ORIGINAL RESEARCH
The multi-objective decision making methods based
on MULTIMOORA and MOOSRA for the laptop selection
problem
Esra Aytac¸ Adalı
1
•
Ays¸egu
¨
l Tus¸Is¸ık
1
Received: 2 May 2016 / Accepted: 30 September 2016 / Published online: 11 October 2016
Ó The Author(s) 2016. This article is published with open access at Springerlink.com
Abstract A decision making process requires the valu es of
conflicting objectives for alternatives and the selection of
the best alternative according to the needs of decision
makers. Multi-objective optimization methods may provide
solution for this selection. In this paper it is aimed to
present the laptop selection problem based on MOORA
plus full multiplicative form (MULTIMOORA) and multi-
objective optimization on the basis of simple ratio analysis
(MOOSRA) which are relatively new multi-objective
optimization methods. The novelty of this paper is solving
this problem with the MULTIMOORA and MOOSRA
methods for the first time.
Keywords Multi-obj ective decision making
MULTIMOORA method MOOSRA method Laptop
selection
Introduction
Today many people cannot imagine their life without
computers. This situation is the proof that the computers
play an important role in the world. Because the computers
make the people’s lives easier and more com fortable in
terms of searching and storing data, crea ting tables and
diagrams, and editing pictures, audio, and video, etc. At the
same time people communicate with the millions of people
while they are in the different points of the wor ld. Personal
computers are generally classified by their sizes and cases.
Laptops are one of the personal computer types. The
people or organizations prefer laptops because of their
ability, portability, and mobility (Srichetta and Thurachon
2012). In the market, there are numerous laptops with
different brands and features. They als o seem same to each
other. So the selection of an effective laptop that suits the
needs of buyers is essential but also the difficult problem.
Like laptop selection problem, many problems in engi-
neering, industry, and other fields involve the simultaneous
optimization of several conflicting objectives. These
problems are called multi-objective optimization problems
(Jaimes et al. 2011). Maximizing profit and minimizing the
cost of a product; maximizing performance and minimizing
fuel consumption of a vehicle are the typical examples of
multi-objective optimization problems (Chakraborty 2011).
The objectives of these problems are measured in different
units. One of the approaches to solve multi objective
optimization problems is multi-criteria decision making
(MCDM) (Jaimes et al. 2011). It requires using different
methods which incorporate the conflicting criteria and help
a decision maker for identifying the best alternative. In the
literature, Erpolat and Cinemre (2011) proposed a hybrid
approach based on data envelopment analysis (DEA) and
analytic hierarchy process (AHP). They compared various
laptop alternatives with two different DEA models as
unrestricted and restricted on weights. Ertug
˘
rul and Kar-
akas¸og
˘
lu (2010) proposed the usage of Elimination Et
Choix Traduisant la Realite
´
(ELECTRE) and fuzzy ana-
lytic hierarchy process (FAHP) for ranking computers.
Miranda Lakshmi et al. (2015) compared the laptop alter-
natives with the Technique for Order Preference by Simi-
larity to Ideal Solution (TOPSIS) method. Pekkaya and
Aktogan (2014) made laptop selection with TOPSIS and
& Esra Aytac¸ Adalı
eaytac@pamukkale.edu.tr
Ays¸egu
¨
l Tus¸Is¸ık
atus@pamukkale.edu.tr
1
Department of Business Administration, Pamukkale
University, 20070 Denizli, Turkey
123
J Ind Eng Int (2017) 13:229–237
DOI 10.1007/s40092-016-0175-5
VIKOR methods. Srichetta and Thurachon (2012) applied
FAHP for finding the relative importance of the decision
criteria and selecting the best notebook computers. Finally,
the literature shows that many authors have handled laptop
selection problem but none of them tried to solve this
problem with multi objective optimization methods. In this
paper, laptop selection problem is solved with the multi-
objective optimization by ratio analysis plus the full mul-
tiplicative form (MULTIMOORA) and multi-objective
optimization on the basis of simple ratio analysis
(MOOSRA) methods, which are multi-objective opti-
mization methods. MULTIMOORA method summarizes
MOORA method, includi ng ratio system, reference point,
and the full multiplicative form whereas MOOSRA method
calculates the simple ratio of beneficial and non-beneficial
criteria during decision making process (Balezentiene et al.
