SELECTION OF RAILWAY LEVEL CROSSINGS FOR INVESTING IN SECURITY EQUIPMENT USING HYBRID DEMATEL-MARIC MODEL: Application of a new method of multi-criteria decision-making

Abstract

According to the European Railway Agency in the European Union every year on railway level crossings (RLC) occurs over 1200 traffic accident in which life loses more than 400 people. In addition to the tunnel and specific locations that are identified as black spots on the roads, RLC have been identified as potential weak points in road infrastructure that significantly jeopardize traffic safety. In Serbia exists about 2350 RLC, one of which is part the secured by systems of active and passive safety (traffic signs, light signals, sound signals, barriers, etc..). Insurance RLC is a material expenditure. The RLC selection process for installation of security equipment accompanied by a greater or lesser degree of criteria vagueness that are necessary for making the relevant decisions. For exploitation these uncertainties and vagueness in this paper was used fuzzy logic. This paper presents the application of a new method of multi-criteria decision-making (Multi-Attributive Real-Ideal Comparative Analysis -MARICA), which represents support in the selection process for RLC to invest in safety equipment. Identified are eight criteria that influence the investment decision. MARICA method was tested on the example of choice of eight RLC for investing in safety equipment.

Full text

1 Assistant profesor, PhD Dragan Pamučar, dipl. eng, Military academy, Belgrade, dpamucar@gmail.com
2 Associate profesor, PhD Ljubislav Vasin, dipl. eng, Military academy, Belgrade, ljvasin@gmail.com
3 Assistant, Mag. Vesko Lukovac, dipl. eng, Military academy, Belgrade, lukovacvesko@yahoo.com 89
SELECTION OF RAILWAY LEVEL CROSSINGS FOR INVESTING
IN SECURITY EQUIPMENT USING HYBRID DEMATEL-MARIC
MODEL
Dragan PAMUČAR 1
Ljubislav VASIN 2
Vesko LUKOVAC 3
Abstract – According to the European Railway Agency in the European Union every year on railway
level crossings (RLC) occurs over 1200 traffic accident in which life loses more than 400 people. In
addition to the tunnel and specific locations that are identified as black spots on the roads, RLC have
been identified as potential weak points in road infrastructure that significantly jeopardize traffic
safety. In Serbia exists about 2350 RLC, one of which is part the secured by systems of active and
passive safety (traffic signs, light signals, sound signals, barriers, etc..). Insurance RLC is a material
expenditure. The RLC selection process for installation of security equipment accompanied by a
greater or lesser degree of criteria vagueness that are necessary for making the relevant decisions.
For exploitation these uncertainties and vagueness in this paper was used fuzzy logic. This paper
presents the application of a new method of multi-criteria decision-making (Multi-Attributive Real-
Ideal Comparative Analysis - MARICA), which represents support in the selection process for RLC to
invest in safety equipment. Identified are eight criteria that influence the investment decision.
MARICA method was tested on the example of choice of eight RLC for investing in safety equipment.
Keywords – Railway level crossings, Railway accidents, Multicriteria decision making,
MARICA, DEMATEL.
1. INTRODUCTION
Railway level crossings represent the intersections of
road and rail transport, and potentially are dangerous
points for road users. In general terms level crossings
may be provided with automatic or mechanical
insurance. In addition, RLC may be and unsecured,
where ramps for drivers do not exist and where they
placed only traffic signs and other equipment. Ensuring a
level crossing with automatic insurance (AO) requires a
great investment because the devices to ensure the RLC
are expensive and because there are a large number of
RLC who are unsecured.
At the RLC a large number of accidents that
accompany major material damage and loss of lifes
happens. It is estimated that in road accidents an average
of 1,308 people lose their lives daily in the world [5]. Of
the approximately 54 million people who die each year
in the world, the number of people killed in road
accidents amounted to 1.17 million (2.17%).
According to the European Railway Agency, of the
total number fatalities in railway accidents, 27%
accounts at level crossings [5]. Traffic accidents at
railway crossings are mostly consequences of improper
and inattentive behaviour of participants in road traffic.
According to the statistics and forecasts of the EU
[3], the volume of rail traffic in the next 30 years will be
doubled, which is a direct indicator of the expected
increase in emergencies at level crossings on all lines,
including lines in Serbia. How the volume of traffic on
the railways will increase, with a high degree of
probability it can be concluded that the number of
accidents at RLC will increase. In this context it will be
necessary and to develop a plan of investing in RLC
insurance in order to raise the level of traffic safety and
accident reduction. Insurance RLC with automatic
security equipment (barriers) is an investment that
requires the allocation of significant funds while making
decisions about investment management has a big
responsibility, as approved funds must give proper
effect. It is therefore very important that management
has adequate tools to facilitate the process of selecting
RLC and making investment decisions.
In this paper the application of MARICA method for
making optimal investment decision in order to improve
safety at RLC is presented. It starts from the premise that

