Description
The fuzzy Delphi method, analytic network process (ANP), and technique for order preference by similarity
to ideal solution (TOPSIS) are integrated in this paper to help Taiwanese service apartments to
effectively select the optimal locations. The fuzzy Delphi method, which can lead to better criteria selection,
is used to modify previous studies to construct the hierarchy. Considering the interdependence
among the selection criteria in the hierarchy, ANP is then used to obtain the weights of the criteria. To
avoid calculation and additional pairwise comparisons of ANP, TOPSIS is used to rank the alternatives.
According to the hierarchy based on three perspectives and 12 important criteria, optimal locations for
Taiwanese service apartments can be more effectively selected. Moreover, by integrating the fuzzy Delphi
method, ANP, and TOPSIS, this study can make better decisions for optimal locations. To illustrate how
the fuzzy Delphi method, ANP, and TOPSIS are applied in the location selection problem, their application
to a real case is also performed.
An ANP based TOPSIS approach for Taiwanese service apartment location
selection
Kuei-Lun Chang
a, *
, Sen-Kuei Liao
b
, Tzeng-Wei Tseng
c
, Chi-Yi Liao
d
a
Department of Communications Management, Ming Chuan University, 250, Zhong Shan North Road, Section 5, Taipei, Taiwan, ROC
b
Department of Business Management, National Taipei University of Technology, 1, Zhong Xiao East Road, Section 3, Taipei, Taiwan, ROC
c
Graduate Institute of Industrial and Business Management, National Taipei University of Technology, 1, Zhong Xiao East Road, Section 3, Taipei, Taiwan, ROC
d
Department of Mass Communication, Chinese Culture University, 55, Hwa Kang Road, Yang Ming Shan, Taipei, Taiwan, ROC
a r t i c l e i n f o
Article history:
Received 28 December 2012
Accepted 4 October 2013
Available online 23 March 2015
Keywords:
Analytic network process
Fuzzy Delphi method
Service apartment
Technique for order preference by similarity
to ideal solution
a b s t r a c t
The fuzzy Delphi method, analytic network process (ANP), and technique for order preference by sim-
ilarity to ideal solution (TOPSIS) are integrated in this paper to help Taiwanese service apartments to
effectively select the optimal locations. The fuzzy Delphi method, which can lead to better criteria se-
lection, is used to modify previous studies to construct the hierarchy. Considering the interdependence
among the selection criteria in the hierarchy, ANP is then used to obtain the weights of the criteria. To
avoid calculation and additional pairwise comparisons of ANP, TOPSIS is used to rank the alternatives.
According to the hierarchy based on three perspectives and 12 important criteria, optimal locations for
Taiwanese service apartments can be more effectively selected. Moreover, by integrating the fuzzy Delphi
method, ANP, and TOPSIS, this study can make better decisions for optimal locations. To illustrate how
the fuzzy Delphi method, ANP, and TOPSIS are applied in the location selection problem, their application
to a real case is also performed.
© 2015, College of Management, National Cheng Kung University. Production and hosting by Elsevier
Taiwan LLC. All rights reserved.
1. Introduction
Location decisions have attracted much attention from the ac-
ademic and business communities (Chou, Hsu, & Chen, 2008). The
decision to select a location has become increasingly vital (Kapoor,
Tak, & Sharma, 2008). For the hotel industry, optimal location not
only helps increase market share and pro?t, but may also enhance
the convenience of passenger lodging. Satisfying customer needs or
enhancing the convenience of customer lodging will directly in-
crease customer loyalty (Chou et al., 2008). In recent years, service
apartments providing long-term hotel services for business per-
sons have become a growing industry in Taiwan. The service
apartment is a good choice for a comfortable, homelike, and
economical residence. In order to decrease the cost to the business
person of ?nding accommodations and to improve operating
performance, location selection has become one of the most
important issues for service apartments.
Hsu and Yang (2000) applied a triangular fuzzy number to
encompass expert opinions and establish a fuzzy Delphi method.