2013; Kumar and Ray 2015). A weight is assigned to each
criterion according to their importance given by the deci-
sion maker. The pairwise comparison matrix of the AHP
method is employed for the weight determin ation and
finally laptop alternatives are ranked by MULTIMOORA
and MOOSRA methods.
The rest of this paper is organized as follows: Firstly the
methodological backgrounds of the MULTIMOORA and
MOOSRA methods are provi ded, respectively. Then the
applications of these methods are demonstrated with the
laptop selection of a company. At last, the results of the
applications are presented and recommendations for the
future studies are discussed.
The MULTIMOORA method
The MULTIMOORA method rose from the MOORA
method. Brauers and Zavadskas (2010)addedthefull
multiplicative form to the MOORA then the new method
was called MULTIMOORA. The MOORA method is
one of the multi objective optimization methods and it
was first developed by Brauers and Zavadskas (2006). It
requires a matrix of responses of the alternatives to the
objectives. Then a ratio system is developed in which
each response of an alternative on an objective is com-
pared to a denominator, which is the representative f or
all alternatives concerning that objective. There are two
different methods under the name of the MOORA as the
ratio system and the reference point approaches (Brauers
2013). In the literature, the MOORA method has been
applied s uccessfully to many decision problems. Brauers
and Zavadskas (2006) applied the MOORA method to
the privatization in a transition economy. Brauers et al.
(2008a) ranked the contractors with the MOORA
method. Brauers et al. (2008b) evaluat ed the road design
alternatives and selected the best road design alternative
with the MOORA method. Chakraborty (2011)presented
the solutions of the problems in manufacturing envi-
ronment. Gadakh (2011) selected suitable milling pro-
cess parameters in different milling processes. El-
Santawy and El-Dean (2012) combine d the MOORA
method with the standard deviation weight m ethod. They
presented an example of consulti ng firm selection.
Stanujkic et al. (2012a)proposedonlygreyextensionof
the ratio system of the MOORA method whereas
Stanujkic et al. (2012b) proposed the grey extensions of
the ratio system and the reference point approaches of
the MOORA method. Stanujkic et al. (2013)rankedthe
Serbian banks with SAW, ARAS, COPRAS, MOORA,
GRA, CP, VIKOR, and TOPSIS methods. Brauers
(2013) evaluated the projects of seaport planning.
O
¨
zdag
˘
og
˘
lu (2014) investigated the effects of different
normalization m ethods in MOORA method. Adhikary
and Kundu (2014) evaluated and selected the small
hydropower project alternatives with the weight ed pro-
duct and MOORA methods. Achebo and Odinikuku
(2015) used the standard deviation and MOORA method
to optimize the wel ding process paramet ers for gas m etal
arc welding of mild steel plates. Madic
´
et al . (2015)
solved the complex non-conven tion al machining p r o-
cesses selection with the MOOR A met hod. In the liter-
ature some papers integrated t he MOORA method and
fuzzy set theory then the fuzzy MOORA method was
applied for the selection of the ERP systems (Karande
and Chakraborty 2012a), the supplier and warehouse
locations ( Dey et al. 2012), the manufacturing systems
(Mandal and Sarkar 2012
), the grinding circuits designs
(Stanujkic 2014), the suppliers (Seema et al. 2014), the
cutting-machines (Vatansever and Kazanc¸og
˘
lu 2014),
and the administrators of vocational schools within
universities (O
¨
zbek 2015).
The MULTIMOORA method also found wide applica-
tion areas like the MOORA method. Brauers (2002)
applied the MULTIMOORA method to rank the fighter
planes. Kracka et al. (2010) presented the MOORA and
MULTIMOORA methods for solving the energy heating
loss problems in buildings. Brauers (2012) used the
MULTIMOORA method for the project evaluation in a
country with controlled market economy. Karande and
Chakraborty (2012b) solved four real time material selec-
tion problems with the MULTIMOORA method. Streimi-
kiene and Balezentis (2013) applied the MULTIMOORA
method for the prioritization of the climate change. Brauers
and Zavadskas (2012) presented the robustness of the
MULTIMOORA method with an example. Aksoy et al.
(2015) evaluated the performances of eight sub companies,
operated by Turkish Coal Enterprises using the AHP-based
MULTIMOORA and COPRAS methods. Lazauskas et al.
