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5th In tern ation al C onference
"E cono mics and M anagem ent-B ased on New Technologies"
EMoNT-2015
18-21 June 2 01 5, V rnjačk a Ba nja , Serbia
Plenary and Invitation Paper
APPLICATION OF COMBINED AHP-TOPSIS MODEL FOR DECISION
MAKING IN MANAGEMENT
v 1 2 3 4
Zeljko Stević , A sib Alihodžić , Z drav ko Božičković , Marko Vasiljević ,
Đorđo V asiljević5
University of East Sarajevo, Faculty of Transport, Doboj, BOSNIA AND HERZEGOVINA,
1 E-mail: zelj kostevic88@yahoo.com, 2 E-mail: asib.dr@gmail.com,
3 E-mail: zdravko.bozickovic@gmail.com, 4 E-mail: drmarkovasilj evic@gmail.com
5 International University of Brčko, Brčko, BOSNIA AND HERZEGOVINA,
E-mail: vasiljevic.dj @teol.net
Summary: The aim o f this study is decision making in management, i.e. the selection o f the most suitable o f
potential companies fo r the procurement o f materials. It is the procurement o f steel pipes that are used fo r the
manufacture o f pre-insulated pipes. The selection is m ade among fiv e companies based on fiv e criteria applying
the combined AHP-TOPSIS model. A very important thing in solving this type o f problem s is the importance of
certain criteria, which can greatly affect the fin al solution. The study applies the AHP method fo r the
determination o f criterion importance, and the use of TOPSIS m ethod provides a fin al solution. In determining
the weighted values o f criteria, we have taken into account the current needs and demands o f the market in
which the company, the subject o f this research, is trying to gain a competitive advantage.
Keywords: AHP, TOPSIS, procurement, criteria.
1. INTRODUCTION
The application of multi-criteria analysis is very popular, especially recently when more attention has
been paid to making the right decisions. It is used to solve different types of problems, and is widely
used in management, where certain decisions are made on the basis of multi-criteria methods. The
biggest challenge is making the right decisions that will enable efficient business, on the one hand, and
fulfill more criteria, on the other. According to Kovačić (2008), the multi-criteria analysis from a
methodological aspect is a systematic approach, and thus, methodologically, the most efficient and
most functional approach to problem solving.
To ensure the continuous manufacturing flow, it is necessary to timely obtain the required components
and materials, taking into account the optimization of costs caused by this subsystem of logistics. The
research object is a company engaged in the manufacture of pre-insulated pipes which requires the
procurement of steel.
2. LITERATURE REVIEW
Daily use of multi-criteria analysis methods has certainly contributed to the popularization of this area,
so that some of the methods, such as Analytic Hierarchy Process and TOPSIS, are used for decision
making in various fields. According to E. Triantaphyllou and S. H. Mann, the multiple-criteria
33
decision making plays an important role in solving real-life problems, and Backović and Babić (2013)
use multiple-criteria optimization for the selection of life insurance. Referring to AHP method, there
are conferences that are dedicated only to the problems resolved by this method. Decision making in
management is a very important process, which affects the efficiency of business performance, and the
use of these methods can provide a favorable solution. Regarding the procurement process, decisions
are more often made on the basis of these methods. The indicator for this are Bobar and Lalić (2013)
who made decisions in the public procurement procedure or Mandić et al. (2013), who evaluated
suppliers. The AHP method is also used in the field of information systems (Sarhan 2011). Some other
areas for the application of this method are: location problems for the selection of logistics center
location (Stević et al. 2015), a freight village (Yildirim and Onder 2014), an intermodal freight
logistics center (Kayikci 2010). In addition, there are more and more domestic publications in this area
as evidenced by Tomić et al. (2014), while some papers combine several multi-criteria analysis
techniques in order to reach a solution as in the case of Stević and Vasiljević (2013). It is often used in
the field of transport (Sivilevičius and Maskeliunaite 2010), then for decision making in relation to the
purchase of a new means of transport (Stević et al. 2012).
In addition to the method of Analytic Hierarchy Process, the TOPSIS method has also wide
application, and it is used to make certain investment decisions (Puška 2012), the evaluation and
ranking of business strategies (Đorđić 2013), location selection for a postal center (Miletić 2007), etc.
3. PROBLEM AND METHODOLOGY SETTING
To select the most suitable solution, we use a combination of multi-criteria analysis methods. To
determine the importance of criteria, we use Analytic Hierarchy Process that compares the criteria
using the Saaty Scale (Saaty 1980), while for the selection of the most acceptable solution of the set,
we use the TOPSIS method.
Table 1 shows the characteristics of potential companies and the criteria by which it is necessary to
make a decision: price per length meter, pipe length, delivery time, payment method and mode of
transportation on the basis of which it should be decided on the most suitable company to obtain steel
pipes in order to ensure the continuous manufacturing flow. The potential solutions are the companies
presented in Table 1, of which three are located in the territory of Bosnia and Herzegovina, and the
other two in the territory of Serbia.
