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54
Tadić S. et al. Ranking of Logistics System Scenarios Using Combined Fuzzy AHP-VIKOR Model
RANKING OF LOGISTICS SYSTEM SCENARIOS USING COMBINED
FUZZY AHP-VIKOR MODEL
Snežana Tadić1, Slobodan Zečević2, Mladen Krstić3
1, 2, 3 University of Belgrade, Faculty of Transport and Traffic Engineering, Vojvode Stepe 305, 11000,
Belgrade, Serbia
Received 13 November 2014; accepted 28 December 2014
Abstract: Ranking of the logistics system scenarios of the Central Business District (CBD)
of the city is performed in this article using the multi-criteria decision-making (MCDM)
model which combined the methods of fuzzy “Analytical Hierarchy Process” (FAHP) and
“Višekriterijumska Optimizacija i kompromisno Rešenje” (VIKOR). FAHP is applied for
obtaining the weights of the criteria defined on the basis of conflicting goals of different
stakeholders, and VIKOR method is applied for obtaining the final ranking of the logistics
system scenarios.
Keywords: city logistics, central business district, logistics system scenario, FAHP-VIKOR.
1 Corresponding author: s.tadic@sf.bg.ac.rs
UDC: 658.286(497.11)
656.073(497.11) DOI: http://dx.doi.org/10.7708/ijtte.2015.5(1).07
1. Introduction
Logistics system scenario for the city or
certain urban area is defined in accordance
with the requirements of stakeholders,
i.e. participants of city logistics (shippers,
receivers, carriers, logistics service providers,
residents, cit y government). Consider ing that
participants have different, often conflicting
goals and interests, it is necessary to find a
compromise solution. This problem can be
solved by defining a large number of criteria
and applying MCDM methods.
In this article, the problem of ranking
logistics system scenarios for the Central
Business Danube District (CBDD) of
Belgrade is solved using the MCDM model
which combines AHP in fuzzy environment
(FAHP) and VIKOR in conventional form.
This area is foreseen for the development of
various business and commercial facilities,
and new plan also requires new logistics
solutions, defined in this article in the form
of three scenarios. Ranking of scenarios is
carried out in relation to the criteria defined
in accordance with the requirements of
different structures and functions of the
city. The weights of criteria are obtained by
using FAHP method which is simple to use,
easily adaptable to the problems of different
dimensions and can take into account
both quantitative and qualitative criteria.
However it can be problematic in terms
of presenting the dependencies between
the criteria and alternatives, therefore the
VIKOR method is used in this article for
obtaining the final order of the alternatives
(scenarios). The methods results in the
compromise solutions, established by mutual
concessions, based on which the ranking of
alternatives is performing.
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International Journal for Traffic and Transport Engineering, 2015, 5(1): 54 - 63
2. Defining the Problem
Evolution of urban areas caused the change
of the form and physical components of
procurement, storage and distribution of
goods. In the initial stages of development,
ports, harbors and squares represented the
commodity gates for urban areas. With the
spatial expansion of cities, the development
of transport infrastr ucture and rising prices
of urban land, the stopping points of macro-
distribution f lows are moving towards
the peripheral zones. The growth of road
transportation, the expansion of network
of warehouses, logistics centers, as well as
increased demands in terms of quality and
variety of logistics services have resulted
in a significant increase in the number of
commercial vehicles and worrying loss of
vitality of come cities. Existing regulations
and policies of urban freight transport and
logistics, in most cases cannot fully respond
to the significant changes that have taken
place in the use of the land, as well as in
the sectors of production, distribution and
consumption. The space devoted to logistics
activities (freight terminals, city ports,
warehouses) disappears from the cities.
Expensive urban land changes its purpose,
i.e. new commercial and housing facilities
that generate significant f lows of goods and
require a modern concept of logistics are
developing.
Belgrade is, like many other cities on the
riverside, mainly developed and radial-
concentric spread in regard to the traditional
center and the river port. In the initial stages
of development, many trade and distr ibution
as well as industria l firms favorably inhabited
the port and its surroundings and developed
their own warehousing and distribution
activities. Therefore the area of CBDD, in
spite of bei ng a very valuable la nd, is occupied
by the storage and handling systems with the
outdated technologies, runs a large number
of vehicles and in many cases performs the
logistics function for users who are not in
the immediate area of the city of Belgrade.
In addition to the outdated concept of
structuring, inadequate utilization of space
and outdated technology, this area also lacks
logistics scenario that would be consistent
with the city development concepts.