The maximum and minimumvalue of expert opinions are taken as
the two terminal points of triangular fuzzy numbers, and the
geometric mean is taken as the membership degree of triangular
fuzzy numbers to derive the statistical unbiased effect and avoid
the impact of extreme values. The advantage of the fuzzy Delphi
method is its simplicity. All of the expert opinions can be
encompassed in one investigation. Hence, this method can create
more effective criteria selection (Ma, Shao, Ma, & Ye, 2011). ANP
produces more accurate weighting of criteria, since it enables
consideration of the dependence among factors in decision-
making problems. Unfortunately, ANP requires many pairwise
comparisons depending on the number and interdependence of
factors and alternatives. This disadvantage of ANP is eliminated via
the use of the (TOPSIS). Thus, the selection process is shortened
(Da gdeviren, 2010).
By combining the fuzzy Delphi method, ANP, and TOPSIS, this
study can make better decisions in selecting locations for Taiwa-
nese service apartments within a shorter time, by considering the
* Corresponding author. Department of Communications Management, Ming
Chuan University, 250, Zhong Shan North Road, Section 5, Taipei, Taiwan, ROC.
E-mail address: [email protected] (K.-L. Chang).
Peer review under responsibility of College of Management, National Cheng
Kung University.
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Asia Paci?c Management Review 20 (2015) 49e55
dependence among factors, which distinguishes this study from
others in the literature. We ?rst present a literature review of the
location selection. Next, the ANP and TOPSIS as selection tools are
described. The integrated method within the context of selecting
the optimal location for a Taiwanese service apartment is shown in
Section 5. The conclusion is given in Section 6.
2. Location selection
Many approaches for location selection have been developed.
Cheng, Li, and Yu (2007) used geographic information systems to
select a location for shopping malls. Wu, Lin, and Chen (2007)
used the modi?ed Delphi method, analytic hierarchy process
(AHP), and sensitivity analysis, to select the optimal location for a
regional hospital in Taiwan. Anagnostopoulos, Doukas, and
Psarras (2008) proposed a fuzzy multicriteria algorithm to
solve the distribution center location selection problem. Chou,
Chang, and Shen (2008) present a new fuzzy multiple attri-
butes decision-making method to answer facility location se-
lection problems. Chou et al. (2008) apply fuzzy AHP to select
international tourist hotel locations. Kapoor et al. (2008) used
fuzzy cluster analysis for the location selection problem. Tabari,
Kaboli, Aryanezhad, Shahanaghi, and Siadat (2008) selected the
optimal location based on the concept of fuzzy AHP. Guneri,
Cengiz, and Seker (2009) applied fuzzy ANP to select a suitable
location for a shipyard. Hsu (2010) utilized ANP to select the
optimal location for an international business of?ce center in
China. Kayikci (2010) combined fuzzy AHP and arti?cial neural
networks for location selection. Lin and Tsai (2010) integrated
ANP and TOPSIS to select locations for foreign direct investments
in new hospitals in China.
€
Onüt, Efendigil, and Kara (2010) used
fuzzy AHP and fuzzy TOPSIS to select a shopping center site.
Bottero and Ferretti (2011) applied ANP to rank sites for the
location of a waste incinerator plant for the Province of Torino in
Italy. Li, Liu, and Chen (2011) selected a logistic center location on
the basis of the axiomatic fuzzy set (AFS) clustering approach
and TOPSIS. Athawale, Chatterjee, and Chakraborty (2012)
applied the preference ranking organization method for enrich-
ment evaluation (PROMETHEE II) to solve facility location se-
lection problems. Choudhary and Shankar (2012) used fuzzy AHP
and TOPSIS to select locations for a thermal power plant.
Ishizaka, Nemery, and Lidouh (2013) selected the location of
casinos in the Greater London region using the weighted sum
method, TOPSIS, and PROMETHEE.
Several previous studies treat the selection criteria as inde-
pendent. After discussions with senior executives, we ?nd that
selection criteria are not independent in actual selection situations.
To address this issue, this paper combines ANP with TOPSIS to make
better decisions in selecting optimal locations for Taiwanese service
apartments. ANP, which captures the interdependence, is applied to
generate the weights of the selection criteria. TOPSIS is used to rank
the alternatives.
3. ANP
ANP (Saaty, 1996) is a comprehensive decision-making tech-
nique that captures the outcome of dependency between criteria.
