Operational Research in Engineering Sciences: Theory and Applications
Vol. 3, Issue 1, 2020, pp. 41-56
ISSN: 2620-1607
eISSN: 2620-1747
DOI: https:// doi: 10.31181/oresta2002041s
* Corresponding author.
marko.subotic@sf.ues.rs.ba (M. Subotić), biljana.jeremic47@gmail.com (B. Stević),
bojana.ristic@sf.ues.rs.ba (B. Ristić), sanja.simic@sf.ues.rs.ba (S. Simić)
THE SELECTION OF A LOCATION FOR POTENTIAL
ROUNDABOUT CONSTRUCTION – A CASE STUDY OF
DOBOJ
Marko Subotić*, Biljana Stević, Bojana Ristić, Sanja Simić
University of East Sarajevo, Faculty of Transport and Traffic Engineering Doboj, Bosnia
and Herzegovina
Received: 25 February 2020
Accepted: 13 March 2020
First online: 17 March 2020
Original scientific paper
Abstract: The increase in the number of traffic accidents, as well as the development of
modern traffic signaling, have influenced realistic traffic solutions at intersections to be
aimed at constructing roundabouts, which has increased the capacity and safety of
traffic participants. This paper has several goals that refer to the development of
methodology for evaluating potential locations for roundabout construction. The
subject of this research is based on the development of a model for the construction of a
roundabout in Doboj using the integrated BWM (Best Worst Method) and MABAC
(Multi-Attributive Border Approximation area Comparison) approach. Taking into
account the fact that Doboj is a transport hub where many roads intersect and that it is
a very important transit point, the necessity of constructing roundabouts is justified.
Therefore, as part of the paper, an adequate methodology has been developed for an
optimal selection of a potential location for the construction of a roundabout.
Key words: roundabout, location, sustainable traffic, BWM, MABAC,
1. Introduction
In European countries, experts believe that roundabouts reduce the number of
accidents and cause capacity increase, making their usage attractive since the 1980s.
In the Netherlands, France, Norway, Denmark and other European countries, the
number of roundabouts has been increasing progressively. In the Netherlands
(Vasilyeva and Sazonova, 2017), turbo-roundabouts are being introduced with 20 to
30% higher speeds of movement in them and with greater safety. At intersections
regulated by light signals, the problem occurs since pedestrian and vehicle flows
intersect, which adversely affects pedestrians as a "vulnerable" category. This case is
especially dominant at Russian signalized intersections, where drivers often drive
under the influence of alcohol or pass the crossroad on red light. (Vasilyeva and
mailto:marko.subotic@sf.ues.rs.ba
mailto:biljana.jeremic47@gmail.com
mailto:bojana.ristic@sf.ues.rs.ba
mailto:sanja.simic@sf.ues.rs.ba
Subotić et al./Oper. Res. Eng. Sci. Theor. Appl. 3(1) (2020) 41-56
42
Sazonova, 2017) According to the research (Møller and Hels, 2007), the performance
of roundabouts was considered by the criteria of road properties, capacity and
location. Their research consists of observing two types of roundabouts, with and
without pedestrian crossings and cycle paths.
The trend of constructing roundabouts has also shifted to smaller urban areas, so
when looking at the territory of the Republic of Srpska it is possible to see a constant
increase of roundabouts in urban areas. Urban areas Bijeljina, Derventa, Trebinje,
Prnjavor and others are an example of that. To solve traffic congestion and increase
safety on main roads, roundabouts are being constructed extensively. When it comes
to the territory of the city of Doboj and the main roads passing through the city, the
number of roundabouts is zero. Taking into account the fact that Doboj is a transport
hub where many roads intersect and that it is a very important transit point, the
necessity of constructing roundabouts is justified.
The subject of this paper is to define potential locations for the construction of
roundabouts in the area of the City of Doboj. The main objective of the paper is to
identify priority intersections on the entire street network of the City of Doboj. A
roundabout falls into the category of at-grade intersections, where all entering
streams flow in and exiting streams flow out of usually one-way traffic flow around
the central island of the intersection. Based on this, it has been formed a hypothetical
assumption which implies that the introduction of a roundabout on the current street
network is functionally dependent on traffic conditions and their effects on the current
traffic infrastructure in the urban area of the City of Doboj. In addition, the location of
a roundabout in Doboj depends on the potential urban-planning and technical
conditions for the implementation of the intersection, and any potential solution can
influence the change in modernity of the traffic infrastructure.