The observed urban area, CBDD, becomes
an attractive location for more profitable
business and commercial contents, which
requires the restructuring of existing urban
units. The basic idea is to free the observed
space of unnecessary logistical structures,
to maintain and modernize the system of
logistics for the CBD and coordinate it with
the concept of a combined centralized-
decentralized logistics system of the city
(Master plan of Belgrade, 2021). Analysis of
logistics scenario of the CBDD and selection
of the best solution for a broad set of interests
is a central issue and task discussed through
the case study in this article.
3. CBDD Logistics Systems Scenarios
The key elements for defi ning fut ure logist ics
concept for CBDD are: causes for settlement
of the observed area; the possibility of
displacement, dislocation; the necessity of
certain systems existence at t he location; the
place and role of CBDD’s logistics system in
the logistics of the city; and compatibility
of logistics facilities with new development
plans. In addition to that, cha nges of the port
system ownership and their business visions
had a significant impact on the setting of
the three scenarios of the CBDD logistics
system (Zečević, 2006):
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Tadić S. et al. Ranking of Logistics System Scenarios Using Combined Fuzzy AHP-VIKOR Model
• Sc.1: The scenar io of minimal infrastructural
changes.
• Sc.2: The scenario of significant changes.
• Sc.3: The scenario of complete changes.
Scenario Sc.1 involves the retention and
modernization of existing structures and
subsystems at the observed area (Fig. 1).
The port, which would remain in CBDD,
would retain certain functions, primarily
intermodal transport function. In this case,
it is expected further development and
modernization of intermodal ter minals. The
existing storage and distribution systems
could increase thei r efficienc y with the use of
new technologies and it is possible to expect
the development of new, modern logistics
systems, which would be acceptable solutions
for observed area in terms of architecture
and civil engineering. In functional sense,
new logistics systems would be the answer
to the growing need for VAL services
(Value Added Logistics), deliveries to
specific assumption zones (pickup points),
professional warehousing services, reverse
logistics services, etc.
Port with
freight
terminals
Rail freight
station
Generator of
logistics flows
Deliveries to generators in
central city area and
metropolitan area of
Belgrade
Rail connection
of intermodal
terminals
Intermodal
Terminal
CBDD
Rail freight
station
Connection of
rail freight
stations
Danube River
Customs and
forwarding
systems
Logistics, warehousing
and distribution
systems of companies
Long haul
trucking
Long haul
trucking
Fig. 1.
Logistics System of CBDD According to Scenario Sc.1
Source: Tadić and Zečević (2009)
Scenario Sc.2 is based on the reduction of
distribution and storage systems, as well as
shippi ng, custom s and other related activit ies
that are not necessary for the supply of CBD.
This scenario implies the modernization of
intermodal terminal as trimodal node and
the development of a CLT for consolidated
deliveries to generators in the gravity
area (Fig. 2). These two sub-systems have
the ability for railway connection with
intermodal terminals in other locations,
freight villages (FV) on the edge of the
city, using the system of shuttle trains. This
would lead to sign ificant reduction of railway
facilities, but it would enhance the role of
railway in effective connection of this area.
CLT would supply the CBD with a variant
of small commercial eco-vehicles.
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International Journal for Traffic and Transport Engineering, 2015, 5(1): 54 - 63
Intermodal
Terminal
Rail connections
between
intermodal
terminals -
Shuttle trains
Generator of
logistics flows
IT
CLT
FV
FV
Rail connections
between
intermodal
terminals -
Shuttle trains
Freight
Village
CBDD
City Logistics
Terminal
Danube River
Consolidated deliveries for
generators in central city
area ussing eco-vehicles
Fig. 2.
Logistics System of CBDD According to Scenario Sc.2
Source: Tadić and Zečević (2009)
Scenario S3 imply dislocation of all existing
port complex facilities and railway freight
station, while the entire observed area of
CBDD remains business and shopping center
with associated restaurants, cultural and
sports facilities. This scenario would be in
accorda nce with the “log istics sprawl” (Dablanc
and Rakotonarivo, 2010) which becomes a
worldwide phenomenon, and imply that
logistics is increasingly taken away from the
heart of the city. However, commercial contents
that would settle the area of CBDD, together
with the existing commercial contents in
central cit y area can’t operate without logistics.
Attractiveness and f unctionality of the system
requires accompany ing logistics system w ith a
minimum and efficient configuration which,
in the physical and traffic terms, can be done
by introducing CLT. The goods would be
delivered to the terminal from the logistics
center in another location in the city, using
the cargo tram and goods distribution to the
generators in the CBD would be performed
with electric vehicles (Fig. 3).
