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Copyright © 2019 e Author(s). Published by VGTU Press
Journal of Civil Engineering and Management
ISSN 1392-3730 / eISSN 1822-3605
2019 Volume 25 Issue 4: 306–321
https://doi.org/10.3846/jcem.2019.9644
*Corresponding author. E-mail: rachelpalha@gmail.com
SORTING SUBCONTRACTORS’ ACTIVITIES IN CONSTRUCTION
PROJECTS WITH A NOVEL ADDITIVE-VETO SORTING APPROACH
Rachel Perez PALHA 1*, Adiel Teixeira DE ALMEIDA 2,
Danielle Costa MORAIS 2, Keith W. HIPEL 3
1Department of Civil and Environmental Engineering, Universidade Federal de Pernambuco,
Av. Acadêmico Hélio Ramos, s/n – Cidade Universitária, Recife, PE, CEP 50.740-530, Brazil
2CDSID – Center for Decision Systems and Information Development,
Universidade Federal de Pernambuco, Recife, PE, CEP 50.740-530, Brazil
3Department of Systems Design Engineering, University of Waterloo, Waterloo, ON, Canada
Received 28 June 2018; accepted 19 February 2019
Abstract. Selection processes in civil engineering infrastructure projects might require more time and eort than the decision-
makers involved in these projects are normally prepared to devote to running them. A novel approach is proposed to sort these
activities into classes that represent their impact on the project, namely additive-veto sorting model, which should be considered
before any bidding procedure. erefore, problems regarding the client’s satisfaction caused by subcontractors can be avoided,
and the decision-makers involved in the selection problem can devote to each class an eort compatible with the impact that
activity might have on the project. e novelty of this method is that it was built to reect the quasi-compensatory rationality of
decision-makers in the construction industry; it provides them with insights on subcontractors’ activities, and it is grounded on
and inspired by a real case study. e new parameters proposed within this model introduce the idea of vetoing an activity be-
ing assigned to a class when this activity is incompatible with the decision-maker’s preferences. By using this novel method, the
authors succeeded in nding results that avoided a complete compensation amongst the factors considered, taking into account
ranges that would be of signicant importance in the decision process.
Keywords: subcontractor management, multiple criteria analysis, Additive-veto sorting approach, sorting.
Introduction
Selecting subcontractors in the construction industry is
a complex problem that is usually evaluated based on
managers’ intuition and experience (Biruk, Jaśkowski, &
Czarnigowska, 2017). However, making such selections
influences contractors’ competitiveness (Tan, Xue, &
Cheung, 2017) and contractors frequently have to make
a decision on whether or not to subcontract during the
bidding phase (Arditi & Chotibhongs, 2005). Although
this is still an open discussion, this problem has been ad-
dressed in the literature for many years since subcontract-
ing activities is a common practice in this industry (Holt,
Olomolaiye, & Harris, 1995). Subcontractor selection is
one of the most critical tasks because of the important role
that subcontractors play in the success of a project and
their impact over the main contractor’s competitiveness
(Abbasianjahromi, Rajaie, & Shakeri, 2013).
Selecting and managing subcontractors is a relevant is-
sue since subcontractors account for 80–90% of the activi-
ties performed in a project (Polat, 2016) and they are hired
to perform particular activities, which represent dierent
risks to a project and to the decision-makers (DMs) in-
volved in its management. Kumaraswamy and Matthews
(2000) discussed the importance of the subcontractor se-
lection process, given the oversupply of specialist rms and
the problems that this activity had caused in the construc-
tion industry. ey advocate that since it is easy to enter
this marketplace, these companies have been established
with little capital investment and many are unable to func-
tion satisfactorily. erefore, Holt, Olomolaiye, and Harris
(1994) and Sönmez, Holt, Yang, and Graham (2002) pro-
posed using prequalication criteria prior to the selection
itself in order to avoid issues such as lack of quality, delays,
Journal of Civil Engineering and Management, 2019, 25(4): 306–321 307
and additional costs. is approach is enhanced with the
methodology proposed in this paper.
e contributions of this paper are as follows: (i) it
provides insights for civil engineering and management by
addressing the process for selecting subcontractors in the
construction industry, bearing in mind that this is an im-
portant managerial issue for contractors; (ii) the insights
obtained from the real situation studied gave rise to pro-
posing a new model to categorize the activities to be sub-
contracted, and thus, the DM will be able to apply dier-
ent selection methodologies for each class; (iii) the authors
developed a novel approach to enable a quasi-compensa-
tory evaluation, the additive-veto sorting model; and (iv)
to allow the veto, the authors proposed new parameters
which are used to veto activities being sorted into classes
that are incompatible with the DM’s preferences. In a gen-
eralization of the model, these activities might be any type
of alternatives. e methodological contribution may be
applied to any multicriteria decision problem that requires
using the concept of veto, which has hitherto only been
proposed for non-compensatory rationality. When the
DM presents non-compensatory rationality, the preference
relation between two alternatives depends only on the sub-
set of criteria that favor the alternatives, irrespective of the
dierences in the performance of the alternatives for each
criterion (Fishburn, 1976). If the DM presents compensa-
tory rationality, this means that by gaining in one variable,
a loss in another variable can be compensated for (Munda,
2016). However, when the dierences among variables are
very large, it is no longer possible to compensate. What
is then needed is to use non-compensatory basic indices,
which leads to a partially compensatory approach (Martel
& Matarazzo, 2016) which this paper calls a “quasi-com-
pensatory” approach.
An application of this model to a real case situation of
a contractor in Brazil is presented. is problem was raised
by Palha, de Almeida, and Alencar (2016). However, since
there was still room for improvements, the additive-veto
model for sorting problematic was proposed. is applica-
tion considers the same three classes of assignment created
in accordance with their criticality, but the model was cre-
ated to reect the rationality and correct some misrepre-
sentations of the model previously used in the rst phase
of the project. is led to a new Multi-Criteria Decision
Making/Analysis (MCDM/A) approach being proposed
in order to cope with construction management issues
that arose within the rst phase of the construction of the
brewery facility project. is enabled practical construc-
tion management and methodological insights to be ob-
tained. erefore, this allowed managerial implications
to be checked by examining the dierences in the results
which were achieved by using alternative methodologies
such as SAW, ROR-UTADIS (Palha etal., 2016), and the
novel sorting approach proposed in this article. e in-
sights from this analysis are presented in Section 4 which
discusses managerial/practical implications. is showed
that, when using all features, better results are achieved
from the construction management perspective, there-
by revealing a practical situation in which this approach
would be required. e method now proposed enables
DMs in dierent contexts to save time and eort on se-
lection processes. Moreover, they nd the method easy to
understand, because they are used to making trade-os
among objectives during decision processes (Mungle, Be-
nyoucef, Son, & Tiwari, 2013). ey are also used to veto-
ing bidders that in some way lack the performance needed
in some criterion that comes to light during the bidding
process (Holt etal., 1995).
is paper oers insights not only into the manage-
rial and subcontracting process, but also a new method
which is appropriate for problems related to subcontract-
ing in many other contexts and dierent kinds of produc-
tion systems. is article is structured into ve sections.
An overview of literature is given in Section 2. Section 3
presents the research methodology used in this article. e
Additive-veto sorting approach for multicriteria decision
problem is presented in Section 4, and in Section 5 an in-
novative application to the construction industry context
is described. Section 6 contains nal remarks, draws some
conclusions and indicates possible lines of future research
studies.