After the introduction, the second section presents an overview of the situation in
the field of interest with a brief review of multi-criteria decision-making methods. The
third section provides the algorithms of the methods used in this paper: MABAC, BEST
WORST. The fourth section is a case study of selecting a location for the construction
of a roundabout in the City of Doboj using the BWM-MABAC model. The paper ends
with conclusions presenting contributions of the paper and directions for future
research.
2. Brief literature review
Increasing capacity in road engineering according to (Li et al., 2014) has become
an important way of solving traffic problems, and roundabouts, in addition to a large
number of benefits, also cause the increase in traffic capacity (Prateli, 2006), and
higher traffic flow rate (Retting et al. 2006). A properly constructed roundabout,
according to (Prateli et al., 2018), can have a significant impact on increasing traffic
safety, which is also confirmed by (Antov et al., 2009), who find that the construction
of roundabouts is an efficient measure to increase safety.
Depending on the type of location problem, different methods are used as shown
above. In the last decade, multi-criteria decision-making (MCDM) methods have been
applied widely in addressing location problems (Chauhan and Singh, 2016; Nie et al.,
2017; Samanlioglu and Ayag, 2017; Zhao et al., 2018; Nazari et al., 2018). Zhao et al.
(2018) use a combination of AHP and TOPSIS methods to develop a metro-integrated
logistics system. Using the TOPSIS method, they performed a significance evaluation
The selection of a location for potential roundabout construction – a case study of Doboj
43
for each metro station. Nazari et al. (2018) conducted a study to select a suitable site
for photovoltaic installation in Iran.
3. Methods
Psychology provides an explanation why individuals frequently make irrational
decisions, while economics proposes normative theories (Morselli, 2015). According
to (Triantaphyllou and Mann, 1995), multi-criteria decision-making plays an
important role in real-life problems since there are many everyday decisions to be
made that involve a large number of criteria, whereas, according to (Chen et al., 2015),
multi-criteria decision-making is an efficient, systematic and quantitative method of
solving vital real-life problems in the presence of a large number of alternatives and
several (opposing) criteria.
The BEST WORST (Rezai, 2015) method was used to determine the weight values
of criteria, while the MABAC method was used to evaluate the intersection locations
for the construction of a roundabout.
In addition, to determine model validity through a sensitivity analysis, four other
multi-criteria decision-making methods were used: ARAS (Zavadskas and Turksis,
2010) WASPAS (Zavadskas and Turksis, 2012), SAW (Macrimon, 1968), and EDAS
(Ghoarabaee et al., 2016).
3.1. Best – Worst Method
The following section presents the algorithm of the BW method based on interval
rough numbers. Determining the weight coefficients of evaluation criteria using the
IRN-BW method includes the following steps:
Step 1. Determining a set of evaluation criteria. In this step, we consider a set of
evaluation criteria C = {C1, C2, .... Cn}, where n represents the total number of criteria.
Step 2. Determining the most significant (most influential) and worst (least
influential) criterion. If there are two or more criteria that are best, i.e. worst, it is
arbitrary to choose the best, i.e. the worst criterion.
Step 3. Determining the preferences of the most significant (most influential)
criterion in a set C over all other criteria in a defined set. The scale of numbers in the
interval of 1-9 is used to determine the preferences. As a result, the best-to-others
(BO) vector is obtained:
𝐴𝐵 = (𝑎𝐵1, 𝑎𝐵2,…..,𝑎𝐵𝑛 ) (1)
where 𝑎𝐵𝑗 represents the influence (preference) of the best criterion B over the
criterion j, while 𝑎𝐵𝐵 = 1 .
Step 4. Determining the preferences of all criteria in a set C over the worst (least
influential) criterion in a defined set. To determine the preferences, as in Step 3, a scale
of numbers in the interval of 1-9 is used. The result is obtaining the others-to-worst
(OW) vector:
𝐴𝑊 = (𝑎1𝑊 , 𝑎2𝑊 , . . . , 𝑎𝑛𝑊 ) (2)
where Bj
a
represents the influence (preference) of the criterion j over the worst criterion W,
while 𝑎𝐵𝐵 = 1.