(2015) applied the AHP, ARAS, MOORA, and
230 J Ind Eng Int (2017) 13:229–237
123
MULTIMOORA methods for unfinished building solu-
tions. Brauers et al. (2011) proposed first fuzzy extension
of the MULTIMOORA method and used the fuzzy number
theory in all three parts of the MULTIMOORA method.
Then, the fuzzy MULTIMOORA method was used for
forming a multi-criteria decision making framework for the
prioritization of energy crops (Balezentiene et al. 2013),
clearing of oil palm plantations (Hamdani and Mustofa
2015), and the selection of personnel (Balezentis et al.
2012) and student (Deliktas¸ and U
¨
stu
¨
n 2015).
The general overview of the MULTIMOORA is shown
in Fig. 1 (Brauers and Zavadskas 2012). The application
steps of the ratio system, the reference point, and the full
multiplicative form, which are the main parts of MULTI-
MOORA, are presented in the following (Brauers and
Zavadskas 2006; Brauers 2002; Kracka et al. 2010 ).
The ratio system part of MOORA method
Step 1: The first step of the MOORA method is con-
structing the decision matrix of the problem. The criteria
(objectives) and alternatives are listed in the column and
row of the decision matrix, respectively. The decision
matrix shows the performance of different alternatives with
respect to the various criteria.
X ¼ x
ij
mxn
¼
x
11
x
12
x
1n
x
21
x
22
x
2n
.
.
.
.
.
.
.
.
.
.
.
.
x
m1
x
m2
x
mn
2
6
6
6
4
3
7
7
7
5
ð1Þ
x
ij
presents the performance value of ith alternative on jth
criterion, m and n are the numbers of alternatives and
criteria, respectively.
Step 2: Each performance value of an alternative on a
criterion against the other alternative performances on that
criterion is computed as:
x
ij
¼
x
ij
ffiffiffiffiffiffiffiffiffiffiffi
P
m
i¼1
x
2
ij
s
i ¼ 1; 2; ...; m and j ¼ 1; 2; ...; n ð2Þ
x
ij
is a dimensionless number between [0,1] and the nor-
malized performance of ith alternative on jth criterion.
Step 3: Normalized performance values of beneficial
criteria are added. Then, the same procedure is repeated for
the non-beneficial criteria. Finally, the sums for non-ben-
eficial criteria are subtracted from the sums for beneficial
criteria as seen Eq. (3). The result is the overall perfor-
mance score of each alternative ( y
i
).
y
i
¼
X
g
j¼1
x
ij
X
n
j¼gþ1
x
ij
ð3Þ
In this formula, g and (n - g) are the number of criteria
to be maximized and minimized, respectively. Sometimes,
decision makers want to give more importance to a crite-
rion than the others. In this situation, Eq. (3) is reformu-
lated by considering the weights of criteria as (Chakraborty
2011):
y
i
¼
X
g
j¼1
w
j
x
ij
X
n
j¼gþ1
w
j
x
ij
ð4Þ
w
j
is the weight of jth criterion (significance coefficient)
and may be derived from weighting methods like the AHP
or entropy methods (Madic
´
et al. 2015). In this p aper,
criterion weights are derived from the AHP method
because of its simplicity. More detailed information about
The full
multiplicative
form
The reference
point approach
Raw data
The ratio system
The MOORA
method
The MULTIMOORA method
Matrix of responses
X
ij
obj.1 obj.2….obj.i…obj.n
Alternative 1 x x………x………x
Alternative 2 x x………x………x
Alternative j x x………x………x
Alternative m x x………x………x
Fig. 1 The general overview of the MULTIMOORA method (Brauers and Zavadskas 2012)
J Ind Eng Int (2017) 13:229–237 231
123
the procedure of the AHP method is to be found in the
paper of Saaty (1980).
Step 4: Finall y, the alternatives are ranked in descending
order of y
i
values. For an alternative, the more y
i
gives the
higher rank. Obtaining the ranking of the alternatives ter-
minates the ratio system part of the MOORA method.