AHP serves as a starting point for ANP. Priorities are established in
the same way that they are in AHP using pairwise comparisons. The
weight assigned to each perspective and criterion may be esti-
mated either from the data, or subjectively by decision makers. It is
desirable to measure the consistency of the decision makers'
judgment. AHP provides a measure through the consistency ratio
(C.R.) which is an indicator of the reliability of the model. This ratio
is designed in such a way that the values of the ratio exceeding 0.1
indicate inconsistent judgment (Saaty, 1980). ANP comprises four
major steps (Saaty, 1996).
Step 1. Construct hierarchy and structure problem
The problem should be clearly stated and hierarchy structure
constructed. The hierarchy can be determined by the decision
makers' opinion via brainstorming or other appropriate methods,
such as literature reviews.
Step 2. Determine the perspectives and criteria weights
In this step, the decision-making committee makes a series of
pairwise comparisons to establish the relative importance of per-
spectives and criteria. In these comparisons, a 1e9 scale is applied to
compare two perspectives or criteria according to the interdepen-
dency of perspectives and criteria. The eigenvector of the observ-
able pairwise comparison matrix provides the perspectives and
criteria weights at this level, which will be used in the supermatrix.
Step 3. Construct and solve the supermatrix
The perspectives and criteria weights derived from Step 2 are
used to obtain the column of the supermatrix. Finally, the super-
matrix will be steady by multiplying the supermatrix by itself until
the row values of the supermatrix converge to the same value for
each column of the matrix. We call that the limiting matrix.
Step 4. Select the best alternative
Based on the limiting matrix and the weights of alternatives
with respect to the criteria, we can aggregate the total weight of
each alternative. We rank the alternatives according to their total
weights.
In the literature on the application of ANP, Ertay, Büyük€ ozkan,
Kahraman, and Ruan (2005) tried to implement quality function
deployment (QFD) under a fuzzy environment. Moreover, ANP is
used to prioritize design requirements. Kahraman, Ertay, and
Büyük€ ozkan (2006) combined ANP and a fuzzy logic approach to
incorporate the customer needs and the product technical re-
quirements systematically into the product design phase in QFD.
Chang, Wey, and Tseng (2009) used the fuzzy Delphi method, ANP,
and zero one goal programming to select revitalization strategy
projects for the historic Alishan forest railway. Chen, Huang, and
Cheng (2009) used ANP and the balanced scorecard (BSC) for
measuring knowledge management (KM) performance. Guneri
et al. (2009) applied fuzzy ANP to select a suitable location for a
shipyard. Hsu and Hu (2009) used ANP to select suppliers by adding
the concept of hazardous substance management. Lee, Tzeng, Guan,
Chien, and Huang (2009) established an investment decision model
based on the Gordon model. ANP is applied to generate the weight
of criteria because of interrelations and self-feedback relationships
among the criteria. Liao and Chang (2009a) used ANP to measure
the performance of hospitals. Liao and Chang (2009b) applied ANP
to select television sportscasters for the Olympic Games. Liao and
Chang (2009c) combined ANP with BSC to select the key capabil-
ities of Taiwanese TV shopping companies. Liao and Chang (2009d)
applied ANP to choose public relations personnel for Taiwanese
hospitals. Lin (2009) combined ANP with fuzzy preference pro-
gramming to select suppliers and then allocated orders among the
selected suppliers using multi-objective linear programming. Oh,
Suh, Hong, and Hwang (2009) applied ANP and BSC to evaluate
the feasibility of a newtelecomservice. They point out that ANP can
obtain more realistic results. Wu, Lin, and Peng (2009) combined
ANP with conjoint analysis to simplify ANP for hospital
K.-L. Chang et al. / Asia Paci?c Management Review 20 (2015) 49e55 50
policymakers making appropriate management policies. Aznar,
Ferrís-O~ nate, and Guijarro (2010) used ANP for property pricing.