1. An overview of the literature
ere is a wide range of methodologies that might be
used to select subcontractors. Selecting contractors and
subcontractors used to be based on tender price alone, but
construction clients are becoming more aware that this
type of selection is risky and may lead to poor quality and
time delay (Singh & Tiong, 2005) which can be associated
with the costs incurred on rework because subcontract-
ing services were unsatisfactory (Love, Edwards, Smith,
& Walker, 2009). In addition, DMs frequently make their
decisions based on their experience and without using an
evaluation technique (Ulubeyli, Manisali, & Kazaz, 2010).
us, Keshavarz Ghorabaee, Amiri, Salehi Sadaghiani, and
Hassani Goodarzi (2014) classify this process as a mul-
ticriteria problem for which qualitative and quantitative
criteria may well be used. Wan and Li (2013) proposed
using linear programming for making a multidimensional
analysis of preference. is includes using intuitionistic
fuzzy sets, trapezoidal fuzzy numbers, intervals, and real
numbers to reect the DM’s uncertainty as to his/her pref-
erences
Ng and Skitmore (2014) proposed a framework to eval-
uate subcontractors by using a balanced scorecard model
using ten evaluation criteria. Ballesteros-Perez, Skitmore,
Pellicer, and Zhang (2016) analyzed the relationship be-
tween the Bid Scoring Formula (BSF) and the competi-
tiveness behavior of bidders in the Spanish construction
industry to verify how to control bidder’s aggressiveness
and avoid problems associated with over-competitiveness.
Schöttle and Arroyo (2017) compared three multicriteria
methods regarding their performance in the construction
industry for which they undertook a sensitivity analysis
and a case study.
308 R. P. Palha et al. Sorting subcontractors’ activities in construction projects with a novel Additive-veto sorting...
Another way to address the problem of outsourcing is
to combine AHP (Analytic Hierarchy Process) with PRO-
METHEE (Preference Ranking Organization Method for
Enrichment Evaluations) methods (Polat, 2016) when a
non-compensatory approach is required. However, these
methodologies were built to evaluate bidders who are tak-
ing part in a selection or to verify which criteria DMs take
into account when making these evaluations. erefore,
the DMs are subjected to the same level of eort to evalu-
ate any of the activities that need to be subcontracted in a
project. Under this assumption, activities that would not
inuence the contractor’s competitiveness are subjected to
the same selection procedures as activities that might do
so. us, sorting the activities according to their impact on
the construction would lead to a dierent outcome.
Within the context of the construction industry, DMs
usually think in a way that is more closely associated with
compensatory rationality. ese DMs acknowledge that
on reducing certain costs, the time required to perform an
activity may increase and that on improving quality, the
project might become more expensive, and so on (Mungle
etal., 2013). erefore they are usually willing to compen-
sate the criteria by conducting trade-os (Keeney & Raia,
1993). us, it would not be suitable to use an outranking
method in this context, and therefore this eliminates the
possibilities of using ELECTRE-TRI-B (Roy & Bouyssou,
1993) and PROMSORT (Araz & Ozkarahan, 2007).
Preference elicitation methods require the DM to spec-
ify a range of technical and preferential information so as
to calibrate the sorting model. When using a holistic ap-
proach, the DM has to assign well-known exemplary alter-
natives to predened pre-ordered classes. Based on these
assignments the DM’s preference information is built us-
ing regression-based techniques (Zopounidis & Doum-
pos, 2002). e main problem of using a holistic method
in this context is that projects greatly vary in size, risk, and
the activities involved. In addition, where the project it-
self is located might change the class of assignment of an
activity. erefore, by applying a holistic method right at
the beginning of a project, the DM could present biased
preference information, because he/she could evaluate the
alternatives based on previous projects that did not relate
in any way to the situation faced in the current one. us,
it is important to consider a method which uses preference
elicitation and therefore avoids using DMs’ experiences.
Instead, their preferences should be used.
e last possibility would be to apply an additive meth-
od, such as SAW (Simple Additive Weight). Nevertheless,
problems of an unbalanced set of alternatives might arise.
is occurs when an alternative has a top performance in
one or more criteria but a very low one in others. us, the
compensation that can arise under this method might be
undesirable at certain levels. is same problem might oc-
cur when using AHPSort (Ishizaka, Pearman, & Nemery,
2012) or TOPSIS-Sort (Sabokbar, Hosseini, Banaitis, & Ba-
naitiene, 2016) because these methods are fully compen-
satory. e veto concept would be an alternative way to
address the issue of an unbalanced set of alternatives. Al-
though the veto concept is traditionally linked to the out-
ranking approaches, it has been used by de Almeida (2013)
in the additive model for choice and ranking problems.
According to Vetschera, Chen, Hipel, and Kilgour
(2010), sorting problems are signicantly dierent from
choice or ranking ones as they need proper parametriza-
tion and the use of specic methods. erefore, ranking
methods might be adapted to sorting problems by consid-
ering proper parametrization (Ishizaka etal., 2012), since
the assignment of an alternative to a class includes describ-
ing it and incorporates preference information that can be
used by the DM (Doumpos & Zopounidis, 2004). us the
meaning to be given to an alternative is linked to the class
to which it belongs.
is gap in the literature is lled by the novel MCDM
approach proposed in Section 3. It adds the possibility
of using the veto concept for additive sorting problems,
thereby enabling a quasi-compensatory approach. is
approach lets issues be dealt with that arise from an un-
balanced set of alternatives. What prompted considering
it was a real-world situation observed in a civil engineer-
ing managerial process and a case study associated with
it. us, Section 3 presents the Additive-veto sorting ap-
proach with a preference elicitation method, thus extend-
ing the additive-veto for ranking proposed by de Almeida
(2013) to sorting problems. It does so by considering a
new set of parameters and novel decision rules to intro-
duce the idea of vetoing the classication of an alternative
when assigning it to a class prole.
2. Research methodology
is study was built as the development of prior re-
search presented by Palha et al. (2016) and following
the MCDM/A framework presented by de Almeida etal.
(2015), taking into consideration the methodological
steps for structuring and solving an MCDM/A problem.
roughout this methodological framework, methods are
dened that t the DMs’ preferences and which can in-
clude compensatory or non-compensatory rationality and
the characteristics of the problem, such as types of activi-
ties, risks, and contract sizes.
Based on this particular problem, it has been devel-
oped and applied the novel MCDM method proposed in
this paper, enabling to test the novel approach to compare
and analyze its results with those presented by Palha etal.
(2016) when using ROR UTADIS (Kadziński, Ciomek, &
Słowiński, 2015).
e study by Palha etal. (2016) concerned the con-
struction of a brewery in the State of Pernambuco in
Northeast Brazil which was designed to have a productive
capacity of 600 million liters of beer per year. e plant
consists of 19 buildings, of which 15 are industrial, and
the site covers an area of 297,000m². e expected cost
of this construction was US$70 million. It was a cost-plus
contract, which led the contractor to subcontract most of
the activities. is required more attention to be paid to
the process for selecting sub-contractors throughout the
Journal of Civil Engineering and Management, 2019, 25(4): 306–321 309
project. In addition, in case of liabilities, both the contrac-
tor and the owner of the brewery will be prosecuted. is
means that satisfying this client relies not only on develop-
ing the project itself but also on avoiding penalty charges
being incurred. In the context of this project, the Director
of the Construction (DC) is the DM and is responsible for
the project, both legally and to the contractor.