RAILCON ’14 TRAFFIC AND TRANSPORT
90
the observed RLCNO at a time when there are resources
for a limited number of RLC on which to install new
safety equipment for AO.
This paper presents a hybrid model of multi-criteria
decision-making in which is implemented fuzzy
DEMATEL method [2,4,6] and a new method of multi-
criteria decision-making methods MARICA, which was
developed at the Center for Logistics Research of
Defense University in Belgrade. A modified fuzzy
DEMATEL method was used in the evaluation process
and criteria for determining weight coefficients. After
determining the weight criteria, using the method
MARICA, the value of criterion function are calculated.
After determining criterion function the ranking of
alternatives and the selection of the optimal railway level
crossings for investing in safety equipment is peformed.
2. SETTING OF HYBRID DEMATEL-
MARICA MODEL
Problem is formally presented by choosing one of the
m options (alternatives) Ai,i =1,2….m, which we
evaluate and compare among themselves on the basis of
n criteria (Xj,j =1,2….n) whose values are known to us.
Alternatives vectors are shown with xij, where is xij value
of i-th alternative by j-th criteria. Because the criteria in
varying degrees impact on final grade of alternatives, to
each criterion we ascribe weighting coefficient
, 1,2,...,
j
wj n (where is 11
n
j
jw

) which reflects
its relative importance in the evaluation of alternatives.
Weighting coefficients in this paper were obtained by
applying fuzzy DEMATEL method. In the process of
determining the weight coefficients of criteria most
commonly more experts are included. Due to this, in the
following section the process of implementing
DEMATEL method in groups decision-making process
is explained.
In the first step of fuzzy DEMATEL method the
expert ratings is collected and calculated the average
matrix

Z
. For comparison of criteria pair experts use
fuzzy scale in which are linguistic expressions
represented by triangular fuzzy numbers

,, ,
() ( ) ( )
, , , 1,2,...,
ij ij e ij e ij e
elmr
zzzze m
, where e represents
the label an expert, and m represents the total number
of experts. By aggregation of expert opinions the final
matrix

ij
Z
z


 is obtained. The elements of the
matrix

Z
are obtained by using the expression (1), (2)
and (3)



,,
() ()
min , 1,2,..., ,...,
ij e ij e
ll
M
zzMem (1)
,,
() ()
1
1
ij e ij k
m
mm
k
zz
m
 (2)



,,
() ()
max , 1,2,..., ,...,
ij e ij e
rr
M
zzMem (3)
where ,
()
ij e
l
z, ,
()
ij e
m
z i ,
()
ij e
r
z represent the preference of the
eth expert, M represents a set of experts who
participate in the research, e represents the label an
expert, and m represents the total number of experts.
After calculation of matrix elements

Z
, in the next
step, elements of the normalized initial direct-relation
matrix


ij
Dd





are calculated, where every element
of matrix

D
belongs to the interval [0,1]. Calculation
of matrix elements

D
(4) is performed by using the
expression (5) and (6).




 
 
11 12 1
21 22 2
12
...
...
... ... ... ...
...
n
n
nn nn
dd d
dd d
D
dd d















(4)
The elements of the matrix

D
is obtained by
summing the elements of the matrix

Z
by rows. After
that, by applying expression (6), among the
summarized elements the maximum element

R
are
indentified. With simple normalization, expression
(5), each element of the matrix

Z
is divided by the
value which we get by applying the expression (6).