Chen and Chen (2010) applied decision-making trial and evaluation
laboratory (DEMATEL), fuzzy ANP, and TOPSIS to develop a new
innovation support system. Da gdeviren (2010) employed ANP and
modi?ed TOPSIS to select personnel. Hsu (2010) utilized ANP to
select optimal location for an international business of?ce center in
China. Liao and Chang (2010) combined ANP with BSC for
measuring the managerial performance of TV companies. Liao,
Chang, and Tseng (2010) selected program suppliers for TV com-
panies using ANP. Lin and Tsai (2010) integrated ANP and TOPSIS to
select locations for foreign direct investments in new hospitals in
China. Tseng (2010) used ANP, DEMATEL, and fuzzy set theory to
obtain the relative weight of BSC factors for a university perfor-
mance measurement. Yang, Hui, Leung, and Chen (2010) applied
ANP to select logistics service providers for air cargo. Yüksel and
Da gdeviren (2010) integrated fuzzy ANP and BSC to measure the
performance of a manufacturing ?rminTurkey. Bottero and Ferretti
(2011) applied ANP to rank sites for the location of a waste incin-
erator plant for the Province of Torino in Italy. Ertay, Akyol, and Araz
(2011) applied fuzzy ANP to rank engineering characteristics for
implementing QFD. Liao, Chen, Chang, and Tseng (2011) used ANP
and TOPSIS for assessing the performance of Taiwanese tour guides.
Fazli and Jafari (2012) applied DEMATEL, ANP, and VlseKriter-
ijumska Optimizacija I Kompromisno Resenje (VIKOR) to select the
best alternative for investment in stock exchange. Hu, Wang, and
Hung (2012a) utilized ANP to evaluate e-service quality of micro-
blogging. Hu, Wang, and Wang (2012b) used ANP to evaluate the
performance of Taiwan homestay industry.
ANP, widely applied in decision making, is more accurate and
feasible under interdependent situations. However, after discus-
sions with senior executives, we found that the selection criteria for
locations are interrelated. ANP, which captures the interdepen-
dence, appears to be one of the more feasible and accurate solu-
tions for generating the weights of the selection criteria.
4. TOPSIS
TOPSIS, proposed by Hwang and Yoon (1981), enables decision
makers to determine the positive ideal solution (A
*
) and negative
ideal solution (A
À
). On the basis of TOPSIS, the chosen alternative
should have the shortest distance from the positive ideal solution
and the farthest from the negative ideal solution. The computing
process is presented as follows.
Step 1. Construct the standardized appraisal matrix
r
ij
¼
x
ij
????????????????
m
i¼1
x
2
ij
_ (1)
where i indicates the alternatives, j denotes the selection criteria,
and x
ij
means the i alternative under the j criterion to be assessed.
Step 2. Construct the weighted standardized appraisal matrix
Weights of selection criteria, w ¼ ðw
1
; w
2
; :::; w
n
Þ, multiplied by
the standardized appraisal matrix, may be expressed as:
v ¼
_
¸
¸
_
v
11
v
12
… v
1n
v
21
v
22
… v
2n
« « / «
v
m1
v
m2
/ v
nm
_
¸
¸
_
¼
_
¸
¸
_
w
1
r
11
w
2
r
12
… w
n
r
1n
w
1
r
21
w
2
r
22
… w
n
r
2n
« « / «
w
1
r
m1
w
2
r
m2
/ w
n
r
mn
_
¸
¸
_
(2)
Step 3. Identify the positive ideal solution and negative ideal
solution
A
*
¼
_
v
*
1
; v
*
2
; :::; v
*
j
; :::; v
*
n
_
¼
__
max
i
v
ij
jj2J
_
ji ¼ 1; :::; m
_
; (3)
A
À
¼
_
v
À
1
; v
À
2
; :::; v
À
j
; :::; v
À
n
_
¼
__
min
i
v
ij
jj2J
_
ji ¼ 1; :::; m
_
:
Step 4. Calculate the Euclidean distance between the positive ideal
solution (S
*
i
) and negative ideal solution (S
À
i
) for each alternative
S
*
i
¼
???????????????????????????????
n
j¼1
_
v
ij
À v
*
i
_
2
¸
¸
¸
_
; i ¼ 1; :::; m; (4)
S
À
i
¼
????????????????????????????????
n
j¼1
_
v
ij
À v
À
i
_
2
¸
¸
¸
_
; i ¼ 1; :::; m:
Step 5. Calculate the relative closeness to the positive ideal solution
for each alternative
C
*
i
¼
S
À
i
S
*
i
þ S
À
i
(5)
An alternative A
i
is closer to A
*
and farther from A
À
asC
*
i
approaches 1.
Step 6. Rank the preference order by C
*
i
According to C
*
i
, larger index values indicate better performance
of the alternatives.