The reference point part of MOORA method
The reference point approach uses the normalized per-
formance of ith alternative on jth criterion which is
calculated by Eq. (2). A maximum criterion reference
point is determined among normalized perfo rmances and
this point is more realistic and non-subjective as the
coordinates (r
j
) (Brauers et al. 2008a). Brauers and
Zavadskas (2006, 2009) and Brauers et al. (2008a)
emphasized that the Tchebycheff Min–Max metric is the
most appropriate for the reference point approach and
formulated as:
min
i
max
j
r
j
x
ij
ð5Þ
In this formula, x
ij
is the normalized perform ance of ith
alternative on jth criterion. r
j
is the jth coordinate of the
reference point, i.e., the most desirable performances of all
alternatives with respect to jth criterion. For determining r
j
,
Eq. (6) may be used (Stanujkic et al. 2012a):
r
j
max
i
x
ij
for criteria to be maximized
min
i
x
ij
for criteria to be minimized
(
ð6Þ
If the decision makers want to give more importance to
a criterion than the others, Eq. (5) is reformulated by
considering weights of criteria as:
min
i
max
j
w
j
r
j
w
j
x
ij
ð7Þ
Finally, the alternatives are ranked and the best alter-
native is chosen with the minimum total deviation from the
reference points (Karande and Chakraborty 2012b).
The full multiplicative form
The full multiplicative form of multipl e criteria consists
both maximization and minimization of a purely multi-
plicative utility function. It was first developed by Miller
and Starr (1969). The main characteristics of this form are
being nonlinear, non-additive, and not using attribute
weights (Kracka et al. 2010). Overall utility of the ith
alternative (U
i
) is computed as:
U
i
¼
Y
n
j¼1
x
ij
i ¼ 1; 2; ...; m and j ¼ 1; 2; ...; n ð8Þ
In this formula, m and n are the numbers of alternatives
and criteria, respectively, and x
ij
is the performance of ith
alternative on the jth objective. The overall utilities are
obtained by the multiplication of different units of mea-
surement and become dimensionless. If the decision mak-
ers want to combine the minimization problem with the
maximization of other criteria then Eq. (8) becomes
Eq. (9) (Brauers and Zavadskas 2012 ):
U
i
¼
A
i
B
i
ð9Þ
In this formula A
i
and B
i
are found as A
i
¼
Q
g
j¼1
x
ij
and
B
i
¼
Q
n
j¼gþ1
x
ij
. g and (n - g) are the number of criteria to
be maximized and minimized, respectively (Brauers 2012).
If x
ij
equals 0 then withdrawal of that criteri on from the
decision matrix was suggested by Brauers (2002), because
taking 0 value means the absence of a particular criterion in
the decision matrix (Karande and Chakraborty 2012b).
The MOOSRA method
The MOOSRA method is one of the multi objective opti-
mization methods. If the MOOSRA method is compared to
the MOORA method, the negative performance scores in
the MOORA method do not appear and the MOOSRA
method is less sensitive to large variation in the values of
the criteria (Jagadish and Ray 2014). It was used for
forming a multi-criteria decision making framework for
obtaining the optimum cutting parameters on surface
roughness (Bhowmik 2014), selecting the optimum cutting
fluid for a gear hobbing process among three types of
cutting fluid (Jagadish and Ray 2014), selecting material
(Kumar and Ray 2015), and non-traditional machine
(Sarkar et al. 2015 ).
The application steps of MOOSRA method are similar
to the MOORA method. Namely, the first step is con-
structing the decision matrix of the problem and the second
step is the normalization of the decision matrix. While
calculating the overall performance score of each alterna-
tive (y
i
), the MOOSRA method uses simple ratio of the
sum of normalized performance values for beneficial cri-
teria to the sum of normalized performance values for non-
beneficial criteria. Then formula becomes as (Kumar and
Ray 2015):
y
i
¼
P
g
j¼1
x
ij
P
n
j¼gþ1
x
ij
ð10Þ
In this formula, g and (n - g) are the number of criteria
to be maximized and minimized, respectively. When the
weights of criteria are considered, Eq. (4) becomes Eq . (5)
as:
232 J Ind Eng Int (2017) 13:229–237
123
y
i
¼
P
g
j¼1
w
j
x
ij
P
n
j¼gþ1
w
j
x
ij
ð11Þ
w
j
is the weight of jth criterion. Ranking of the alternatives
is obtained according to the overall performance score of
each alternative (y
i
). The alternative with the highest
overall performance score is the best (Jagadish and Ray
2014).