() ( ) ( )
() ( ) ( )
,,
ij ij ij
lmr
ij
ij lmr
zz z
z
drr r
R






(5)





() ( ) ( )
1
max , ,
nlmr
ij
j
R
zrrr


 (6)
where n represents the total number of criteria.
In the next step, the elements of the total relation
matrix

T are calculated. The total-influence matrix

T
is calculated by applying equation (7), where I
represent identity matrix.









1
2
lim ... w
w
TDDDDID


 (7)
In the final step of DEMATEL method, elements
of the matrix

T are summed by rows and columns, bz
the expressions (8) and (9).

1, 1,2,...,
n
iij
i
D
ti n


 (8)

1, 1,2,...,
n
iij
j
R
tj n


 (9)
where n represents the number of criteria.
Based on the values obtained by the expressions
(8) and (9) the weight coefficients of criteria are
calculated. The weight coefficients of criteria are
determined using expressions (10) and (11)

XVI International Scientific-expert Conference on Railways Serbia, Niš, October 09-10, 2014
91







1/2
22
ii
ii i
WGR GR




(10)



1
i
in
i
i
W
w
W

 (11)
where

i
w represents the final weights of criteria
which are used in the process evaluation of
alternatives [4].
By determining the weight coefficients of criteria
conditions for representing mathematical formulation
of MARICA method are created. A basic setting of
MARICA method reflected in determining the gap
between the ideal and the empirical ponders. By
summing the gap for each criteria of observed
alternative the total gap for each alternative is
determined. At the end, the ranking of alternatives is
carried out; where for the best ranked alternative the
one which has the lowest value of the total gap is
chosen. The alternative with the lowest total gap
represents an alternative that for the highest number of
criteria had values that were closest to the ideal ponders
(ideal values of criteria). MARICA method is
implemented through six steps:
Step 1. The definition of the initial decision matrix
(X). In the initial decision matrix the values of criteria
( , 1,2,... ; 1,2,...
ij
x
injm) for each of the
considered alternatives are determined.
The elements of the matrix X are obtained on the
basis of personal preferences of decision maker or
aggregation of expert decisions.
Step 2. Determination of preferences according to
alternatives i
A
P choice. It is assumed that the decision
maker (DM) does not take into account the probability
of some alternatives selection, i.e. there are no
preferences according alternative choices. Then he can
observe alternatives such way that each takes place
with equal probability.
1
1; 1, 1,2,...,
ii
m
AA
i
PPim
m

 (12)
where m is the total number of alternatives that are
chosen from.
In the analysis of decision-making with the a priori
probabilities we assume that DM is neutral in relation
to risk. In this case, all preferences according choice
of the individual alternatives are equal i.e.
12
... m
AA A
PP P (13)
Step 3. The calculation of matrix elements of
theoretical ponders ( p
T). The matrix of theoretical
ponders (Tp), size n x 1 (n represents the total number
of criteria) is defined. The elements of the matrix are
calculated as the product of preference of choice
alternatives i
A
P and the criteria weight coefficients
(wn).
12
12
...
...
ii i i
n
pAA A An
ww w
T P Pw Pw Pw





  (14)
where n represents the total number of criteria and tpi
represents the theoretical ponder.
Step 4. Determination of the actual ponders ( r
T)
matrix elements.
12
111 12 1
221 22 2
12
...
...
... ... ... ... ...
...
n
rr rn
rr rn
r
mrm rm rmn
CC C
At t t
At t t
T
At t t













(15)
where n represents the total number of criteria and m
represents the total number of alternatives.
Calculation of actual ponders ( r
T) matrix elements
is done by multiplying the matrix elements of
theoretical ponders ( p
T) and the elements of initial
decision matrix (
X
) according to the expression:
 For criteria of „benefit“ type (higher value of
criteria is preferable)
ij i
rij pij
ii
x
x
tt
x
x








 (16)
 For criteria of „cost“ type (lower value of
criteria is preferable)
ij i
rij pij
ii
x
x
tt
x
x








 (17)
Step 5. Calculation of the total gap matrix (G).
The elements of the matrix are obtained as the
difference (gap) between the theoretical ( pij
t) and
actual ponders ( rij
t).
Step 6. The calculation of the final values of
criterion functions ( i
Q) by alternatives. Values of
criterion functions are obtained by summing the gap
(ij
g) by alternatives (summing the elements of the
matrix (G) by columns):
1
, 1,2,...,
n
iij
j
Qgi m