TOPSIS has been widely explored in the literature. Da gdeviren,
Yavuz, and K?l?nç (2009) used AHP and fuzzy TOPSIS to select
weapons. Gumus (2009) employed fuzzy AHP and TOPSIS to eval-
uate hazardous transportation ?rms. Saremi, Mousavi, and Sanayei
(2009) applied fuzzy TOPSIS to select an external total quality
management (TQM) consultant. Sun and Lin (2009) used fuzzy
TOPSIS to generate the weight of each criterion and rank four
shopping websites. Wang, Cheng, and Huang (2009) developed a
fuzzy hierarchical TOPSIS that improves the idea of Chen (2000) for
selecting a lithium-ion battery protection integrated circuit (LI-
BPIC) supplier. Chen and Chen (2010) applied DEMATEL, fuzzy ANP,
and TOPSIS to develop a new innovation support system for
Taiwanese higher education. Da gdeviren (2010) employed ANP and
modi?edTOPSIStoselect personnel. Kelemenis andAskounis (2010)
proposed a new approach on the basis of fuzzy TOPSIS to select in-
formation technology professionals. Lin and Tsai (2010) integrated
ANP and TOPSIS to select locations for foreign direct investments in
new hospitals in China.
€
Onüt et al. (2010) used fuzzy AHP and fuzzy
TOPSIS to select a shopping center site. Liao et al. (2011) used ANP
and TOPSIS for assessing the performance of Taiwanese tour guides.
Li et al. (2011) selected a logistic center location based on the AFS
clustering approach and TOPSIS. Choudhary and Shankar (2012)
used fuzzy AHP and TOPSIS to select locations for thermal power
plants. Ishizaka et al. (2013) selected the location of a casino in the
Greater Londonregionusing the weightedsummethod, TOPSIS, and
PROMETHEE. The authors foundthat PROMETHEE and the weighted
sum method are more suitable than TOPSIS.
Although TOPSIS is comprehensible and the computations are
uncomplicated, it suffers from the inherent problem of assigning
reliable subjective preferences to criteria (Shyur, 2006). Due to the
K.-L. Chang et al. / Asia Paci?c Management Review 20 (2015) 49e55 51
interdependent criteria, ANP is applied in this paper to generate the
weights for the selection criteria. TOPSIS is used to rank the
alternatives.
5. A case study
We employ the fuzzy Delphi method, ANP, and TOPSIS in a case
study of a real-life ?rm to select optimal locations. The company is
the ?rst electronic business platform in Taipei established to pro-
vide professional service apartment chain services. It has several
service apartments in Taipei City, Taiwan, which are all located in
well-to-do residential communities. In addition to modern room
facilities, professional housekeeping services, and a secure and
comfortable residence environment, all services can be customized
according to customers' requirements. The decision committee
includes two managers. There are three locations as alternatives.
We depict the selection process as follows.
Step 1. Construct hierarchy and structure problem
The fuzzy Delphi method can create better criteria selection
(Ma et al., 2011). We apply the concept of the fuzzy Delphi method to
revise the hierarchy of Chou et al. (2008) and select optimal locations
for service apartments. Firstly, basedonChouet al. (2008b), we obtain
the selection criteria. Then, questionnaires based on a 9-point Likert
scale, with 1 as the most unimportant and 9 as the most important,
are sent to 31 senior executives to obtain their opinions about the
importance of the criteria. In this paper, the geometric mean of each
criterion is used to denote the consensus of the experts' evaluation
value of the criteria. According to the geometric mean, we retain the
top 12 criteria as shown in Table 1 to structure the hierarchy for
Taiwanese service apartment location selection (Fig. 1).
Step 2. Determine the perspectives and criteria weights
In this step, the decision-making committee makes a series of
pairwise comparisons to establish the relative importance of per-
spectives. Inthesecomparisons, a 1e9scale is appliedtocompare the
two perspectives. The pairwise comparison matrix and the devel-
opment of each perspective priority weight are shown in Table 2.
Based on the interdependency of criteria, we apply pairwise
comparisons again to establish the criteria relationships within
each perspective. The eigenvector of the observable pairwise
comparison matrix provide the criteria weights at this level, which
will be used in the supermatrix. With respect to airport, for
example, a pairwise comparison within the traf?c perspective can
be shown in Table 3. In this way, we can derive the weight of each
criterion to obtain the supermatrix.