It took a long time to construct the brewery, and this
took place over two phases. is allowed the DM to revisit
her preferences and re-evaluate the data. In the period of
this research, several changes occurred in the civil engi-
neering market in Brazil, which prompted the DM to feel
uncomfortable about providing preference information
based on holistic assignments. In addition, aer the rst
sorting interaction, the DM veried when selecting sup-
pliers that some of the sorting assignments were incom-
patible with the impact on the owner, the contractor and
the project itself of subcontracting the activity. us, the
project required a new method to be developed for which
preference elicitation could be used and which was, at least
partially, compensatory. e method developed was the
Additive-veto sorting approach for multicriteria decision
problems. is was created based on this problem, but it
might be used in other sorting problems as well. erefore,
each decision is aected by the DM’s style and problem
context. us, there will be situations where a fully com-
pensatory or a non-compensatory approach may be re-
quired, and also, situations where an intermediate kind of
approach would be more suitable, and which would, there-
fore, require a “quasi-compensatory” one. e approach
presented in Section 3 was tested in the construction of
the brewery where the problem arose for which a hypo-
thetical-deductive research method validated similarly as
in Polat (2016) and Abbasianjahromi, Rajaie, Shakeri, and
Kazemi (2016), based on the validity of the assumption of
the study.
3. e Additive-veto sorting approach for
multicriteria decision problems
Using the veto concept does not permit an alternative to
be sorted when based only on its overall value, but this
must also consider restrictions that the DM has included
in his/her quasi-compensatory preference information.
erefore, parametric information, such as the proles
of classes and the upper and lower thresholds are elicited
from the DM and considered with two veto conditions: the
criterion veto index, and the criteria weight coalition veto
.
e procedure presented considers three steps. Fig-
ure1 presents how the rst two steps are conducted. First,
the global value of the alternatives and proles are calcu-
lated, and the alternatives are analysed in order to deter-
mine the class assignments. Secondly, decision rules are
applied to the alternatives to veto their classication to
classes of assignment. Aer the analysis is completed, a
recommendation is presented to the DM, aer which he/
she can review his/her preference information and run a
sensitivity analysis.
3.1. Evaluation of alternatives and proles
e rst step of this approach consists of determining the
overall value of the alternatives and specifying the pro-
le for each class. is value is calculated using Eqn(1).
us, the scale constants must be elicited from the DM,
using the trade-o method (Keeney & Raia, 1993). Con-
sider a nite set of m alternatives,
{ }
12
, , , m
A xx x= …
,
which is evaluated using a nite set
{ }
12
, , ,
n
g gg g= …
of n evaluation criteria. In the context of the additive-veto
model for sorting problems, the criteria are the ordinal
descriptions of an alternative (Zopounidis & Doumpos,
2002). e classes describe the alternatives, and in sort-
ing problems, they also incorporate preferential informa-
tion from a decision making context, unlike what happens
in classication methods, where the classes describe the
alternatives in a nominal way (Zopounidis & Doumpos,
2002). In terms of the selection problem that gave rise to
the method, the criteria are the characteristics that each
activity might have and that can be used to evaluate their
impact over the project, while the alternatives are the ac-
tivities that will be subcontracted and the classes represent
the impact that an alternative might have over the project
and are used to dene how the project should manage the
selection process and the subcontractor:
( ) ( )
1
n
j ii j
i
V x kv x
=
=∑
, (1)
where
( )
j
Vx
is the overall value of alternative
j
x
; ki is
the scale constant of criterion i and
1
1
n
i
i
k
=
=
∑
;
( )
ij
vx
is
the value of the consequence of criterion i.
e value of the consequence,
( )
ij
vx
, is a function
that represents the value of an alternative j on the attrib-
ute i. e shape of this function and its parameters are ob-
tained by using an elicitation process with the DM. us,
( )
ij
vx
may be a linear or non-linear function (Keeney &
Raia, 1993).
e set of alternatives sometimes consists of alterna-
tives, which have a high performance in one criterion and
a low performance in another, to such an extent that these
low performances are fully compensated for by the higher
ones. Even though the idea of the additive method is to
allow this compensation, sometimes the value of the al-
ternative in one criterion is well above an acceptable level,
thereby making it necessary to eliminate that evaluation
or limit its eect. In order to provide balance to the set of
alternatives and to avoid possible misclassication, a veto
condition is proposed.
For sorting problems, there are two ways to introduce
the veto concept. First, in one approach, an alternative as-
signed to a specic class can be vetoed, in which case it
is sorted to a more appropriate lower class. In a second
procedure, the performance of the alternative could be pe-
nalized as described in Eqn(3) and thereby be assigned to
a suitable lower class. is veto condition was presented
by de Almeida (2013) for ranking problems and, in this
310 R. P. Palha et al. Sorting subcontractors’ activities in construction projects with a novel Additive-veto sorting...
model, it is applied in the rst step as a penalty by using
Eqns(2) and (3) across the overall value of the alternatives.
( ) ( )
( )
( ) ( )
0,
1,
,
ij i
ij ij i
ij i
i ij i
ii
if v x l
z x if v x u
vx l
if l v x u
ul
≤
= ≥
−
<<
−
, (2)
where
( )
ij
zx
is the penalization function of alternative
xj for criterion i;
i
u
is the upper threshold for criterion i;
i
l
is the lower threshold for criterion i.
( ) ( ) ( )
1
,
n
j j ii j
i
V x r x kv x
=
′=
∑
(3)
where
( )
j
Vx
′
is the penalized global function of alterna-
tive xj;
( )
j
rx
is the penalization index of alternative xj,
where
( ) ( )
1
n
j ij
i
rx r x
=
=∑
;
( )
ij
rx
is the weighted penaliza-
tion function for alternative xj, where
( ) ( )
ij iji
rx zx k=
.
e upper threshold (ui) is the minimum acceptable
value of performance for criterion i for any alternative be-
low which the DM believes a penalization must be used
in the overall value of that alternative; whereas the lower
threshold (li) is the maximum value of criterion i for which
the performance of the alternative starts to be unaccept-
Figure 1. e Additive-veto sorting approach
Journal of Civil Engineering and Management, 2019, 25(4): 306–321 311
able. erefore, that criterion should not contribute to cal-
culating the overall value of the alternative (de Almeida,
2013). e DM must provide both parameters. Addition-
ally, whenever the DM does not wish to introduce the pe-
nalization in a criterion, both thresholds must be set to the
minimum value in the scale.
Let
h
C
, be q predened preference-ordered classes in
such a way that
1 21qq
CC CC
−
…
. e assignment
of an alternative to a class is conducted by comparing an
alternative with the reference alternative of the class under
consideration. e prole is the reference alternative that is
the boundary between two classes (Doumpos & Zopouni-
dis, 2004). us,
h
b
is the vector of the performance of
this reference alternative with respect to each criterion and
represents the limit between class
h
C
and class
1h
C+
(Roy
& Bouyssou, 1993). e threshold of a class or limit pro-
le is the overall value of its reference alternative, which is
calculated using equation
( ) ( )
1
n
h ii h
i
V b kv b
=
=
∑
. e thres-
hold is specied with
( )
ih
vb
for each criterion and aggre-
gated with the formulation given above for
( )
h
Vb
. When
using the proposed approach, the analyst should consider
that the limit proles of each category have been dened pri-
or to dening the veto parameters. us, as the veto param-
eters are a function of the values set for the prole bounda-
ries, these would not work to veto the reference alternative,
and therefore would prevent further inconsistencies.
e model presented is divided into a global and a
local analysis. e main idea of the global analysis is to
compare the penalized global value of each alternative xj
(V’(xj)) with the limit prole
( )
h
Vb
and to state whether
or not the alternative can belong to class h. When it can-
not, then it is compared to lower classes until a suitable
class is found. When the alternative might belong to class
h, the appropriateness of this classication must be veri-
ed. is comparison is carried out by using the following
rule presented in Eqn(4):
( )
( )
( )
( )
, 1, , ; , ,1
,
j
j h jh
j h jh
x A j mhq
if V x V b thenx P
if V x V b thenx P
∈=…=…
≥∈
<∉
′
′
(4)
where Ph is the subset of
A
that might belong to class Ch.