Subotić et al./Oper. Res. Eng. Sci. Theor. Appl. 3(1) (2020) 41-56
44
Step 5. Calculation of optimal values of the weight coefficients of the criteria in a set
C, (𝑤1
∗, 𝑤2
∗, … . , 𝑤𝑛
∗ ). The aim is to determine the optimal values of the evaluation
criteria, which should satisfy the condition that the maximum absolute gaps (3)
w
B a
Bjw
j
and
w
j
a
jWww
−
−
(3)
for all values of j be minimized. In order to satisfy these conditions, a solution that
satisfies the maximum gaps by absolute value
B
Bj
j
w
a
w
−
and
j
jW
w
w
a
w
−
should be
minimized for all values of j. This condition can be shown through the following min-
max model:
1
. .
1
0
min max ,
n
j
j
j
s t
w
w j
ww jB a a
Bj jWj w wwj
=
=
− −
(4)
The presented model (4) is equivalent to the following model:
1
1
0
min
. .
,
,
n
j
j
j
j
w
w j
s t
w
B a j
Bjw
j
w
j
a
jWww
=
=
−
−
(5)
By solving the system of equations and inequations of model (5), we obtain the
optimal values of the weight coefficients of the evaluation criteria (𝑤1
∗, 𝑤2
∗, . . . , 𝑤𝑛
∗ ) and
𝜉∗ .
The selection of a location for potential roundabout construction – a case study of Doboj
45
Definition 1. The criterion comparison is consistent when the condition that
𝑎𝐵𝑗 × 𝑎𝑗𝑊 = 𝑎𝐵𝑊 is fulfilled for all criteria j, where 𝑎𝐵𝑗 , 𝑎𝑗𝑊 and 𝑎𝐵𝑊 respectively
represent the influence (preference) of the best criterion over the criterion j, the
influence (preference) of the criterion j over the worst criterion, and preference of the
best criterion over the worst criterion.
However, when comparing criteria, it may be that for some pairs of criteria j, the
comparisons are not fully consistent. Therefore, the following section defines a
consistency ratio (CR) that provides information on the consistency of the BO and OW
comparisons. To show the determination of CR, we start from the calculation of the
minimum consistency in the comparison of criteria, which is explained in the following
section.
As noted above, pair-wise comparisons of criteria are made on the basis of the
scale 𝑎𝑖𝑗 ∈ {1,2, . . . , 𝑎𝐵𝑊 }, where the highest value from scale 𝑎𝐵𝑊 is a value of 9 or any
other maximum value of a scale defined by the decision-maker. The consistency of the
comparison decreases when 𝑎𝐵𝑗 × 𝑎𝑗𝑊 is lower or higher than 𝑎𝐵𝑊 , i.e. when 𝑎𝐵𝑗 ×
𝑎𝑗𝑊 ≠ 𝑎𝐵𝑊.
It is clear that the greatest inequality occurs when 𝑎𝐵𝑗 and 𝑎𝑗𝑊 have maximum
values that are equal to 𝑎𝐵𝑊 , which further affects the values of 𝜉. Based on the
relations defined above, we can conclude that there is a relation as follows:
(𝑤𝐵 𝑤𝑗⁄ ) × (𝑤𝑗 𝑤𝑊⁄ ) = 𝑤𝐵 𝑤𝑊⁄ (6)
Since the greatest inequality occurs when 𝑎𝐵𝑗 and 𝑎𝑗𝑊 have maximum values
(𝑎𝐵𝑊 ), then the value of 𝜉 needs to be subtracted from 𝑎𝐵𝑗 and 𝑎𝑗𝑊 and added to 𝑎𝐵𝑊 .
Thus, we obtain Expression (7):
(𝑎𝐵𝑗 − 𝜉) × (𝑎𝑗𝑊 − 𝜉) = (𝑎𝐵𝑊 + 𝜉) (7)
Since the minimum consistency implies the equality that 𝑎𝐵𝑗 = 𝑎𝑗𝑊 = 𝑎𝐵𝑊,
Expression (7) is presented as follows:
( ) ( ) ( ) ( ) ( )2 2 1 2 0a a a a a aBW BW BW BW BW BW − − = + − − + − =
(8)
For different values of 𝑎𝐵𝑊 ∈ {1,2, . . . ,9} based on Expression (8), we obtain maximum
values of (max ξ). Table 1 presents the maximum values of ξ (consistency index) for
different values of 𝑎𝐵𝑊 ∈ {1,2, . . . ,9}.