Step 3. Construct and solve the supermatrix
The criteria weights derived in Step 2 are used to obtain the
column of the supermatrix as shown in Table 4. Finally, the system
solution is derived by multiplying the supermatrix of model vari-
ables by itself, which accounts for the variable interaction, until the
system's row values converge to the same value for each column of
the matrix, as shown in Table 5. According toTables 2 and 5, we can
aggregate the total weight of each criterion, as shown in Table 6.
Step 4. Construct the standardized and weighted standardized
appraisal matrix.
The decision-making committee is asked to establish the
appraisal matrix by comparing three alternatives with respect to
each criterion. After the appraisal matrix Eq. (1) is used to obtain
Figure 1. Hierarchy for Taiwanese service apartments to select optimal locations.
Table 1
Descriptions of the selection criteria.
Criteria De?nition
Public facilities Distance to public facilities
Competitiveness Regional competitiveness
Security Regional public security
Airport Distance to the airport
Downtown Distance to the downtown
Traf?c facilities Easy to travel main traf?c facilities
Traf?c routes Extensiveness of traf?c routes
Indoor facilities Variety of indoor facilities
Human resources Suf?cient human resources
Quality Quality of manpower
Cost Rent cost
Regulations Regulation restrictions
K.-L. Chang et al. / Asia Paci?c Management Review 20 (2015) 49e55 52
the standardized appraisal matrix, shown in Table 7. The criteria
weights derived from ANP shown in Table 6 are multiplied by the
standardized appraisal matrix to obtain the weighted standardized
appraisal matrix.
Step 5. Identify the positive ideal solution and negative ideal
solution
The positive ideal solution and negative ideal solution are
de?ned according to Eq. (3) as:
A
*
¼(0.0666, 0.0168, 0.0679, 0.0299, 0.0358, 0.0558, 0.0587, 0.0734,
0.0374, 0.0362, 0.0357, 0.0481),
A
À
¼ (0.0822, 0.0756, 0.0485, 0.0399, 0.0413, 0.0372, 0.0367,
0.0315, 0.0321, 0.0271, 0.0667, 0.0481).
Step 6. Calculate the Euclidean distance between the positive ideal
solution and negative ideal solution for each alternative
The Euclidean distance between the positive ideal solution and
negative ideal solution for each alternative can be measured by Eq.
(4).
Step 7. Calculate the relative closeness to the positive ideal solution
for each alternative
The C
*
i
value of each alternative can be obtained by Eq. (5).
Table 2
The pairwise comparisons of perspectives.
Geography Traf?c Management Priority weights
l
max
¼ 3.0536 C.R. ¼ 0.0406
Geography 1.0000 1.4142 0.7071 0.3319
Traf?c 0.7071 1.0000 1.0000 0.2956
Management 1.4142 1.0000 1.0000 0.3725
C.R. ¼ consistency ratio.
Table 3
The pairwise comparisons within traf?c perspective with respect to airport.
Downtown Traf?c facilities Traf?c
routes
Priority
weights
l
max
¼ 3.0377 C.R. ¼ 0.0286
Downtown 1.0000 1.4142 1.1180 0.3853
Traf?c facilities 0.7071 1.0000 1.4142 0.3308
Traf?c routes 0.8944 0.7071 1.0000 0.2839
C.R. ¼ consistency ratio.
Table 4
The supermatrix prior to convergence.
C
1
C
2
C
3
C
4
C
5
C
6
C
7
C
8
C
9
C
10
C
11
C
12
C
1
0.0000 0.6667 0.5858
C
2
0.4142 0.0000 0.4142
C
3
0.5858 0.3333 0.0000
C
4
0.0000 0.2679 0.2997 0.2128
C
5
0.3853 0.0000 0.2379 0.2556
C
6
0.3308 0.2679 0.0000 0.5316
C
7
0.2839 0.4641 0.4624 0.0000
C
8
0.0000 0.2210 0.1927 0.3028 0.4234
C
9
0.3141 0.0000 0.1344 0.1547 0.1475
C
10
0.1078 0.1233 0.0000 0.2879 0.1585
C
11
0.3141 0.3100 0.3557 0.0000 0.2705
C
12
0.2641 0.3458 0.3172 0.2546 0.0000
Table 5
The supermatrix after convergence.