Every alternative has to be assigned to one class, and,
since Class C1 is the worst possible class, if one alternative
cannot be assigned to any other class, it will be assigned
to Class C1. erefore, for h = 1,
( )
10Vb =
. e verica-
tion of the suitability of an alternative to a class occurs only
over the alternatives belonging to Ph. is will be further
veried to conrm whether or not the alternative belongs
to Class Ch, and depends on the local analysis.
In the local analysis, the performance of the alterna-
tives belonging to subset Ph, are compared with that of the
reference alternative
h
b
. is analysis is the last analysis
of the rst step, namely, to conrm if the alternative be-
longs to class Ch or if it is necessary to use the second step.
Eqn(5) presents the rule for the second lter of the model.
If the alternative is at least as good as the reference alter-
native for class Ch, then it certainly belongs to it. If in at
least one criterion the alternative fails, then the procedure
moves on to the second step.
( )
( )
( )
( )
( )
( )
( )
( )
112 2
, 1, , , 1, , , 1, , ,
.
jh
j h j h n j nh j h
i j ih
x P j mi nh q
ifvxvbvxvb vxvb thenxC
if v x v b for some i then apply decision rule for veto
∀∈ =… =… =…
≥ ∧ ≥ ∧… ∧ ≥ ∈
<
(5)
3.2. Decision rule for veto in the sorting problems
e idea of using a veto is currently being used in non-
compensatory methods, such as in ELECTRE, and has
been adapted for use with some compensatory methods,
such as the Additive-veto model for choice and ranking
problems (de Almeida, 2013) and the TOPSIS (Technique
for Order Preference by Similarity to Ideal Solution) meth-
od (Kelemenis & Askounis, 2010). e veto condition has
also been used in the context of group decision by using
a veto function based on the principles of social choices
(Moulin, 1981), and with the Additive Model (Aguayo,
Mateos, & Jiménez, 2014; Sabio, Jiménez-Martín, & Ma-
teos, 2015), as well as in the context of negotiation, by
vetoing possible solutions (Filzmoser & Gettinger, 2013)
or by scoring negotiation oers with TOPSIS (Wachow-
icz & Blaszczyk, 2013) and fuzzy-TOPSIS (Roszkowska &
Wachowicz, 2015).
In the Additive-veto model for ranking problems, the
veto rejects an alternative from its original ranking posi-
tion (de Almeida, 2013). Bregar (2018) proposed an ap-
proach similar to the additive-veto model for ranking
which was associated with the ELECTRE sorting rules.
is enabled incomparability to be considered present in
the problem model. e novel approach presented in this
paper proposes new decision rules that allow the alterna-
tives to be sorted into classes and all alternatives have to
be sorted in one unique class with a dierent set of param-
eters and does not enable incomparability. In TOPSIS, the
veto condition expresses the rejection of an alternative as
a solution. In the proposed model, the role of the veto is to
reject the alternative as a solution for that specic class and
direct the analysis to another class to reach a nal recom-
mendation.
e second step consists of determining if the alterna-
tives belonging to subset Ph must belong to class Ch. ere-
fore, two other analyses have to be carried out, whereby
one is local and the other global. e criteria weight co-
alition veto (ch) provides a global veto and the criterion
veto index (nch), a local one. ese veto conditions are
312 R. P. Palha et al. Sorting subcontractors’ activities in construction projects with a novel Additive-veto sorting...
presented in Denitions 1 and 2. ese two parameters
can be used either separately or combined. When a deni-
tion should be used depends on the context of the problem
and the DM’s preference structure.
Denition 1. e criterion veto index (nch) is a value
that reects preference information provided by the DM
such that the performance of the alternatives cannot be
below the performance of the reference alternative in
h–nch classes below it. For instance, if nch is 2 for the fourth
class, its performance in any criterion cannot be less than
that expected for the second class. Hence, if the alternative
has an overall value compatible with the fourth class but in
some criterion, its performance is lower than the reference
alternative of class two, the alternative has to be analyzed
in class three. In this case, the DM in the construction in-
dustry would believe that the activity should be placed in a
lower class if by comparing it with
h
nc
classes below class
h
C
, the alternative does not outperform this prole. e
local veto analysis is given in Eqn(6) and is based on De-
nition 1, by considering the criterion veto index as a meas-
ure of vetoing the alternative to be assigned to some class h.
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
21 1 2
21 1 2
, , ... ... ... .1,,, 1,,, 2,,, 0,, 1
,
2
,
,
2
,
..
h
h
hh
jh
ij i j h
h nc
ij i j h
h nc
i j ii j
i j ii j
x P nc j m i n h q nc q
if v x v b i then x C
if h
if v x v b for some i then x C
if v x v b b b i then x C
if h
if v x v b b b for some i then x C
+
−
−
∀∈∈
∈
∉
= = = = −
≥∀
><
≥θ − ∈+∀
=<θ − ∉+
,
1, 0
h
if h nc
=
=
(6)
where
i
θ
is the criteria veto index threshold for criterion
i provided by the DM based on the range between proles
2
b
and
1
b
. is parameter is presented as a percentage
and, the DM might decide to not use this component, set-
ting it to zero, thus forcing the comparison to match the
worst possible class. An aspect that is important to clarify
is that
( )
1i
vb
is not zero. e values presented for this
prole are the least preferable values in each criterion.
is index consists of comparing the performance of
all criteria that should belong to Class
h
C
, with the per-
formance of a number of classes below it, dened by the
criterion veto index. is analysis oers the DM exibility
and the idea is that even though the overall value is greater
than
( )
h
Vb
, individually the criteria did not conrm the
assignment. As a quasi-compensatory procedure, one cri-
terion should compensate for the other, so the DM decides
up to what limit this compensation is acceptable, which
means that this compensation is acceptable if all criteria
are at least as good as the one acceptable for
h
nc
classes
below it. is veto analysis has no meaning for alternatives
sorted in class C1, because they are the alternatives that
were not sorted in any other class, meaning they could not
be sorted in any class below this one. erefore, for class
C1 this index is zero. In addition, this proposition does not
take into account median proles, only boundaries. ere-
fore, nch has to be positive and integer to make the com-
parison feasible. Also, the DM might decide not to use this
condition; in that case, he/she must dene the criterion
veto index as one class below the class of analysis, h, and,
thus, all
( )
h
ih nc
vb
−
will be the prole of class C1 to all cri-
teria, thereby disabling the veto condition associated with
this index. By relaxing it completely, all criteria are to be
compared with the least preferable prole.
Denition 2. e criterion weight coalition veto (ch)
is the lower limit of the sum of the scale constants of the
criteria whose performance is at least as good as the one
required for the class of analysis that allows an alternative
to be assigned to that group. is preference condition dis-
allows assigning an alternative to Class Ch whenever the
number of criteria with a performance lower than the limit
prole is weighted, and the result is lower than ch.
For the approach presented in Denition 2, the DM
can easily interpret the outcomes for all criteria and can
detect low performances for a given criterion; which lev-
el is undesirable and which requires a veto. However, this
concept for veto is not related to a direct change of clas-
sication of that alternative. Rather, it is a verication of
how many criteria the alternative has to fail before it starts
to be unacceptable to assign it into the class under consid-
eration. e DM needs this approach when he/she is not
willing to compare the alternatives with several dierent
classes. In this case, the DM in the construction industry
would believe that the activity should be placed in a lower
class if a percentage of the criteria that he/she considers is
relevant, is not compatible with the class under analysis.
Eqn(7) presents the rule that uses the criteria weight coa-
lition veto:
∈≥
∈≥
∀
≥∈
= =
∈=
<∉
∑
∑
() ()
() ()
,
1,..., , 1,..., , 1,..., ,
i j ih
i j ih
jh
h
i jh
iv x vb
h
i jh
iv x vb
j mi nh
f
xP
if k c then x C
i k c then
q
xC
(7)
where: ki is the scale constant of criterion i and
1
1
n
i
i
k
=
=
∑
;
h
P
is the subset of
A
that might belong to the class
h
C
;
ch is the weight coalition veto informed by the DM.