Table 1. Consistency Index (CI) values
BW
a
1 2 3 4 5 6 7 8 9
CI
( max ) 0.00 0.44 1.00 1.63 2.30 3.00 3.73 4.47 5.23
Based on CI (Table 2), we obtain a consistency ratio (CR)
𝐶𝑅 =
𝜉∗
𝐶𝐼
(9)
CR takes values from the interval 0,1 , where values closer to zero show high
consistency, while CR values closer to one show low consistency.
Subotić et al./Oper. Res. Eng. Sci. Theor. Appl. 3(1) (2020) 41-56
46
The solution space of model (5) includes all positive values of 𝑤𝑗 (𝑗 = 1,2, . . . 𝑛) that
satisfy two conditions: (1) the sum of all weight coefficients should be equal to one and
(2 ) the ratio of the weighted coefficients of the criteria which are compared should be
at most equal to 𝜉.
3.2. MABAC method
The MABAC (Multi-Attributive Border Approximation area Comparison) method is
a recent method. The MABAC method was developed by Dragan Pamučar at the Center
for Defense Logistics Research at the University of Defense in Belgrade and was first
introduced to the scientific community in 2015 (Pamučar and Ćirović, 2015). So far, it
has found wide application and modification in solving various problems in the field
of multi-criteria decision-making.
The basis of the MABAC method is seen in the definition of the distance of the criterion
function of each alternative from the border approximation area. The following
section shows the process of implementing the MABAC method, consisting of six steps:
Step 1. Formation of the initial decision matrix (X).
...
1 2
...
11 12 11
21 22 22
... ... ... ......
...
1 2
C C Cn
x x xA n
x x xA nX
x x xA mnm m m
=
(10)
Step 2. Normalization of the elements from the initial matrix (X).
...
1 2
...
11 12 11
21 22 22
... ... ... ......
...
1 2
C C Cn
t t tA n
t t tA nN
t t tA mnm m m
=
(11)
The elements of the normalized matrix (N) are determined by applying the
following expressions:
For benefit-type criteria (higher criterion value is preferable)
x x
ij i
t
ij x x
i i
−
−
= + −
−
(12)
For cost-type criteria (lower criterion value is preferable)
x x
ij i
t
ij x x
i i
+
−
= − +
−
(13)
The selection of a location for potential roundabout construction – a case study of Doboj
47
where
𝑥𝑖𝑗 , 𝑥𝑖
+i 𝑥𝑖
− are the elements of the initial decision matrix (X), where 𝑥𝑖
+ and 𝑥𝑖
− are
defined as follows:
𝑥𝑖
+ = max (𝑥1, 𝑥2, . . . , 𝑥𝑚 ) and represents the maximum values of the observed
criterion by alternatives.
Step 3. Calculation of the elements from the weighted matrix (V).
𝑣𝑖𝑗 = 𝑤𝑖 ⋅ 𝑡𝑖𝑗 + 𝑤𝑖 (14)
where 𝑡𝑖𝑗 represents the elements of the normalized matrix (N), 𝑤𝑖 represents the
weight coefficients of criteria. By applying Expression (14), we obtain the weighted
matrix V.
11 12 1
21 22 2
1 2
...
1 11 1 2 12 2 1
...
1 21 1 2 22 2 2
... ... ... ...
...
1 1 1 2 2 2
...
... ... ... ...
...
n
n
m m mn
w t w w t w w t wn nn
w t w w t w w t wn nn
w t w w t w w t wn mn nm m
v v v
v v v
V
v v v
+ + +
+ + +
+ + +
= =
where n represents the total number of criteria, m represents the total number of
alternatives.
Step 4. Determining the border approximation area matrix (G).
1/
1
m
m
g v
i ij
j
=
= (15)
where 𝑣𝑖𝑗 represents the elements of the weighted matrix (V), m represents the total
number of alternatives.
After calculating the values of 𝑔𝑖 by criteria, a border approximation area matrix G
(16) of the form 𝑛 𝑥 1 is created (n represents the total number of criteria by which
the offered alternatives are selected).
...
1 2
...
1 2
C C Cn
G g g gn
=
(16)
Step 5. Calculation of matrix elements of alternative distance from the border
approximation area (Q).
...
11 12 1
21 22 2
... ... ... ...
...
1 2
q q q
n
q q q
nQ
q q qmnm m
=
(17)
The distance of alternatives from the border approximation area (𝑞𝑖𝑗 ) is
determined as the difference of the weighted matrix elements (V) and the values of the
border approximation areas (G)
Subotić et al./Oper. Res. Eng. Sci. Theor. Appl. 3(1) (2020) 41-56
48
...
11 12 1
21 22 2 ...