C
1
C
2
C
3
C
4
C
5
C
6
C
7
C
8
C
9
C
10
C
11
C
12
C
1
0.3843 0.3843 0.3843
C
2
0.2929 0.2929 0.2929
C
3
0.3228 0.3228 0.3228
C
4
0.2057 0.2057 0.2057 0.2057
C
5
0.2208 0.2208 0.2208 0.2208
C
6
0.2821 0.2821 0.2821 0.2821
C
7
0.2914 0.2914 0.2914 0.2914
C
8
0.2305 0.2305 0.2305 0.2305 0.2305
C
9
0.1618 0.1618 0.1618 0.1618 0.1618
C
10
0.1481 0.1481 0.1481 0.1481 0.1481
C
11
0.2358 0.2358 0.2358 0.2358 0.2358
C
12
0.2238 0.2238 0.2238 0.2238 0.2238
Table 6
The total weight of each criterion.
Weights from
perspectives
Weights from supermatrix
after convergence
Total weights
of criteria
C
1
0.3319 0.3843 0.1275
C
2
0.3319 0.2929 0.0972
C
3
0.3319 0.3228 0.1071
C
4
0.2956 0.2057 0.0608
C
5
0.2956 0.2208 0.0653
C
6
0.2956 0.2821 0.0834
C
7
0.2956 0.2914 0.0861
C
8
0.3725 0.2305 0.0858
C
9
0.3725 0.1618 0.0603
C
10
0.3725 0.1481 0.0552
C
11
0.3725 0.2358 0.0878
C
12
0.3725 0.2238 0.0834
K.-L. Chang et al. / Asia Paci?c Management Review 20 (2015) 49e55 53
Step 8. Rank the alternatives
According to Table 8, the optimal location is selected. Therefore,
it is obvious that the ranking for the optimal locations is Alternative
2, Alternative 1, and Alternative 3.
The case company takes this result to operate service apart-
ments in Alternative 1 and Alternative 2. After interviewing the two
managers, they point out that a service apartment operated in
Alternative 2 is better based on their survey and annual perfor-
mance evaluation data.
6. Conclusion
This study presents an effective framework applying the fuzzy
Delphi method, ANP, and TOPSIS to select the optimal locations for
Taiwanese service apartments. The fuzzy Delphi method is used to
revise the work of previous studies and construct a hierarchy.
Questionnaires based on a 9-point Likert scale are sent to 31 senior
executives to obtain their rankings of the importance of the criteria.
The top 12 criteria are selected and taken into three perspectives,
namely, geography, traf?c, and management, to structure the hi-
erarchy for selecting the optimal locations. To solve the problem of
selection criteria interdependency, ANP is used to obtain the
weights of the criteria. To prevent excessive calculation and addi-
tional pairwise comparisons of ANP, TOPSIS is used to rank the
locations. By combining the fuzzy Delphi method, ANP, and TOPSIS,
this study can make better decisions in selecting the optimal lo-
cations for Taiwanese service apartments. The proposed framework
has increased the ef?ciency of the decision-making process in
location selection. The fuzzy Delphi method can create a better
criteria selection. TOPSIS eliminates many procedures that are
performed in ANP and enables the systemto reach a conclusion in a
shorter time. Additionally, this model can assist managers of
Taiwanese service apartments in performing similar multiple
criteria tasks objectively and systematically during optimal location
selection. In this paper, the C.R. of each pairwise comparison is
The fuzzy Delphi method, analytic network process (ANP), and technique for order preference by similarity
to ideal solution (TOPSIS) are integrated in this paper to help Taiwanese service apartments to
effectively select the optimal locations. The fuzzy Delphi method, which can lead to better criteria selection,
is used to modify previous studies to construct the hierarchy. Considering the interdependence
among the selection criteria in the hierarchy, ANP is then used to obtain the weights of the criteria. To
avoid calculation and additional pairwise comparisons of ANP, TOPSIS is used to rank the alternatives.