Table 1: The characteristics of potential suppliers
Pezos Export-
Import Trgometal Metal Flex Bogner
Edelstahl Poliko
Price per length
meter [BAM/m] 78.3 88.55 89.59 91 95.5
Pipe length [m] 12 12 11.60-11.70 5.8-6.2 10-12
Delivery time
[day] immediately immediately 5-7 3 30
Payment method 100% in
advance
100% in
advance, 45
days delayed
70% in
advance, the
rest to 30
days
100% in
advance
50% in
advance and
50% prior to
delivery
Mode of
transportation without without with with without
Price per length meter is expressed in convertible marks (BAM), pipe length in meters and delivery
time in days. The payment method for all alternatives is an advance payment, with certain differences
depending on the alternatives. So, for the alternative one and four we have 100% advance payment
without a possibility of different arrangements, while for the alternative two it can be 100% in advance
or 45 days delayed providing a bank guarantee. The alternative three requests 70% in advance and the
rest to 30 days, while the alternative five offers 50% in advance and 50% prior to delivery, i.e. the
34
ability to pay in 30 days, because they need that much time to deliver the material. Referring to the
mode of transportation, the alternatives three and four provide transportation that is not charged
separately i.e. it is included in the price of materials, and in the procurement of materials for other
alternatives, transportation must be provided by Energotehika company.
4. DETERMINATION OF WEIGHT COEFFICIENTS USING THE AHP METHOD
Analytic Hierarchy Process is a method which consists of the decomposition of problems into the
hierarchy, where the target is located at the top, then criteria, sub-criteria and a set of potential
solutions (Karleuša et al. 2014). It is used extensively for decision making in management, which is
confirmed by Konstantinos (2014). According to Saaty (2008), AHP is a theory of measurement by
comparing pairs and it relies on the opinion of experts to perform the priority scales, and according to
Blagojević et al. (2012), Analytical Hierarchy Process (AHP) is a method to support the decision
making process that is based on the establishment of a hierarchy of problems and original procedure
for the evaluation of elements at the levels of hierarchy until the final synthesis determines the weight
of all elements, and as the final result, we obtain the weight of alternatives at the lowest level in
relation to the element at the highest level (main target).
In order to apply the TOPSIS method for obtaining the most suitable solution, it is necessary to
determine the significance of the criteria, i.e. their weight values. First, it is necessary to compare
criteria in order to determine priorities.
Tab e 2: T ie comparison of criteria
K1K2K3K4K5
K111/5 1/5 3 7
K251 1 5 9
K3 51 1 5 7
K4 1/3 1/5 1/5 15
K51/7 1/9 1/7 1/5 1
The comparison of the pairs of criteria was completed in relation to current needs and demands of the
market. The workers from the commercial service of Energotehnika company, which was the subject
of the research, were included in a criterion comparison process.
After the comparison of criteria, we obtained results shown in Figure 1 where we can see that the most
important are two criteria, the length of the pipe with the level of significance of 0.385, and the second
most important criterion is the time of delivery, which has slightly lower priority with the level of
significance of 0.374. The other three criteria have much lower priority than the previous two
mentioned. It is important to note that the sum of all values of the criteria must be equal to one.
0,5
0,4
0,3
0,2
0,1
0
£ j _ 0,134
r
0,078 r
-^ ■ ? * 8G lo,03
Price per Pipe Delivery Pavment Mode of
length length time method transportation
meter Figure 1: The significance of criteria
35
AHP is one of popular methods and it has the ability to identify and analyze the subjectivity of
decision-makers in the estimation and evaluation process of hierarchy elements. A man is rarely
consistent in assessing the value or relation of the quality elements in the hierarchy. AHP in a specific
way solves this problem by measuring the degree of consistency and inform decision-makers about
that. The degree of consistency regarding the comparison of criteria is 0.09, which means that the
results are valid because it is lower than 0.10 (if the results are in the range of up to 0.10, they are
considered to be valid).
5. DECISION MAKING BY THE APPLICATION OF TOPSIS METHOD
According to Ozgurler et al. (2011), TOPSIS method is a practical and useful technique for ranking
and selection of a number of determined alternatives. This method evaluates the alternatives based on
their distance from the positive ideal and negative ideal solution. "The best" is an alternative that has
the shortest distance from the positive ideal solution and the longest distance from the negative ideal
solution.
For this method, first it is required to determine the orientation of criteria, so that they need to be
minimized or maximized (Polednikova 2014). The following are the steps of the algorithm for solving
the multi-criteria tasks of TOPSIS method:X =
Initial matrix n (1)
Table 3: Initial matrix
K1K2K3K4K5
A 1 78.3 12 0 1 1
A 2 88.5 12 0 71
A3 89.6 11.6 6 4 7
A4 91 6317
A5 95.5 11 30 5 3
min max min max max
Table 3 shows the initial matrix with the values of alternatives in relation to the criteria by which it is
necessary to rank potential solutions. The first and third criterion needs to be minimized, since it is
price and delivery time, while the other criteria need to be maximized. Pipe length as the second
criteria needs to be as large as possible, and according to the market demands, the best length is 12 m.