1 2... ... ... ...
...
1 2
v v v
n
v v v
nQ V G g g gn
v v vmnm m
= − = −
(18)
... ...
11 1 12 2 1 11 12 1
...
21 1 22 2 2 21 22 2
... ... ... ... ... ... ... ...
... ...
1 1 2 2 1 2
v g v g v g q q qnn n
v g v g v g q q qnn nQ
v g v g v g q q qmn n mnm m m m
− − −
− − −
= =
− − −
(19)
where 𝑔𝑖 represents the border approximation area for the criterion 𝐶𝑖 ,
𝑣𝑖𝑗 represents the elements of the weighted matrix (V), n represents the number of
criteria, m represents the number of alternatives.
The alternative 𝐴𝑖 can belong to the border approximation area (G), the upper
approximation area (𝐺 +) or the lower approximation area (𝐺 −), i.e. 𝐴𝑖 ∈ {𝐺 ∨ 𝐺
+ ∨
𝐺 −}
The upper approximation area (𝐺 +) represents the area where the ideal alternative
(𝐴+) is located, while the lower approximation area (𝐺 −) represents the area where
the anti-ideal alternative (𝐴−) is located. The affiliation of the alternative 𝐴𝑖 to the
approximation area (𝐺, 𝐺 + or 𝐺 −) is determined on the basis of Expression (20)
G if q g
ij i
A G if q g
i ij i
G if q g
ij i
+
=
−
(20)
In order for the alternative 𝐴𝑖 to be selected as the best alternative of the set, it
should belong to the upper approximation area (𝐺+) by as many criteria as possible.
For instance, if the alternative belongs to the upper approximation area by five criteria
(out of a total of six criteria), and to the lower approximation area (𝐺 −) by one
criterion, it means that the alternative is close or equal to the ideal alternative by five
criteria, while it is close or equal to the anti-ideal alternative by one criterion. If the
value of 𝑞𝑖𝑗 > 0, i.e. 𝑞𝑖𝑗 ∈ 𝐺
+, then the alternative 𝐴𝑖 is close or equal to the ideal
alternative. The value of 𝑞𝑖𝑗 < 0, i.e. 𝑞𝑖𝑗 ∈ 𝐺
−, indicates that the alternative 𝐴𝑖 is close or
equal to the anti-ideal alternative.
Step 6. Ranking alternatives. The calculation of the values of criterion functions by
alternatives (21) is obtained as the sum of the distances of alternatives from the
border approximation area (𝑞𝑖). By summing the elements of the matrix 𝑄 by rows, we
obtain the final values of the criterion functions of alternatives
, 1, 2,..., , 1, 2,...,
1
n
S q j n i m
i ij
j
= = =
=
(21)
The selection of a location for potential roundabout construction – a case study of Doboj
49
where n represents the number of criteria, m represents the number of
alternatives.
4. A case study in the city of Doboj – Description of the situation in the
City of Doboj
The selection of the location for the construction of a roundabout consists of
several stages that are described in detail below. The first stage implies the formation
of a multi-criteria model based on the realistic needs for traffic infrastructure in the
city of Doboj. The second stage implies the collection of data on the basis of
measurements of traffic indicators and other sources, such as the Ministry of Interior,
where data on the number of traffic accidents at the locations for roundabout
construction were obtained. The third stage refers to the expert evaluation of the
significance of criteria as the first step and the determination of the weights of the
criteria using the BWM method as the second step. The fourth stage is the evaluation
of the locations based on the MABAC method. This paper will analyze six potential
locations for the introduction of a roundabout intersection in the city of Doboj, where
no roundabout has been constructed so far. As already mentioned, the city of Doboj,
by its geographical position, is located at the crossroads of the most important main
and regional roads in the Republic of Srpska and Bosnia and Herzegovina.
This research involved traffic experts. They are on average 50 years old and there
were 62 respondents.
The 105 main road (M1) passes in the north-south direction and, in the east, it is
connected to the 110 main road from (M1) the direction of Tuzla (Federation of BiH).
The most frequent part of the 105 main road (M1) is on the Šešlije - Doboj - Karuše -
Federation of BiH route.
The intersections of city streets with access to the main roads are not well resolved
in the city, which significantly hinders a normal flow of traffic, especially at peak hours.