Journal of Civil Engineering and Management, 2019, 25(4): 306–321 313
e weight coalition index consists of summing up all
the scale constants of the criteria that achieve a perfor-
mance better than the one required for the class being con-
sidered. If the DM decides not to apply this veto condition
to disable this parameter, the criteria weight coalition veto
has to be parametrized as zero. Hence, any value found for
the criteria weight coalition will be greater than its veto.
Besides the two foregoing approaches, the DM may be-
lieve that they must be combined. In this case, the activity
should be sorted into a lower class if at least a percentage
of the criteria is compatible with that class, and this is not
sucient for the assignment since the DM wants to com-
pare the performance of the alternative with classes below
the class of assignment. Whenever this is the situation, the
DM has to provide both veto indices. is analysis is made
by considering both cases as presented in Eqn(8), which is
more restrictive than the previous two since the alternative
has to overcome both conditions:
( )
( )
( )
( )
() ()
() ()
() ()
1, , , 1 .
2
, ,. , , , 2, ,.. ... . .,, 0 , 1
,
..
,
2
.
h
i j ih
h
i j ih
i j ih
hh
jh
h
i ij i j h
h nc
iv x vb
h
i ij i j h
h nc
iv x vb
h
i
iv x vb
x P nc j m i n h q nc q
if k c v x v b i then x C
if h
if k c v x v b for some i then x C
if k c
if h
+
−
∈≥
−
∈≥
∈≥
∀====−
≥∧ ≥ ∀
><∨ <
∈∈
≥∧
∈
∉
=
∑
∑
∑
( )
( )
( )
( )
( )
( )
21 2
)
1
121 2
( ()
,
,
,
1, 0
i j ih
i j ii j
h
i i j ii j
iv x vb
h
v x v b b i then x C
if k c v x v b b for some i then x C
if h nc
b
b
∈≥
≥θ + ∀
<∨ <θ +
=
−∈
−∉
=
∑
. (8)
3.3. Recommendation and sensitivity analysis
e evaluation ends with the third step, which consists of
making a recommendation to the DM based on conduct-
ing Steps 1 and 2 and taking the DM’s preference infor-
mation into consideration. To verify the robustness of the
recommendation, it is important to conduct a sensitivity
analysis of all parameters since this might bring some de-
gree of hesitation to the solution if the results are sensitive
to small modications. Sensitivity Analysis (SA) can be
carried out by using a Monte Carlo simulation on model
parameters, such as scaling constants and limit proles
in order to verify, if on using dierent parameter values,
how likely it would be for alternatives to change classes
by considering all the veto parameters that the DM has
provided. SA has to be conducted using whichever param-
eters the DM does not feel comfortable about. Moreover, it
is important to determine if, by introducing any modica-
tion to the set of parameters, this would cause signicant
changes to the recommendation. e model might be sen-
sitive to modications to either the criteria weight coali-
tion index or the criterion veto index. ere are dierent
approaches available in the literature for global SA (Iooss
& Lemaître, 2015) and therefore for verifying robustness.
When using a Monte Carlo Simulation, the analysis may
consider all parameters at the same time or a subset of
parameters. Since parameter ranges are considered for
simulation, the sensitivity for each parameter may be veri-
ed using a uniform or triangular distribution (Medeiros,
Alencar, & de Almeida, 2017).
4. Sorting activities in the heavy construction
context
e model was developed to reect the DM’s rational-
ity and to correct some misrepresentations of the model
used in the rst phase of the project, reported in Palha
etal. (2016). e criteria were determined by consider-
ing the DC’s objectives regarding the problem and are
presented and explained in Table1, which considers data
from dierent sources on the assessment of each criterion
in a given scale. e project had over thirty activities to
Table 1. Criteria used to analyze the activities of the construction of the brewery (adapted from Palha etal., 2016)
Criteria Description Scale Min/Max
Cost (g1)e budget to conduct the activity. Monetary Max
Duration of activity (g2)Time expected to complete the activity. Days Max
Number of suppliers (g3)e number of suppliers available in nearby markets. Unit Min
Available resources (g4)Availability of resources, such as labor, equipment, and
material in the neighborhood
Qualitative (1 to 5) Min
Exposure to risk (g5)Exposure to risk related to technical responsibility and
permanence of labor on the construction site.
Qualitative (1 to 5) Max
Need for maintenance (g6)Evaluation of the need for maintenance to attain the activity. Qualitative (1 to 4) Max
Interaction with other activities (g7)Proxy attribute to take into account possible impact from the
activity on other activities regarding security risks and duration.
Qualitative (1 to 5) Max
314 R. P. Palha et al. Sorting subcontractors’ activities in construction projects with a novel Additive-veto sorting...
be subcontracted, but to simplify matters, only seventeen
were considered under this analysis. All values presented
in Table 2 are real and were used to evaluate the activities.
Since the intention of sorting the activities into classes is
to minimize the time and eort required from DMs to
select subcontractors, the criteria are evaluated consider-
ing that the worst situation should be sorted in the top-
ranked class while the best situation, which would require
less commitment from the DMs in the decision process,
should be sorted in bottom-ranked classes. erefore, one
might think that the criterion of cost, for example, should
be minimized, but this would lead to costly activities be-
ing ranked in the low impact class and thus, this criterion
should be maximized.
ree clearly dened classes were found (Palha etal.,
2016): high impact activities (C3), medium impact activi-
ties (C2), and low impact activities (C1). It is expected that
the activities sorted in each class will be managed accord-
ing to their impact on the project, the risks involved, and
the client’s perceptions. High impact activities are costly,
might be a specialized service, directly aect the schedule
of the project and the client’s perception of success, and
have workers employed by the subcontractor working on
the construction site. Medium impact activities may con-
sist of long-term relations, have many available suppliers,
suer from delays that can be recovered by splitting the
activity among dierent subcontractors, and strongly af-
fect the client’s satisfaction. Low impact activities can be
handled more easily. Usually, these represent short-time
relationships with lower costs, have a low impact on the
client’s satisfaction, and do not usually include workers’
activities on the construction site. In this problem, since
the DM is concerned about the impact of the activity on
the project, it is assumed that the high impact class will
have greater values and is the preferable class. e signi-
cance of this is that the activities sorted in this class will re-
quire more attention from the DM and are quite dierent
from the ones sorted in the lower impact classes.
In order to calculate the limit proles, the DM speci-
ed ctitious reference alternatives for each class. e cost
was analyzed considering the governance model set be-
tween the contractor and the client while the other criteria
were analyzed based on the DM’s preferences. e scale
constants were elicited by using the trade-o method. For
the DC, exposure to risk was in the rst position, because
this could cause the contractor to have problems and could
decrease the client’s satisfaction. Cost was ranked second
because this would certainly inuence the client’s percep-
tion and the prots of the project. Next was the expected
duration because the contractor could not delay the pro-
ject. e others were the available resources, the number
of suppliers, interaction with other activities and, lastly,
the need for maintenance. In addition, the function ob-
tained in the elicitation process was linear for all criteria.
erefore, the value of the consequences of each activity in
each criterion is presented in Table3 and was calculated
using a normalization procedure presented in Eqn(9) (de
Almeida etal., 2015) in order to have all values on a scale
[0,1].
( ) ( )
( )
/
i j ji least most least
vx x x x x=−−
, (9)
where
ji
x
is the specic outcome of
j
x
in criterion
i
;
most
x
is the most preferred outcome found among the ac-
tivities in criterion
i
;
least
x
is the least preferred outcome
found among the activities in criterion
i
.