Freight
Village
City Logistics
Terminal
Generator of
logistics flows
FV
Consolidated deliveries
for generators in central
city area ussing eco-
vehicles
Cargo tram
LC
Logistics
Center
CBDD
CLT
Danube River
Fig. 3.
Logistics System of CBDD According to Scenario Sc.3
Source: Tadić and Zečević (2009)
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Tadić S. et al. Ranking of Logistics System Scenarios Using Combined Fuzzy AHP-VIKOR Model
4. Criteria for Assessing Logistics System
Scenarios
Criter ia used for the evaluation of the CBDD
logistics system are described below (Tadić
et al., 2014b):
C1. The degree of congestion caused by
heavy freight vehicles on the access
points and roads in CBDD. Wit h
dislocation of systems which, in
technological and spatial sense, are
not related to the port and intermodal
transport and with the consolidated
distribution of goods in scenarios Sc.2
and Sc.3, the number of freig ht vehicles
would be significantly reduced, and
thus the degree of traffic congestion.
C2. The degree of space occupancy by the
logistics systems that are not needed
in the CBDD. According to scenario
Sc.1, a certain number of CBDD
logistics system users make deliveries
to recipients outside of Belgrade from
this site. By d islocating these activities
and concentrating only on supplying
the CBD, occupied areas can be
significantly reduced in scenario Sc.2,
and especially in scenario Sc.3.
C3. Investment for the development of
systems. Investments for systems
development according to scenarios
Sc.2 and Sc.3 are significant and
depend on the micro-location, size
and structure of the planned facilities.
C4. Costs of goods delivery. According to
previous researches, delivery costs are
reducing by using CLT and concept of
flows consolidation for multiple users.
C5. Time losses in inbound-outbound
transport. These losses could be
substantial in scenario Sc.1.
C6. The quality of logistics service. By
using modern storage systems and
systems for track ing and vehicle
navigation during delivery, logistics
service quality parameters could be
significantly improved. Accordingly
scenarios Sc.2 and Sc.3 are better
solutions for all users who may, in the
future, be supplied from CBDD.
C7. Ecological and energy aspects. By
eliminating long haul, and applying
the concept of consolidation and
environmentally acceptable systems
and technologies of transport, the
total number of road freight vehicles,
and thus the negative environmental
impacts and energy consumption could
be significantly reduced compared to
current state.
C8. Security aspect. Reduction of the
amount of traffic and congestion
on city roads reduces the number
of conflicting situations. According
to this parameter it is evident an
advantage of scenarios Sc.2 and Sc.3.
C9. Logistics chains complexity. Every
stopping of the goods flow and its
transformation in logistics centers
increases the logistics chains
complexity. Application of scenario
Sc.3 requires the highest degree of
cooperation and consolidation, i.e. it
represent s the most complex realization
of logistics chains.
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International Journal for Traffic and Transport Engineering, 2015, 5(1): 54 - 63
C10. Technological and visual integration of
logistics systems in urban environment.
A difference in relation to logistics
systems in scenario Sc.1 can be created
by constructing modern commercial
facilities. On the other hand, in
scenarios Sc.2 and Sc.3, logistics
solutions and environment can be
technologically and visually aligned
and brought together.
5. Ranking of Logistics System Scenarios
A combination of fuzzy AHP and V IKOR
methods is used in this article to solve
the problem of logistics system scenarios
ranking. In the literature, there are various
examples of the combinations of MCDM
methods, in the conventional form or in a
fuzzy environment, for solving different
problems in the field of logistics: city
logistics concept selection (Tadić et al.,
2014a), city logistics terminal location
select ion (Tadić et al., 2012), global logistics
strategies identification (Sheu, 2004), solid
waste transhipment site selection (Onut and
Soner, 2008), etc. The first part of the model
includes the application of the fuzzy AHP
method (Van Laarhoven and Pedrycz, 1983),
as a fuzzy e xtension of the conventional A HP
method (Saaty, 1980). The first step of the
method is the formation of the hierarchical
structure of the problem: the ultimate
goal on the top, a number of criteria and
alternatives at the bottom. For the problem
set in this way an analysis is performed in
order to determine the relative weights of
the criteria at each level, as well as the values
of the alternatives, i.e. scenarios, in relation
to the criteria. The analysis involves the
comparison of all pairs of criteria as well
as comparison of all pairs of scenarios with
respect to the criteria. A linguistic scale
shown in Table 1 which can be converted
into triangular fuzzy numbers is used for
comparison. In the second part of the model
the VIKOR method (Opricović, 1998) is
used for the final ranking of scenarios. It
determines the compromise solution, i.e. a
feasible solution closest to the ideal, and a
compromise means an agreement established
by mutual concessions.