Taking into account the transport significance of the city of Doboj, as well as the fact
that nearby towns, such as Modriča, Derventa, Teslić and many other smaller towns
and municipalities already have roundabouts, six potential intersections have been
selected for the construction of a roundabout in the city, as well as on the 105 main
road (M1). The following table gives an overview of the potential coordinates for the
roundabout.
Table 2. Coordinates for the roundabout
Location A1 A2 A3 A4 A5 A6
Coordinates
44.743443
18.095140
44.735776
18.096611
44.733405
18.096111
44.726579
18.091869
44.713155
18.080535
44.730244
18.081451
4.1. Forming a multi-criteria model
Six locations, out of which one is located in the very center of the city, four locations
representing the connection between the streets for the entrance into/exit from the
city and the first-order main road, and one location where the first-order main roads
intersect, are evaluated on the basis of a total of eight criteria presented in Table 3.
Subotić et al./Oper. Res. Eng. Sci. Theor. Appl. 3(1) (2020) 41-56
50
Table 3. Criteria in a multi-criteria model and their description
No. Criterion Criterion description
1 Flow of vehicles
The number of vehicles passing through the
observed road intersection in a unit of time in
both directions
2 Flow of pedestrians
The number of pedestrians crossing the
observed intersection at the point for
pedestrian movement (pedestrian crossing,
zebra, etc.) at a given time interval
3 Traffic Safety Indicator
The number of traffic accidents on the observed
section of road
4
Cost of construction and
exploitation
Cost estimation (construction, exploitation and
maintenance)
5 Type of intersection Three-way or four-way intersections
6
Average vehicle
intensity per access arm
The limit intensity is the intensity at the entry
arm into the intersection of 360 PA/h
7
Functional criterion of
spatial fitting
What is the primary role of the intersection
observed? This section analyzes what
type of intersection is the most acceptable due
to its role in traffic
8 Public opinion
It implies a survey of local people who have
chosen one of the offered locations as a priority
for the construction of a roundabout.
The criteria were selected according to the current needs of the City of Doboj and
relevant literature that considered similar studies (Day et al., 2013; Benekohal and
Atluri, 2009; Deluka-Tibljaš et al., 2010; Steiner et al., 2014). In all the aforementioned
studies, the criteria are organized into several categories: traffic criteria, safety
criteria, functional criteria, performance, cost, etc. The criteria used in this study are
the most commonly used criteria in Croatia: functional criterion, spatially-urbanistic
criterion, traffic flow criterion, design and technical criterion, traffic safety criterion,
capacity criterion, environmental criterion, economic criterion; in Serbia and Slovenia:
functional criterion, capacity criterion, spatial criterion, design and technical criterion,
traffic safety criterion and economic criterion (Kozić et al., 2016). The results provided
by the study (Retting et al., 2007) indicate that public support increases with time
since traffic participants become more familiar and comfortable with this form of
traffic control. Considering this, the use of the last criterion in this research has its
justification.
4.2. Evaluating and ranking the locations for roundabout construction using
the MABAC method
Flow measurement was performed at the sampling level in the period September-
November 2017. The data collected for each location based on established criteria are
presented in Table 4.
The selection of a location for potential roundabout construction – a case study of Doboj
51
Table 4. Values of alternatives according to criteria
C1 C2 C3 C4 C5 C6 C7 C8
A1 1256 8 2 3 3 419 7 85
A2 2194 4 2 9 3 731 5 89
A3 1037 5 4 7 3 346 3 45
A4 2878 32 3 7 4 720 5 8
A5 1052 2 4 5 4 263 5 27
A6 4197 124 1 3 4 1050 7 74
Table 4 shows the values for all the locations by established criteria. It can be noticed
that the highest intensity of traffic flows of vehicles and pedestrians belongs to the
sixth location with 4197 vehicles and 124 pedestrians in one hour. Locations 4 and 2
have slightly less intensity regarding vehicle flows, while the intensity of pedestrians
is 32 for the fourth, and only four for the second location. The remaining locations have
double less intensity than the two previously mentioned locations, and almost four
times less than the sixth location. If the sixth and fourth locations are excluded, the
flows of pedestrians are very low. The reason is that the sixth location is in the city
center, and the fourth location represents the connection between entering the city
and the railway station. Regarding the number of traffic accidents, the largest number
of accidents occurred at locations 3 and 5, four accidents per each, while the lowest
number of accidents occurred at the sixth location. The average vehicle intensity per
an arm (Table 4) is the largest at the sixth location, 1050, while for the second and
fourth location it is almost identical, 731 and 720, respectively. The minimum intensity
per an arm is at the fifth location since this location has four arms and an additional
arm that is not presented in the paper as an arm, as it is a side road with no frequent
traffic. Based on the public opinion survey for potential locations, the largest number
of citizens have characterized the first two locations as a priority for the construction
of a roundabout, and as the third one, they designated the sixth location.