Table 2. Evaluation matrix of the activities considered (adapted from Palhaet al., 2016)
Description Criteria
g1g2g3g4g5g6g7
Air conditioning 70,000.00 90.00 3.00 3.00 3.00 1.00 3.00
Asphalt paving 90,000.00 4.00 2.00 5.00 5.00 4.00 2.00
Concrete 4,000,000.00 360.00 5.00 3.00 5.00 4.00 5.00
Concrete paving 700,000.00 60.00 4.00 1.00 5.00 4.00 5.00
Containers 370,000.00 360.00 5.00 1.00 1.00 1.00 1.00
Continuous ight auger (CFA) stake 700,000.00 180.00 12.00 1.00 5.00 4.00 4.00
Earthworks 1,800,000.00 90.00 6.00 5.00 5.00 4.00 5.00
Food supply 1,200,000.00 360.00 5.00 2.00 3.00 1.00 3.00
Gypsum liner 35,000.00 21.00 2.00 1.00 5.00 1.00 2.00
Heavy equipment 400,000.00 360.00 6.00 4.00 3.00 3.00 5.00
Hydroseeding 110,000.00 15.00 2.00 1.00 5.00 4.00 2.00
Molds, shoring and scaolding 150,000.00 360.00 4.00 4.00 5.00 1.00 5.00
Precast concrete 2,700,000.00 270.00 2.00 5.00 4.00 1.00 4.00
Security of property 500,000.00 360.00 4.00 5.00 3.00 1.00 3.00
Transport of personnel 1,500,000.00 360.00 4.00 5.00 3.00 4.00 3.00
Suppression of vegetation 19,000.00 15.00 1.00 5.00 5.00 1.00 4.00
Waterproong 25,000.00 60.00 2.00 5.00 5.00 1.00 2.00
Journal of Civil Engineering and Management, 2019, 25(4): 306–321 315
e DM had to consider the approach presented in the
rst step of the model to have the upper and lower thresh-
olds elicited. By considering this preference information,
the DM does not directly veto the activities but penalizes
them in some criteria that he/she believes to have an unac-
ceptable performance. For instance, if the cost of the ac-
tivities varies strongly and could be compensated by the
amount of time required to complete them, the DM could
specify a lower threshold for cost, such that no activity
that had a performance below it would have that criterion
considered in its overall value. If he/she specied an up-
per threshold and the given activity had a performance
between the upper and lower thresholds, then the criteri-
on would be partially considered for inclusion in the cal-
culation of the overall value of the activity. Finally, if the
performance were above the upper threshold, then no pen-
alty would be levied. Table 4 presents the upper and lower
thresholds, the scale constants and the proles of the classes.
e decision rules for veto, even though they can be
classied in the two kinds of approaches, behave dierent-
ly and have dierent meanings for the DM. e criterion
veto index (nch) is classied as the second approach, and
when the DM decides to use it, it means that he/she will be
comparing the activities not only with the class of analysis
but also with classes below it. In this problem, the DM spec-
ied a criterion veto index of 1, thus, nch = 1, meaning that
she only wants to compare the performance of the activ-
ity with the class immediately below it. In addition, for the
DM, it was not necessary to specify
i
θ
, so it was set to zero.
e criterion weight coalition veto (ch) is classied in
the rst approach, and the DM’s perception is no longer
relative to the other classes. He/she wants to analyze the
performance of the activity only with the assignment class.
e DM believes that if an activity has a performance
which is at least as good within a small percentage of the
one required for that class, the activity could be consid-
ered sucient to full the assignment. In this problem, the
DM specied a criterion weight coalition veto of 0.5, thus,
ch = 0.5, meaning that when comparing the activity with
the proles, its performance is at least as good as that re-
quired in at least 50% of the criteria. In this problem, the
DM wanted to be as restrictive as possible and decided to
apply both decision rules for veto purposes. e results are
presented below.
Table 3. Normalized evaluation matrix of the activities considered
Description Criteria
g1g2g3g4g5g6g7
Air conditioning 0.0128 0.2416 0.2727 0.1667 0.5000 0.0000 0.5000
Asphalt paving 0.0178 0.0000 0.4545 0.0000 1.0000 1.0000 0.2500
Concrete 1.0000 1.0000 0.1273 0.1667 1.0000 1.0000 1.0000
Concrete paving 0.1711 0.1573 0.1818 1.0000 1.0000 1.0000 1.0000
Containers 0.0882 1.0000 0.1273 1.0000 0.0000 0.0000 0.0000
Continuous ight auger (CFA) stake 0.1711 0.4944 0.0000 1.0000 1.0000 1.0000 0.7500
Earthworks 0.4474 0.2416 0.0909 0.0000 1.0000 1.0000 1.0000
Food supply 0.2967 1.0000 0.1273 0.3750 0.5000 0.0000 0.5000
Gypsum liner 0.0040 0.0478 0.4545 1.0000 1.0000 0.0000 0.2500
Heavy equipment 0.0957 1.0000 0.0909 0.0625 0.5000 0.6667 1.0000
Hydroseeding 0.0229 0.0309 0.4545 1.0000 1.0000 1.0000 0.2500
Molds, shoring and scaolding 0.0329 1.0000 0.1818 0.0625 1.0000 0.0000 1.0000
Precast concrete 0.6734 0.7472 0.4545 0.0000 0.7500 0.0000 0.7500
Security of property 0.1208 1.0000 0.1818 0.0000 0.5000 0.0000 0.5000
Transport of personnel 0.3720 1.0000 0.1818 0.0000 0.5000 1.0000 0.5000
Suppression of vegetation 0.0000 0.0309 1.0000 0.0000 1.0000 0.0000 0.7500
Waterproong 0.0015 0.1573 0.4545 0.0000 1.0000 0.0000 0.2500
Table 4. Parameters from the DM
Parameters Criteria
g1g2g3g4g5g6g7
Scale constants (ki) 0.2276 0.1561 0.0728 0.1085 0.3704 0.0204 0.0442
Upper threshold (ui) 400,000 50 10 5 2 2 2
Lower threshold (li) 220,000 20 10 5 2 2 2
b2600,000 21 54322
b31,200,000 180 2 2 4 3 4
316 R. P. Palha et al. Sorting subcontractors’ activities in construction projects with a novel Additive-veto sorting...
4.1. Discussion of results
e results of this application are presented in Table 5.
e ndings were coherent with the DM’s perception of
the activities, most of which were sorted in the medium
impact class. is behavior is compatible with what the
DM expected regarding this problem since most of the
activities should be long-term relationships with subcon-
tractors that could be easily replaced whenever needed,
or more than one subcontractor could be hired. Only
two activities were sorted in the high impact activities:
concrete and concrete paving. Both should be managed
as high impact activities since the success of the project
relies on the supply of concrete, and paving with concrete
is a very demanding activity. Eleven activities were sorted
in the medium impact class, and the DM felt comfortable
with all of them, except for earthworks, which she thought
could have been managed better if it had been classied
as a high impact activity. is misclassication may have
occurred because of missing criteria, such as evaluation of
long-lasting impacts or quality requirements. e last four
activities were sorted as low impact activities, and this was
compatible with the DM’s expectations.