 (19)
3. APPLICATION OF DEMATEL-MARICA
MODEL
The testing described DEMATEL-MARICA model
was performed on example of prioritizing eight
illustrative railway crossings. The eight criteria for the
selection and evaluation of railway crossings were
defined [3]:

XVI International Scientific-expert Conference on Railways Serbia, Niš, October 09-10, 2014
92
11 11 12 12 1 1
11 12 1
21 21 22 22 2 2
21 22 2
11 2 2
12
...
...
...
...
... ... ... ...
... ... ... ...
...
...
pr pr pnrn
n
p
rpr pnrn
n
pr
p
mrm pm rm pmnrmn
mm mn
tt tt tt
gg g
tttt t t
gg g
GT T
ttt t tt
gg g
 




 


 




 



(18)
K1- The frequency of rail transport on the observed
railway crossing (w=0.12);
K2- The frequency of road transport on the
observed railway crossing (w=0.19);
K3- Number of tracks on the observed railway
crossing (w=0.11);
K4- The maximum permitted speed of trains on the
chainage of level crossing (w=0.08);
K5- The angle of intersection of the railroad and
road (w=0.15);
K6- The number of emergency events on the
observed railway crossing in the past year (w=0.12);
K7- Visibility of observed railroad crossing from
the aspect of road transport (w=0.14);
K8- The investment value of the activity in
function of railroad crossing width (w=0.09).
For the evaluation of qualitative criteria (K5, K7
and K8) fuzzy Likert scale was used [1]:
Table 1. Fuzzy Likert scale
R.b. Linguistic terms Fuzzy numbers
1. Very good (VG) (4.5,5,5)
2. Good (G) (3.5,4,4.5)
3. Fair (F) (2.5,3,3.5)
4. Poor (P) (1.5,2,2.5)
5. Very poor (VP) (1,1,1)
Table 2 shows the eight railway level crossings at
which the presented model is tested.
Table 2. The evaluation of railway level crossings
Alter. C1 C2 C3 C4 C5 C
6
C
7
C8
PPP 1 24 165 2 40 G 3 P G
PPP 2 56 212 2 50 P 5 P F
PPP 3 41 71 2 60 G 7 P VG
PPP 4 36 168 1 50 F 5 VG G
PPP 5 25 153 2 40 P 3 P VG
PPP 5 12 220 2 50 P 5 P F
PPP 6 28 137 4 60 F 6 F VG
PPP 7 35 112 2 60 G 4 F P
PPP 8 24 165 2 40 G 3 P G
*PPP- Railway level crossings
Values of criteria functions (Qi) by alternatives
(Table 3) are obtained by summing the gap (gij) by
alternatives, ie summing the elements of the matrix
(G) by columns, the expression (19).
By using the expression (20) defuzzification of
fuzzy numbers was performed.
 
() () ( ) () 1 ()
=3
rl ml l
defuzzy A a a a a a


  

(19)
where a(l) and a(r) respectively represent the left and
right distribution of confidence interval triangular
fuzzy number, a(m) represents the value in which a
triangular function reaches its maximum value.
Tab. 3. Rank alternative by the method MARICA
Alternative Q Rank
PPP 1 0.0851 7
PPP 2 0.0629 3
PPP 3 0.0668 5
PPP 4 0.0614 2
PPP 5 0.1029 8
PPP 5 0.0729 6
PPP 6 0.0590 1
PPP 7 0.0635 4
It is desirable to have an alternative with the lowest
value of the total gap. So, the highest-ranked
alternative is the one that has the lowest value of the
total gap i.e. alternative 7.
4. CONCLUSION
Through this paper the application of a hybrid
DEMATEL - MARICA model is shown in making an
investment decision on the selection of railway level
crossings for installation the safety equipment.
DEMATEL method is applied in part for determining
weight coefficients. and a new multicriteria method –
MARICA method in part of the alternatives evaluation.
Application of the method has been elaborated through
the steps and shown on the illustrative example.
Beside to the shown application in the selection of
railway level crossings, MARICA method can be used
to solve other problems of multi-criteria decision
making. The main recommendations for further use of
this method is: a simple mathematical form, the
stability of solutions and the ability to combine with
other methods, especially in the part relating to the
determination of weight criteria.
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