After obtaining the matrix Q, it is necessary to sum the elements by rows and rank
them. Table 5 shows the final values of roundabout locations using the MABAC
method.
Table 5. Final values and ranking the alternatives
Values Rank
A1 -0.042 5
A2 0.010 4
A3 -0.043 6
A4 0.074 3
A5 0.132 2
A6 0.167 1
5. Sensitivity analysis
In order to validate the model and test the results obtained by applying the MABAC
method, a sensitivity analysis consisting of the application of the ARAS (Table 6), EDAS
(Table 7), SAW (Table 8), and WASPAS (Table 9) methods is performed in the paper.
Subotić et al./Oper. Res. Eng. Sci. Theor. Appl. 3(1) (2020) 41-56
52
5.1. Ranking the locations using the ARAS method
Compared to MABAC and other methods used in this paper, the initial matrix for
the ARAS method is slightly different. It is reflected through the formation of an
additional row that represents the optimal alternative. This alternative consists of the
best values depending on the type of criteria. If it is a criterion belonging to the benefit
group, the maximum value is taken, while for the criteria belonging to the cost group,
the minimum value is taken. After forming the optimal alternative, the initial matrix is
as shown in Table 6.
Table 6. Ranking the locations using the ARAS method
Si Ki Rank
A1 0.111 0.519 6
A2 0.134 0.626 3
A3 0.122 0.573 5
A4 0.131 0.614 4
A5 0.144 0.673 2
A6 0.144 0.675 1
Ao 0.214 1.000
5.2. Ranking the locations using the EDAS method
Table 7. Results obtained using the EDAS method
SPI NSI NSPI NSNI ASI Rank
A1 0.080 0.177 0.233 0.462 0.348 6
A2 0.167 0.118 0.488 0,.642 0.565 1
A3 0.189 0.210 0.554 0.363 0.459 5
A4 0.149 0.144 0.435 0.563 0.499 4
A5 0.253 0.201 0.740 0.390 0.565 2
A6 0.342 0.329 1.000 0.000 0.500 3
5.3. Ranking the locations using the SAW method
Table 8. Ranking the locations using the SAW method
Values Rank
A1 0.547 6
A2 0.634 3
A3 0.595 5
A4 0.633 4
A5 0.694 2
A6 0.694 1
5.4. Ranking the locations using the WASPAS method
This method, as already mentioned in the paper, contains the previously applied
SAW method in its steps, so that the normalization, weighting of the normalized
matrix, and summarizing the values by alternatives are identical as by the SAW
method, thus there is no need to display those matrices.
The selection of a location for potential roundabout construction – a case study of Doboj
53
Table 9. Ranking the locations using the WASPAS method
WPM Qi Rank
A1 0.508 0.528 6
A2 0.615 0.624 2
A3 0.522 0.558 5
A4 0.564 0.599 4
A5 0.576 0.635 1
A6 0.514 0.604 3
Based on the presented calculation, it can be noticed that the location under the
number 6 is best and a priority for the construction of a roundabout. Since it is the
location that has the largest traffic flow of pedestrians, an alternative solution for this
location is the installation of traffic lights at this intersection, which has been done in
the meantime, as it is well-known that if there is a high rate of pedestrians at a
roundabout, alternative solutions are used. The intensity of pedestrians at this
location for the period of one hour is 124 and, according to the authors’ opinion, it is
not a limitation for the roundabout construction. Location 6 represents the location in
the city center. The second priority location for the construction of a roundabout is
location 5 representing the last exit from the city towards Sarajevo and which is a four-
way intersection with an additional side road. There is often traffic congestion at this
intersection where city streets are its arms, so there is often a situation where drivers
carelessly merge onto the main road, as evidenced by a number of accidents.
Considering the above, the priority for the construction of a roundabout at this
location is justified.
Since there is a change in the ranks of the alternatives, it is necessary to make a
statistical comparison of the ranks, i.e. to determine their correlation. Table 10 shows
Spearman's correlation coefficient of the ranks of the alternatives for all the methods
used.