Application
To demonstrate the applicability of the MULTIMOORA
and MOOSRA methods in solving multi-objective decision
making problems, real case study is considered. The case
study is associated with the supermarket which is the
member of a supermarket chain. The supermarket man-
agement wants to purchase the laptops for their adminis-
trative offices. The purchasing department is responsible
from this task namely identifying the alternatives and
selecting the best laptop. There are three employees, in
other words, three decision mak ers, in the purchasing
department. First of all, they determine the criteria
according to the needs of the company. The criteria are
processor speed (C
1
) (in Ghz), cache memory (C
2
) (in
MB), storage (C
3
) (in GB), display card memory (C
4
) (in
GB), memory (RAM) (in GB) (C
5
), screen resolution (C
6
)
[value judgment on a scale of 1–3; 1: the worst
(1366 9 768 pixels), 2: medium (1600 9 900 pixels), 3:
the best (1920 9 1080 pixels)], screen size (C
7
) (in
inches), brand reliability (C
8
) (value judgment on a scale of
1–10; 1: the worst and 10: the best), weight (C
9
) (in kg),
and cost (C
10
) (in Turki sh Liras). The first eight criteria are
beneficial whereas the last two ones are non-beneficial.
Then seven laptop alternatives are determined. Their
common features are running i7 processors and having
2 year warranty. Necessary data are collected from www.
vatanbilgisayar.com and shown in Table 1. Table 1 shows
the decision matrix of the problem which summarizes the
performance of each alternative with respect to each
criterion. Before applying MULTIMOORA and MOOSRA
methods, pairwise comparison matrix between criteria is
constructed and shown in Table 3. While comparing the
alternatives, Saat y’s nine-point scale shown in Table 2 is
adopted. The consistency ratio (CR) is calculated as 0.032.
As a result of AHP method, criteria weights are shown in
the last column of Table 3.
The application of the MULTIMOORA method
For the ratio system of the MOORA method, first, the
decision matrix is normalized using Eq. (2) as seen in
Table 4. The normalized decision matrix is weighted and
shown in Table 5.
Table 6 shows the overall performanc e and the rankings
of the alternatives. A
3
is the best laptop alternative
according to the ratio system part of MOORA.
The reference point approach uses the weighted nor-
malized decision matrix shown in Table 5 as an initial step.
Then reference points are determined among normalized
and weighted performances and stated last row of the
Table 7.
Table 7 presents the deviations from the maximum and
minimum values for the beneficial and non-beneficial cri-
teria, respectively. For each alternative, maximum devia-
tion among them is determined and maximum deviation is
ranked in descending order. Finally, A
3
is the best laptop
alternative according to the reference point part of
MOORA.
For the full multiplicative form, first, the initial decision
matrix shown in Table 1 is taken into consideration. The
degree of utility value of each alternative is computed by
taking the beneficial and non-beneficial values on the
numerator and denominator, respectively. The necessary
operations are shown in Table 8. According to the full
multiplicative form, A
3
is the best laptop alternative.
Finally, the overall ranks are obtained and shown in
Table 9. MULTIMOORA is the summary of three distinct
approaches as stated by Brauers (2012).
Table 1 Decision matrix of the laptop selection problem
C
1
C
2
C
3
C
4
C
5
C
6
C
7
C
8
C
9
C
10
A
1
3.5 6 1256 4 16 3 17.3 8 2.82 4100
A
2
3.1 4 1000 2 8 1 15.6 5 3.08 3800
A
3
3.6 6 2000 4 16 3 17.3 5 2.9 4000
A
4
3 4 1000 2 8 2 17.3 5 2.6 3500
A
5
3.3 6 1008 4 12 3 15.6 8 2.3 3800
A
6
3.6 6 1000 2 16 3 15.6 5 2.8 4000
A
7
3.5 6 1256 2 16 1 15.6 6 2.9 4000
Table 2 Saaty’s scale
Degree
preferences
Verbal judgment of preference
1 Equal importance
3 Weak importance of one over another
5 Essential or strong importance
7 Demonstrated importance
9 Absolute importance
2, 4, 6, 8 Intermediate preferences between the two
judgments
J Ind Eng Int (2017) 13:229–237 233
123