Table 1
Fuzzy Scale for the Comparison of Criteria/Scenarios
Linguistic term Fuzzy scales
Absolutely preferable/better (AP/B) (8, 9, 10)
Very preferable/better (VP/B) (7, 8, 9)
Strongly preferable/better (SP/B) (6, 7, 8)
Pretty preferable/better (PP/B) (5, 6, 7)
Quite preferable/better (QP/B) (4, 5, 6)
Moderately preferable/better (MP/B) (3, 4, 5)
Remotely preferable/better (RP/B) (2, 3, 4)
Barely preferable/better (BP/B) (1, 2, 3)
Equally important/ good (EI/G) (1, 1, 2)
The FAHP can be solved using various methods
and in t his paper the “log arithmic fuzzy preferenc e
programming” (LFPP) (Wang and Chin, 2011;
Yu and Shing, 2013) method is used, developed
by extending a method of fuzzy preference
programming (FPP) (Mikhailov, 2003).
60
Tadić S. et al. Ranking of Logistics System Scenarios Using Combined Fuzzy AHP-VIKOR Model
FPP method starts with forming a fuzzy
comparison matrix (Ã) elements of which
are triangular fuzzy judgments
of compar ing element i in relation to element
j. Wang and Chin (2011) in LFPP method
take logarithm values of fuzzy judgment
ij
a
~
from matrix à by the following approximate
equation:
(1)
That is, the logarithm of a triangular fuzzy
judgment
ij
a
~
can be seen as an approximate
triang ular fuzzy number, whose membership
function can be defined as:
(2)
where is the membership degree
of belonging to the approximate
tri angul ar fuzz y judgment
, and wi are crisp values of the priorit y vector
( )
0,...,
1>= T
n
wwW
,
∑
=
=
n
i
i
w
1
1
.
It is necessar y to find a crisp priorit y vector
to maximize the minimum membership
degree
( )( ){ }
nijniww
jiij ,...,1;1,...,1|/lnmin +=−==
µ
λ
.
The resultant model can be constructed as:
(3)
or
(4)
To avoid membership degree λ from taking
a negative value, the nonnegative deviation
variables δij and ηij for i=1,...,n-1 and j=1,...,n are
introduced such that t hey meet the following
inequalities:
It is most desirable that the values of the
deviation variables are as small as possible.
Accordingly the following LFPP-based
nonlinear priority model for weight (wi)
derivation for fuzzy AHP is proposed:
(5)
where xi=lnwi for i=1,...,n, and M is a specified
sufficiently large constant such as M=103.
Let
( )
nix
i
,...,1=
∗ be the optimal solution
to model (5). The normalized priorities for
fuzzy pair wise comparison matri x
( )
nn
ij
aA
×
=
~
~
can then be obtained as:
(6)
where exp() is the exponential function,
namely
( )
∗
=
∗i
x
iexexp
for i=1,...,n.
Table 2 shows the fuzzy comparison matrix
for obtaining the criteria weights, i.e. the pair
wise comparison of criteria using linguistic
terms defined in Table 1. In accordance with
the described method the nonlinear model
(5) is solved and by using Eq. (6) normalized
weights of criteria wj are derived and shown
in Table 2.
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International Journal for Traffic and Transport Engineering, 2015, 5(1): 54 - 63
Table 2
Comparison of Criteria and Final Values of Criteria Weights
Criterion C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 wi
C1 / - - - EI - RP QP RP QP 0,074
C2 RP / - EI RP EI QP SP QP SP 0,148
C3 QP RP /RP QP RP SP AP SP AP 0,296
C4 RP --/RP EI QP SP QP SP 0,148
C5 - - - - / - RP QP RP QP 0,074
C6 RP ---RP / QP SP QP SP 0,148
C7 ------/RP EI RP 0,037
C8 - - - - - - - / - EI 0,019
C9 -------RP /RP 0,037
C10 - - - - - - - - - / 0,019
Comparisons of all pairs of scenarios in
relation to the defined criteria by using the
linguistic expressions from Table 1 are shown
in Table 3. The preference values of scenarios
in relation to the criteria are obtained using
the LFPP method (Table 4).
