sub.14] 4 3 6
[E.sub.15] 6 5 3
[E.sub.16] 3 4 6
[E.sub.17] 5 6 4
[E.sub.18] 5 6 3
[E.sub.19] 6 4 5
[E.sub.20] 5 6 4
[E.sub.21] 4 6 5
[E.sub.22] 4 6 3
[E.sub.23] 5 6 1
[E.sub.24] 5 6 3
[E.sub.25] 5 6 2
[E.sub.26] 5 6 4
Sum of rank; 116 133 109
Mean value 4.462 5.115 4.192
Rank 2 1 3
Weight of 0.212 0.244 0.200
criterion
[p.sub.j]
Expert [x.sub.4] [x.sub.5] [x.sub.6]
[E.sub.1] 3 1 2
[E.sub.2] 3 2 4
[E.sub.3] 4 1 2
[E.sub.4] 3 1 2
[E.sub.5] 4 2 1
[E.sub.6] 5 2 1
[E.sub.7] 3 1 2
[E.sub.8] 4 2 6
[E.sub.9] 4 1 2
[E.sub.10] 4 1 2
[E.sub.11] 3 2 1
[E.sub.12] 2 4 1
[E.sub.13] 4 3 1
[E.sub.14] 5 1 2
[E.sub.15] 4 2 1
[E.sub.16] 5 1 2
[E.sub.17] 3 2 1
[E.sub.18] 4 2 1
[E.sub.19] 3 1 2
[E.sub.20] 3 1 2
[E.sub.21] 3 2 1
[E.sub.22] 5 1 2
[E.sub.23] 2 4 3
[E.sub.24] 4 1 2
[E.sub.25] 4 3 1
[E.sub.26] 3 1 2
Sum of rank; 94 45 49
Mean value 3.615 1.731 1.885
Rank 4 6 5
Weight of 0.172 0.082 0.090
criterion
[p.sub.j]
Table 3. Criteria weights according to the AHP method
Determined criteria weights
Expert [x.sub.1] [x.sub.2] [x.sub.3]
[E.sub.1] 0.249 0.379 0.102
[E.sub.2] 0.043 0.249 0.379
[E.sub.3] 0.16 0.249 0.379
[E.sub.4] 0.249 0.102 0.379
[E.sub.5] 0.379 0.249 0.16
[E.sub.6] 0.16 0.102 0.379
[E.sub.7] 0.102 0.379 0.249
[E.sub.8] 0.043 0.16 0.249
[E.sub.9] 0.249 0.379 0.16
[E.sub.10] 0.379 0.249 0.16
[E.sub.11] 0.249 0.379 0.102
[E.sub.12] 0.249 0.379 0.16
[E.sub.13] 0.249 0.065 0.379
[E.sub.14] 0.102 0.16 0.379
[E.sub.15] 0.379 0.249 0.16
[E.sub.16] 0.16 0.102 0.379
[E.sub.17] 0.249 0.379 0.102
[E.sub.18] 0.249 0.379 0.16
[E.sub.19] 0.379 0.102 0.249
[E.sub.20] 0.249 0.379 0.102
[E.sub.21] 0.102 0.379 0.249
[E.sub.22] 0.102 0.379 0.16
[E.sub.23] 0.249 0.379 0.043
[E.sub.24] 0.249 0.379 0.16
[E.sub.25] 0.249 0.379 0.065
[E.sub.26] 0.249 0.379 0.102
[SIGMA] 5.727 7.344 5.547
Established weights
[q.sub.j] 0.221 0.283 0.214
Determined criteria weights
Expert [x.sub.4] [x.sub.5] [x.sub.6]
[E.sub.1] 0.16 0.043 0.065
[E.sub.2] 0.16 0.065 0.102
[E.sub.3] 0.102 0.043 0.065
[E.sub.4] 0.16 0.043 0.065
[E.sub.5] 0.102 0.065 0.043
[E.sub.6] 0.249 0.065 0.043
[E.sub.7] 0.16 0.043 0.065
[E.sub.8] 0.102 0.065 0.379
[E.sub.9] 0.102 0.043 0.065
[E.sub.10] 0.102 0.043 0.065
[E.sub.11] 0.16 0.065 0.043
[E.sub.12] 0.065 0.102 0.043
[E.sub.13] 0.102 0.16 0.043
[E.sub.14] 0.249 0.043 0.065
[E.sub.15] 0.102 0.065 0.043
[E.sub.16] 0.249 0.043 0.065
[E.sub.17] 0.16 0.065 0.043
[E.sub.18] 0.102 0.065 0.043
[E.sub.19] 0.16 0.043 0.065
[E.sub.20] 0.16 0.043 0.065
[E.sub.21] 0.16 0.065 0.043
[E.sub.22] 0.249 0.043 0.065
[E.sub.23] 0.065 0.102 0.16
[E.sub.24] 0.102 0.043 0.065
[E.sub.25] 0.102 0.16 0.043
[E.sub.26] 0.16 0.043 0.065 [SIGMA]
[SIGMA]
[SIGMA] 3.746 1.668 1.916 25.948
Established weights
[q.sub.j] 0.144 0.064 0.074
Table 4. Integrated criteria weights
Criteria
[x.sub.1] [x.sub.2] [x.sub.3] [x.sub.4]
[q.sub.j] 0.221 0.283 0.214 0.144