It is important both to verify what the behavior of the
model would be if the DM had decided to relax some of
the parameters and also to compare results with those
from SAW. It is important to realize that by relaxing all
veto parameters, the additive-veto sorting approach would
present the same results as in SAW. erefore, Tab l e 6 pres-
ents an analysis of the activities by considering this relaxa-
tion of parameters. When using SAW, none of the activities
were assigned to the low impact class, which is compatible
with the behavior mainly found in the construction indus-
try, where DMs usually evaluate all activities as requiring
attention compatible with the high or medium class, in-
stead of considering which activities have a lesser impact
and therefore can be evaluated more simply. is behavior
makes the whole selection process more costly if it is con-
sidered that every activity requires all DMs to get involved
in the selection process and that all subcontractors should
be subjected to the same requirements. Under SAW, six
of the 17 activities were assigned to the high impact class
and eleven to the medium one, meaning that managing
these contracts would require great eort and undertaking
time-consuming procedures. By applying only the penali-
zation, two of the activities previously classied as Class C3
were vetoed and directed to Class C2: Molds, Shoring and
Scaolding; and Hydroseeding. In addition, both Con-
tainers and Air Conditioning (material and installation),
which were previously sorted in Class C2, were redirected
to Class C1. ese results are compatible with the DM’s
perception regarding the impacts these activities may rep-
resent for the project.
Table 6. Analysis of the activities by applying dierent methods to the activities
Activities ROR-UTADIS
(Palha etal., 2016) SAW Only
Penalization cqncqncq and cq
Concrete C3C3C3C3C3C3
Concrete paving C3C3C3C3C3C3
Continuous ight auger stake C3C3C3C3C2C2
Precast Concrete C2C3C3C3C2C2
Molds, shoring, and scaolding C2C3C2C2C2C2
Hydroseeding C3C3C2C2C2C2
Earthworks C3C2C2C2C2C2
Food supply C2C2C2C2C2C2
Gypsum liner C2C2C2C2C2C2
Heavy equipment C2C2C2C2C2C2
Security of property C1C2C2C2C2C2
Transport of personnel C2C2C2C2C2C2
Waterproong C1C2C2C2C2C2
Asphalt paving C1C2C2C1C2C1
Suppression of vegetation C1C2C2C1C2C1
Air conditioning C1C2C1C1C1C1
Containers C1C2C1C1C1C1
Table 5. Results of the application
Classes Activities
C3Concrete; Concrete paving
C2
Continuous ight auger stake; Earthworks;
Food supply; Gypsum liner; Heavy equipment;
Hydroseeding; Molds, shoring, and scaolding;
Precast concrete; Security of property;
Transport of personnel; Waterproong
C1Air conditioning; Asphalt paving; Containers;
Suppression of vegetation
Journal of Civil Engineering and Management, 2019, 25(4): 306–321 317
e use of the criterion veto index was more restric-
tive than considering only the penalization by directing
two activities to Class C2: CFA Stake, and Precast concrete.
is evaluation is compatible with the impacts these ac-
tivities may have on this project. Using the criterion weight
coalition veto only moved Suppression of vegetation and
Asphalt paving from Class C2 to Class C1. e result is co-
herent with these activities and their impact on the pro-
ject. When analyzing the use of both conditions, their im-
pact together is much more restrictive than applying each
of them individually, thereby keeping the activities in the
lowest possible classes of assignment.
e additive-veto sorting approach can be better ap-
preciated when it is applied to this problem. e param-
eters are intuitive, and the DM can specify the required
information without prior knowledge of exemplary al-
ternatives. e results are coherent with the DM’s prefer-
ence structure, and the veto conditions corrected several
misclassication errors. When compared to the results
presented by Palha etal. (2016), which used the holistic
method ROR-UTADIS (Kadziński et al., 2015), one nds
that most of the activities were assigned to the same class.
However, some dierences regarding the input informa-
tion and the results can be found.
Before becoming a DC in the construction of this
brewery, this DM worked as a Project Manager in the con-
struction of a railway with 1,200km of extension which
cost US$ 1,750 million. erefore, some bias was brought
from the previous contract into this analysis. is can be
veried by observing services such as Earthwork and CFA
Stake, which were assigned as exemplary alternatives in
Palha etal. (2016) into class C3. When using the additive-
veto sorting approach, the rst activity did not have an
overall value compatible with class C3. Whereas the overall
value of the second activity was higher than that required
to belong to class C3, but 12 rms could execute the activ-
it y, and it had an estimated cost of US$ 700,000.00, which
made it incompatible with the prole of class C3. erefore,
they were sorted into class C2. Also, in Palha etal. (2016) it
was veried that the DM did not agree with the classica-
tion of the Hydroseeding because it was incompatible with
the impact it could have on the project, a problem that was
solved by using the additive-veto sorting approach.
A sensitivity analysis was carried out considering the
parameters in which there could be any degree of hesi-
tation or uncertainty, such as weights and the criterion
weight coalition veto (ch). Parameters that have been de-
ned based on technical aspects have not been considered
in this sensitivity analysis, for instance, the upper and low-
er thresholds. Table7 presents the alternatives that would
change classes when each parameter was modied.
It is possible to verify in Table 7 that Suppression of
Vegetation changed classes when ch or the weights of crite-
rion g1 were decreased by 10–20%, when the weight of cri-
terion g2 was decreased by 15–20% or when the weight of
criterion g5 was increased by 10–20%. is activity, which
was sorted in class C1 when considering the parameters
elicited from the DM, changed to class C2 during the sen-
sitivity analysis. Table6 showed that ch directed this alter-
native to class C1 because it had a bad performance in cri-
teria g1, g2, g4, and g6, which together represent 51.26% of
the weights. In addition, it can be seen from Table3 that
this alternative has the maximum possible performance in
criterion g5, which has the maximum weight in the origi-
nal weight vector (Table4). us, when it is increased, the
overall value of this alternative increases and it is sorted
in a higher class. Asphalt Paving also changed classes in
a situation opposite to the one veried for the Suppres-
sion of vegetation. It was sorted in class C2 but dropped to
class C1 when ch or the weights of criteria g1 and g2 were
Table 7. Sensitivity analysis
Variables –20% –15% –10% +10% +15% +20%
g1
Suppression of
vegetation:
C1 → C2
Suppression of
vegetation:
C1 → C2
Suppression of
vegetation:
C1 → C2
Asphalt paving:
C2 → C1
Asphalt paving:
C2 → C1
Asphalt paving:
C2 → C1
g2
Suppression of
Vegetation:
C1 → C2
Suppression of
Vegetation:
C1 → C2
–Asphalt paving:
C2 → C1
Asphalt paving:
C2 → C1
Asphalt paving:
C2 → C1
g3– – – – – –
g4– – – – Asphalt paving:
C2 → C1
Asphalt paving:
C2 → C1
g5
Asphalt paving:
C2 → C1
Concrete paving:
C3 → C2
Asphalt paving:
C2 → C1
Asphalt paving:
C2 → C1
Suppression of
vegetation:
C1 → C2
Suppression of
vegetation:
C2 → C1
Suppression of
vegetation:
C2 → C1
g6– – – – – –
g7– – – – – –
ch
Suppression of
vegetation:
C1 → C2
Suppression of
vegetation:
C1 → C2
Suppression of
vegetation:
C1 → C2
Asphalt paving:
C2 → C1
Concrete paving:
C3 → C2
Asphalt paving:
C2 → C1
Concrete paving:
C3 → C2
Asphalt paving:
C2 → C1
Concrete paving:
C3 → C2
318 R. P. Palha et al. Sorting subcontractors’ activities in construction projects with a novel Additive-veto sorting...
increased by 10–20%, when the weight of criterion g5 was
decreased by 10–20% or when the weight of criterion g4
was increased by 15–20%. Tables 3 and 6 show that As-
phalt paving has a condition similar to that of Suppression
of vegetation.
Finally, only one alternative which had been sorted in
class C3 was directed to a lower class during the sensitiv-
ity analysis, namely, Concrete Paving when ch became too
restrictive. By increasing this value to 20%, it became 0.6.
us, the DM veried that using a criterion weight coali-
tion veto of 0.5 was appropriate according to her prefer-
ences. e sensitivity analysis is important to aid the DM
to feel comfortable about the parameters provided and to
be aware of any possible inconsistency.