Table 10. Spearman's correlation coefficient of the ranks of the alternatives
for all the methods used
Methods MABAC ARAS WASPAS SAW EDAS Average
MABAC 1.000 0.886 0.657 0886 0.543 0.794
ARAS - 1.000 0.829 1.000 0.771 0.900
WASPAS - - 1.000 0.829 0.943 0.924
SAW - - - 1.000 0.771 0.886
EDAS - - - - 1.000 1.000
Overall average 0.901
Based on the total calculated statistical correlation coefficient (0.910), it can be
concluded that the ranks are in a high correlation in all the created scenarios.
Regarding the rank correlation of MABAC with other methods, there is a high
correlation with ARAS and SAW methods, while there is a lower correlation with the
other two methods, with WASPAS 0.657 and with EDAS 0.543. ARAS has the total
correlation with the SAW method (1.000), with WASPAS (0.829), while it has the
lowest correlation of 0.771 with EDAS. WASPAS and EDAS have the highest correlation
between each other, when considering these two methods, and it is 0.943. By
observing the overall ranks and correlation coefficients, it can be concluded that the
model obtained is very stable and the ranks are in a high correlation since all values
Subotić et al./Oper. Res. Eng. Sci. Theor. Appl. 3(1) (2020) 41-56
54
higher than 0.80 according to (Keshavarz Ghorabaee et al., 2016) represent a very high
correlation of ranks.
6. Conclusion
The developed model that includes the integration of BWM and MABAC methods
has been applied in a case study of selecting the location for the construction of a
roundabout in the City of Doboj, which is one of the important factors for increasing
the mobility and functional sustainability of the city. Taking into account the
geographical position of Doboj, it is imperative to construct roundabouts on the
territory covered by this urban area. Its location affects a significant share of transit
flows, increasing negative externalities to traffic sustainability. The solution is
certainly the construction of roundabouts that significantly eliminate or reduce
current negative effects. The hypotheses set out in the paper have been proven
through the development of the integrated model and analysis of all necessary
parameters, which can be seen from the results obtained. The paper considers six
potential locations, which have been evaluated using the integrated multi-criteria
model.
Based on the obtained results, it can be concluded that the sixth location is best in
terms of the defined optimization criterion and represents a priority location for the
construction of a roundabout. Location 6 represents the location that is in the city
center. The second priority location for the construction of a roundabout is location 5
representing the last exit from the city towards Sarajevo and a four-way intersection
with an additional side road. There is frequently traffic congestion at this intersection
where city streets are its arms. Taking into account the above, the priority for the
construction of a roundabout at the mentioned locations has been evaluated as
justified. The model stability was verified throughout a sensitivity analysis in which
the scenarios were created by applying different approaches.
When observing the current state in the field of interest and infrastructure
construction that involves smaller local projects, it is often one or two criteria
considered when building infrastructure. The development of such a model as in this
research creates the possibility of comprehensive consideration of all the important
factors for infrastructure construction, which is one of the contributions of this
research. In addition to the traffic flows of vehicles that are the main criterion, it is
necessary to take into account the number of traffic accidents that occurred at the
considered locations, pedestrian traffic flows, the economic aspect of construction and
other factors covered in detail throughout the paper.
Future research with respect to this paper refers to the development of a model
that will enable the measurement of parameters that enhance traffic sustainability and
the possibility of developing new approaches in the area of multi-criteria decision-
making.
Acknowledgements: The paper is a part of the research done within the project No.
19.032/961-58/19 “Influence of Geometric Elements of Two-lane Roads in Traffic
Risk Analysis Models” supported by Ministry of Scientific and Technological
Development, Higher Education and Information Society of the Republic of Srpska.
The selection of a location for potential roundabout construction – a case study of Doboj
55
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THE SELECTION OF A LOCATION FOR POTENTIAL ROUNDABOUT CONSTRUCTION – A CASE STUDY OF DOBOJ
Marko Subotić*, Biljana Stević, Bojana Ristić, Sanja Simić
1. Introduction
2. Brief literature review
3. Methods
3.1. Best – Worst Method
3.2. MABAC method
4. A case study in the city of Doboj – Description of the situation in the City of Doboj
4.1. Forming a multi-criteria model
4.2. Evaluating and ranking the locations for roundabout construction using the MABAC method
5. Sensitivity analysis
5.1. Ranking the locations using the ARAS method
5.2. Ranking the locations using the EDAS method
5.3. Ranking the locations using the SAW method
5.4. Ranking the locations using the WASPAS method
6. Conclusion
References