The fourth and fifth criteria are quantified on the scale from one to nine and they should also be
maximized, for example, the aim for payment method criteria is “delayed” as longer as possible
period, while the fifth criterion is also oriented to a maximum (if potential companies, from which the
materials will be supplied, provide transport by their own vehicles which is included in the price of
materials, then the alternative tends to a maximum, taking into account the spatial distances of
alternatives).
> Step 1 - normalization of the initial matrix
M R
Rij= Xij
m
i-1
(2)
(3)
(4)
36
Table 4: Normalized initial matrix
0.394507001 0.498461987 0 0.104257207 0.095782629
0.445898718 0.498461987 0 0.729800449 0.095782629
0.451440961 0.481846587 0.19518001 0.417028828 0.6704784
0.458494726 0.249230993 0.09759001 0.104257207 0.6704784
0.481167543 0.456923488 0.97590007 0.521286035 0.287347886
Table 4 shows the normalized initial matrix that is obtained by using Equation (4). The calculation is
performed by using Excel.
> Step 2 - weighting o f the normalized matrix
llR ll ^
V = Y; w. ■ r-
j ij
(5)
(6)
Table 5: weighted normalized matrix
0.05128591 0.194400175 0 0.008340577 0.002873479
0.057966833 0.194400175 0 0.058384036 0.002873479
0.058687325 0.187920169 0.07221661 0.033362306 0.020114352
0.059604314 0.097200087 0.0361083 0.008340577 0.020114352
0.062551781 0.17820016 0.36108303 0.041702883 0.008620437
Table 5 shows the weighted normalized matrix, i.e. the values from the previous table have been
multiplied by the weighted values of the criteria in Figure 1.
> Step 3 - forming the positive ideal and negative ideal solution:
A+ - the positive ideal solution, which has all best features regarding all criteria:
A+ = max v. j e K' I i I min v {vj+ i = 1, m
is a subset of K consisting of max type criteria.
is a subset of K consisting of min type criteria.
A - the negative ideal solution, which has all worst features regarding all criteria:
(7)
j e K' | i I max v.
On the basis of the relation (7) and (8), it is formed the positive ideal and negative ideal solution.
A+ = {0.05128591; 0.194400175; 0; 0.058384036; 0.020114352}
A- = {0.062551781; 0.097200087; 0.361083027; 0.008340577; 0.002873479.
(8)
> Step 4 - calculating the distance (Euclidean distance) of each alternative from the positive ideal
and negative ideal solution
+ \ 2
Si+ - distance of an alternative from the positive ideal solution
S - = -\ 2
I (v ij - v - )
J=1
Sf - distance of an alternative from the negative ideal solution
(9)
(10)
37
Using the relation (9) and (10), the calculation was completed and the results shown in Table 6 were
obtained.
Table 6: Distances of alternatives from the positive ideal and negative ideal solution
S1+ 0.0529301 Sf 0.374106575
S2+0.018490063 S2"0.377298528
S3+0.018490063 S3"0.304322545
S4+0.077059045 S4"0.32544509
S5+0.36218874 S5"0.087789993
>Step 5 - calculating the relative closeness o f an alternative to the ideal solution:
C = — S—
i S - + S + (11)
0 < c < 1.
i (12)
On the basis of the relation (11), calculated relative closeness of alternatives to the ideal solution is as
follows: C1 = 0.876052565
C2= 0.953282981
C3= 0.797947653
C4= 0.738171649
C5= 0.195098093
y Step 6 - ranking o f alternatives:
Ranking of Q values arranged in descending order (from the highest to lowest value) corresponds to
the ranking of A^ alternatives (from the best to worst).
If an alternative tends to be one, then it is the positive ideal solution. But, if it tends to be zero, then it
is the negative ideal solution. Figure 2 shows the ranking of alternatives with the values of each.
Figure 2: Ranking of alternatives
38
6. CONCLUSION
In order to get the optimal solution, i.e. to obtain valid results that provide a specific problem solution,
in particular in the case of the selection of companies for procurement, it is necessary to fulfill and
follow specific steps in multi-criteria analysis. After all undertaken steps detailed in this paper, it has
been concluded that the final ranking of alternatives is the one given in the previous figure, which
shows that the alternative two, i.e. Trgometal company represents the best solution of the set for
material procurement. It should be noted that it is impossible to make strategic and operational
decisions that simultaneously include different criteria without multi-criteria analysis techniques,
which further emphasizes the importance of this study, in which the optimal selection of material
procurement for the observed company has been performed. Based on the above mentioned, it can be
concluded that the application of multi-criteria analysis methods leads to optimal results which are
applicable in practice.
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