Uncertainty may appear in such problems when de-
ning parameters for the decision model and also in the
scores dened for evaluating the performance of the alter-
natives within each criterion. To avoid unnecessary mod-
elling costs, when sensitivity analysis shows that part of the
information used in the decision process may change the
results considerably, such a sensitive piece of information
is explored so the uncertainty in its value may be reduced.
Multiattribute Utility eory is oen used to model prob-
abilistic consequences with a similar elicitation process
(Keeney & Raia, 1993). For such cases, Bregar (2018) has
veried the impact of a veto component on the DM’s be-
havior with regard to risk (prone or risk-averse).
4.2. Managerial impacts
Besides the benets of improving this managerial deci-
sion process, there is the possibility of reducing the costs
associated with spending too much eort and time on the
hiring procedures of activities that do not represent risks
to the contractor. One possible approach is to sort the ac-
tivities into classes in order to allow them to be dealt with
in a more compatible way by using a selection process and
contract management approach that are based on the im-
pact that the activities are expected to have on the project,
as discussed in Palha etal. (2016). By dividing activities
into classes, the analyst could use dierent procedures for
each class, which are consistent with the impact of the ac-
tivity on the project. In addition, this process allows DMs,
such as the DC, to delegate responsibility and power to
mid-level managers, by identifying the less critical activi-
ties that the latter may handle themselves. is categoriza-
tion could be structured by using a sorting procedure that
reects preference levels.
e hiring process, as well as the management of the
contract, might be tackled dierently depending on the
impact that this may have on the project and the contrac-
tor. Usually, the negotiation process in each class will be
undertaken dierently because more DMs are involved
in the higher impact classes compared to the lower ones.
us, the main objective of proposing a model to sort the
activities into classes before conducting a selection pro-
cedure is to improve the decision process by decreasing
the risk of liabilities during the project. us, DMs need
not get involved in every single bidding procedure, there-
by saving valuable time. Moreover, money can be saved
since the requirements for lower impact activities are not
as strict as they are for higher ones. By concentrating on
reducing risk and liability at a higher level, the contractor
can make more realistic and wiser decisions. In addition,
it might be possible to avoid situations in which problems
were overlooked because the decision was made without
having a rigorous framework.
e results show that when using SAW to sort the ac-
tivities into classes, management might require more ef-
fort and time from DMs because most of the activities are
sorted into the high impact activities class, and none of the
activities is sorted into the low impact class. is nuance
prompts all DMs to get involved in selecting subcontrac-
tors which is more demanding when bidders are being se-
lected. is behavior is usually found in the professional
context, which prompts DMs to realize that some activities
considered as belonging to the high impact class could be
managed as belonging to the medium impact class and,
likewise, activities assigned to the medium impact class
could be managed as belonging to the low impact class.
However, unless DMs have the support of an analytical
tool, they not feel comfortable about assigning these ac-
tivities to more compatible classes, because as they do not
have enough knowledge about the context found in that
project, this leads to conservative decision-making, thus
making the whole selection process more costly than nec-
essary. Also, contractors do not include these costs in the
cost estimation of the project.
e proposed model provides DMs with valuable guid-
ance on managing subcontractors and how to do so more
realistically, thereby reducing not only the costs associated
with these contracts, the liabilities and the risks involved
in conducting the activity but also their negative impacts
on other activities and workers. In addition, the DMs can
easily understand the parameters, because they are used to
making trade-os and they intuitively use the veto com-
ponent. us, it does not take more than two hours from
the DC to evaluate the whole process. And only the DC,
who is the person responsible for the success of the pro-
ject, is involved in this analysis. Another gain regarding
the managerial benets of using this approach is that now
there is a structured decision process which can be audited
and revised if any inconsistencies should be found. Now,
if 20% of the alternatives of the case study are assigned to
class C1, this implies that the time that the DMs involved
in the project would have devoted to these is saved and can
be redeployed to other activities. is amount of time is far
greater than the two hours that were needed to evaluate
the entire elicitation process in the case study. us, DMs
can use their knowledge to favor the project and make de-
cisions that are better informed.
Conclusions and future works
A case study prompted the proposition of a new quasi-
compensatory sorting approach to tackle the decision-
Journal of Civil Engineering and Management, 2019, 25(4): 306–321 319
making process for an important civil engineering project,
which lasted for 3 years. Although, this problem is faced
by all main contractors independently of the country in
which a project is being conducted, the case study was
conducted in one of the biggest contractors in Brazil.
e construction industry may well improve the man-
agement of its subcontractors by using this model to sort
activities prior to bidding, thereby avoiding unnecessary
managerial eorts that arise from taking excessive risk-
averse precautions. erefore, a new MCDM method was
proposed in this paper which has important impacts on
the management of heavy construction civil engineering
projects. e approach used in this paper for sorting sub-
contractors’ activities in construction projects can be ap-
plied to any heavy construction project. is can be done
easily, simply by adjusting parameters according to the
particularities and priorities of a given project. e new
procedure allows the specicities of activities to be taken
into consideration in order to avoid biased assignments.
Based on the aspects of this MCDM approach, the
characteristics of the civil engineering environment and
the case study, the main conclusions can be summarized
as follows:
1. e “quasi-compensatory” parameters proposed in
this model are important to avoid alternatives being
sorted in classes that are not compatible with their
impact on the construction project, as was veried
in the sensitivity analysis.
2. It is important to note that some diculties might
arise during the preference elicitation. erefore, the
whole process relies on how skilful the analyst is at
conducting the interview and on making the com-
puter tool easy to use. Otherwise, the DM might pro-
vide pieces of preference information that will not
lead the model to produce a recommendation that
is compatible with his/her preferences. Examples of
these are: thresholds that lead to one class not be-
ing assigned with any activities; instead of making
trade-os among criteria, they are evaluated based
on their “importance” which is something that is in-
compatible with the additive model; or veto indices
are provided that do not reect the DM´s preferences
because they are too restrictive or because these indi-
ces have been disabled.
3. In addition, it is mandatory to inform the DM about
the impact that such a process might have on the pro-
ject. Otherwise, he/she might dene the classes in a
way that will not only give rise to problems that are
greater than those associated with the costs of selec-
tion but also might adversely aect the performance
of the contractor with regard to his/her relationship
with the owner.
4. At last, in the case of group decision-making, the fa-
cilitator may guide the DMs to a consensus in terms
of parameters or consider deploying a voting proce-
dure. If the voting procedure results on conicting
recommendations the parameters can be aggregated
by considering the weight each DM represent to the
problem.
In future research studies, it is suggested that the mod-
el be applied generally in other elds to other types of sort-
ing problems. It should be considered as a model on how
to manage each of the classes and how the negotiation
process might be driven by these scenarios. In addition,
subcontractor selection may be enhanced by considering
simulation and optimization techniques (Raou, Seresht,
& Fayek, 2017) associated with an agent based mediation
process (Palha, 2019).
Acknowledgements
e authors are grateful to the Brazilian Research Council
(CNPq) for the funding received to support the research
contained in this paper.
Funding
e authors are grateful to the Brazilian Research Council
(CNPq) for the funding received to support the research
contained in this paper.
Author contributions
RPP, ATA, and KWH were responsible for conceptualiza-
tion, methodological development and writing (original
manuscript), RPP was responsible for data collection, and
analysis; RPP and KWH were responsible for manuscript
revisions, RPP, ATA, DCM, and KWH were involved in
the validation. ATA and DCM were responsible for super-
vising RPP’s PhD thesis.
Disclosure statement
e authors declare that there is no conict of interests
regarding the publication of this paper.
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