Table 3
Comparison of Scenarios in Relation to the Criteria
Scenario Sc.1 Sc.2 Sc.3 Sc.1 Sc.2 Sc.3 Sc.1 Sc.2 Sc.3 Sc.1 Sc.2 Sc.3 Sc.1 Sc.2 Sc.3
Criterion C1 C2 C3 C4 C5
Sc.1 / - - / - - / BB MB / - - / - -
Sc.2 MB / - PB / - - / RB RB / - MB / -
Sc.3 PB RB /SB BB / - - / MB BB / QB BB /
Criterion C6 C7 C8 C9 C10
Sc.1 / - - / - - / - - / BB RB / - -
Sc.2 QB / - QB / - QB / - - / BB RB / -
Sc.3 PB BB / PB BB / PB BB / - - / MB BB /
Table 4
Preference Values of Scenarios in Relation to the Criteria
C1 C2 C3 C4 C5 C6 C7 C8 C9 C10
Sc.1 0,031 0,039 0,627 0,059 0,051 0,044 0,044 0,044 0,571 0,059
Sc.2 0,197 0,320 0,314 0,314 0,316 0,319 0,319 0,319 0,286 0,314
Sc.3 0,772 0,641 0,059 0,627 0,633 0,637 0,637 0,637 0,143 0,627
For the final ran king of the scenarios w ith the
VIKOR method, first it is needed to define
the best and worst values of the criterion
functions, i.e. to obtain the ideal ( fi
*) and
the nadir ( fi
-) solutions (Opricović, 1998):
(7)
(8)
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Tadić S. et al. Ranking of Logistics System Scenarios Using Combined Fuzzy AHP-VIKOR Model
where fki is the preference value of scenario
k in relation to criterion i.
Afterwards, the distances of alternatives
from ideal (Sk) and nadir (Rk) solutions are
being calculated:
(9)
(10)
At the end it is necessar y to calculate V IKOR
values Qk for k=1, ..., m, in the following way:
( )
−
−
−+
−
−
=−− *
*
*
*
1RR
RR
v
SS
SS
vQ kk
k
(11)
where S– = maxk Sk, S* = mink Sk , R– = maxk
Rk, R* = mink Rk, , and v is the weight of the
strategy of “the maximum group utility “.
This means that if v is greater than 0.5, the
Qk index w ill incline towards the consensus
of the majority, and if it is less than 0.5 the
Qk index will incline towards the negative
attitude of the majority. For obtaining the
values of Qk, the value v = 0.55 is used in this
article. The final ranking of the alternatives
is obtained by sorting the Qk values i n
increasing order. The values Sk, Rk, Qk, as
well as the final ranking of the alternatives
are shown in Table 5.
Table 5
The Final Ranking of the Logistics System
Scenarios
Scenario Sk Rk Qk Rank
Sc.1 0,667 0,148 0,550 3
Sc.2 0,566 0,163 0,431 1
Sc.3 0,333 0,296 0,450 2
For a defined set of criteria and their mutual
relationships and by using combined FAHP-
VIKOR method, Sc.2 is chosen as the best
logistics system scenario for the central
business district. The same order of scena rios
is obtained by using the PROMETHEE
method (Tadić and Zečev ić, 2009), as well as
by combining fuzzy A HP and fuzzy TOPSIS
methods (Tadić et al., 2014b).
6. Conclusion
MCDM methods provide suppor t to decision-
makers (planners, city administration,
logistics providers, users, etc.) when selecting
the logistics scenario for an urban a rea, which
is performed in this article for the CBDD of
Belgrade. Three logistics system scenarios
are def ined in this ar ticle, where scenar io Sc.1
involves minimal changes while scenarios
Sc.2 and Sc.3 represent modern city logistics
solutions. Each of the defined scenarios is a
complex log istics system therefore all aspects
of their application need to be analyzed for
the final decision. Ten criteria are defined
for the evaluation of scenarios, and ranking
is performed by applying MCDM model that
combines FAHP and VIKOR. According to
the defined criteria scenario Sc.2 is selected
as the most suitable for solving logistics
problems of the central city area.
Ranking of logistics system scenarios for the
CBD of Belgrade have also been solved by
other MCDM methods (Tadić and Zečević,
2009; Tadić et al., 2014b). In all cases, the
order of scenarios was the same, but the
values for the ranking of alternatives differed.
Each method has certain advantages and
disadvantages, and they are compared in order
to establish a balance bet ween the complexity
of implementation and quality of results.
Application of some other methods (e.g. ANP,
DEMATEL, ELECTR E, etc.) may result in
63
International Journal for Traffic and Transport Engineering, 2015, 5(1): 54 - 63
greater differences between the values based
on which the alternatives are being ranked,
thereby reducing the r isk of making the wrong
decisions. However, in some cases, less qual ity
solutions are acceptable, especially if there is
no change of the order of alternatives, and on
the other hand bring certain savings in time,
cost and other resources. This could be the
subject of future research.
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