[p.sub.j] 0.212 0.244 0.2 0.172
[w.sub.j] 0.217 0.263 0.207 0.158
Weights
[x.sub.5] [x.sub.6]
[q.sub.j] 0.064 0.074 AHP
[p.sub.j] 0.082 0.09 Kendall
[w.sub.j] 0.073 0.082 Integrated
[w.sub.j] = [q.sub.j]
[p.sub.j]/[n.summation
over (i=1)]([q.sub.j]
[p.sub.j]); j = [bar.1,n]
Table 6. The problem solution process and results
The problem solution process and results
The initial decision making matrix
Alternative Attributes
[x.sub.1] [x.sub.2] [x.sub.3]
Optimum min min min
Weights w 0.212 0.244 0.200
[a.sub.1] 9.7 405 3.53
[a.sub.2] 10.2 429 3.53
[a.sub.3] 8.6 404 3.38
[a.sub.4] 9.8 320 3.38
[a.sub.5] 7.9 327 3.53
Alternatives Attributes
[x.sub.4] [x.sub.5] [x.sub.6]
Optimum min min min
Weights w 0.172 0.082 0.090
[a.sub.1] 247 2 13.9
[a.sub.2] 247 2.5 9.3
[a.sub.3] 495 2 16.2
[a.sub.4] 246 2.3 7.8
[a.sub.5] 247 2.2 13.8
TOPSIS method
[[??].sub.1] [[??].sub.2] [[??].sub.3] [[??].sub.4]
Optimum min min min min
[a.sub.1] 0.099 0.116 0.091 0.061
[a.sub.2] 0.104 0.123 0.091 0.061
[a.sub.3] 0.088 0.116 0.087 0.122
[a.sub.4] 0.100 0.092 0.087 0.061
[a.sub.5] 0.081 0.094 0.091 0.061
[a.sup.+] 0.081 0.092 0.087 0.061
[a.sup.-] 0.104 0.123 0.091 0.122
[[??].sub.5] [[??].sub.6] [D.sup.+] [D.sup.-]
Optimum min min
[a.sub.1] 0.033 0.044 0.036 0.075
[a.sub.2] 0.042 0.030 0.041 0.075
[a.sub.3] 0.033 0.052 0.071 0.013
[a.sub.4] 0.038 0.025 0.020 0.094
[a.sub.5] 0.037 0.044 0.020 0.090
[a.sup.+] 0.033 0.025 0.000 0.108
[a.sup.-] 0.042 0.052 0.078 0.000
K Rank
[a.sub.1] 0.673 3
[a.sub.2] 0.649 4
[a.sub.3] 0.158 5
[a.sub.4] 0.824 1
[a.sub.5] 0.819 2
[a.sup.+] 1.000
[a.sup.-] 0.000
COPRAS method
[[??].sub.1] [[??].sub.2] [[??].sub.3] [[??].sub.4]
Optimum min min min min
[a.sub.1] 0.045 0.052 0.041 0.029
[a.sub.2] 0.047 0.055 0.041 0.029
[a.sub.3] 0.040 0.052 0.039 0.058
[a.sub.4] 0.045 0.041 0.039 0.029
[a.sub.5] 0.036 0.042 0.041 0.029
[[??].sub.5] [[??].sub.6] [S.sub.-] [S.sub.+]
Optimum min min
[a.sub.1] 0.015 0.020 0.000 0.202
[a.sub.2] 0.019 0.014 0.000 0.204
[a.sub.3] 0.015 0.024 0.000 0.227
[a.sub.4] 0.017 0.011 0.000 0.183
[a.sub.5] 0.016 0.020 0.000 0.185
S K Rank
[a.sub.1] 0.197 0.905 3
[a.sub.2] 0.195 0.895 4
[a.sub.3] 0.175 0.804 5
[a.sub.4] 0.218 1.000 1
[a.sub.5] 0.215 0.989 2
ARAS method
[[??].sub.1] [[??].sub.2] [[??].sub.3] [[??].sub.4]
Optimum min min min min
[a.sub.1] 0.040 0.045 0.039 0.038
[a.sub.2] 0.038 0.042 0.039 0.038
[a.sub.3] 0.045 0.045 0.041 0.019
[a.sub.4] 0.040 0.057 0.041 0.038
[a.sub.5] 0.049 0.055 0.039 0.038
[a.sub.0] 0.049 0.057 0.041 0.038
[[??].sub.5] [[??].sub.6] S
Optimum min min
[a.sub.1] 0.018 0.015 0.195
[a.sub.2] 0.014 0.022 0.194
[a.sub.3] 0.018 0.013 0.181
[a.sub.4] 0.016 0.026 0.217
[a.sub.5] 0.016 0.015 0.213
[a.sub.0] 0.018 0.026 0.217
K Rank
[a.sub.1] 0.897 3
[a.sub.2] 0.893 4
[a.sub.3] 0.831 5
[a.sub.4] 1.000 1
[a.sub.5] 0.981 2
[a.sub.0] 1.000