According to the hierarchy based on three perspectives and 12 important criteria, optimal locations for
Taiwanese service apartments can be more effectively selected. Moreover, by integrating the fuzzy Delphi
method, ANP, and TOPSIS, this study can make better decisions for optimal locations. To illustrate how
the fuzzy Delphi method, ANP, and TOPSIS are applied in the location selection problem, their application
to a real case is also performed.
An ANP based TOPSIS approach for Taiwanese service apartment location
selection
Kuei-Lun Chang
a, *
, Sen-Kuei Liao
b
, Tzeng-Wei Tseng
c
, Chi-Yi Liao
d
a
Department of Communications Management, Ming Chuan University, 250, Zhong Shan North Road, Section 5, Taipei, Taiwan, ROC
b
Department of Business Management, National Taipei University of Technology, 1, Zhong Xiao East Road, Section 3, Taipei, Taiwan, ROC
c
Graduate Institute of Industrial and Business Management, National Taipei University of Technology, 1, Zhong Xiao East Road, Section 3, Taipei, Taiwan, ROC
d
Department of Mass Communication, Chinese Culture University, 55, Hwa Kang Road, Yang Ming Shan, Taipei, Taiwan, ROC
a r t i c l e i n f o
Article history:
Received 28 December 2012
Accepted 4 October 2013
Available online 23 March 2015
Keywords:
Analytic network process
Fuzzy Delphi method
Service apartment
Technique for order preference by similarity
to ideal solution
a b s t r a c t
The fuzzy Delphi method, analytic network process (ANP), and technique for order preference by sim-
ilarity to ideal solution (TOPSIS) are integrated in this paper to help Taiwanese service apartments to
effectively select the optimal locations. The fuzzy Delphi method, which can lead to better criteria se-
lection, is used to modify previous studies to construct the hierarchy. Considering the interdependence
among the selection criteria in the hierarchy, ANP is then used to obtain the weights of the criteria. To
avoid calculation and additional pairwise comparisons of ANP, TOPSIS is used to rank the alternatives.
According to the hierarchy based on three perspectives and 12 important criteria, optimal locations for
Taiwanese service apartments can be more effectively selected. Moreover, by integrating the fuzzy Delphi
method, ANP, and TOPSIS, this study can make better decisions for optimal locations. To illustrate how
the fuzzy Delphi method, ANP, and TOPSIS are applied in the location selection problem, their application
to a real case is also performed.
© 2015, College of Management, National Cheng Kung University. Production and hosting by Elsevier
Taiwan LLC. All rights reserved.
1. Introduction
Location decisions have attracted much attention from the ac-
ademic and business communities (Chou, Hsu, & Chen, 2008). The
decision to select a location has become increasingly vital (Kapoor,
Tak, & Sharma, 2008). For the hotel industry, optimal location not
only helps increase market share and pro?t, but may also enhance
the convenience of passenger lodging. Satisfying customer needs or
enhancing the convenience of customer lodging will directly in-
crease customer loyalty (Chou et al., 2008). In recent years, service
apartments providing long-term hotel services for business per-
sons have become a growing industry in Taiwan. The service
apartment is a good choice for a comfortable, homelike, and
economical residence. In order to decrease the cost to the business
person of ?nding accommodations and to improve operating
performance, location selection has become one of the most
important issues for service apartments.
Hsu and Yang (2000) applied a triangular fuzzy number to
encompass expert opinions and establish a fuzzy Delphi method.
The maximum and minimumvalue of expert opinions are taken as
the two terminal points of triangular fuzzy numbers, and the
geometric mean is taken as the membership degree of triangular
fuzzy numbers to derive the statistical unbiased effect and avoid
the impact of extreme values. The advantage of the fuzzy Delphi
method is its simplicity. All of the expert opinions can be
encompassed in one investigation. Hence, this method can create
more effective criteria selection (Ma, Shao, Ma, & Ye, 2011). ANP
produces more accurate weighting of criteria, since it enables
consideration of the dependence among factors in decision-
making problems. Unfortunately, ANP requires many pairwise
comparisons depending on the number and interdependence of
factors and alternatives. This disadvantage of ANP is eliminated via
the use of the (TOPSIS). Thus, the selection process is shortened
(Da gdeviren, 2010).
By combining the fuzzy Delphi method, ANP, and TOPSIS, this
study can make better decisions in selecting locations for Taiwa-
nese service apartments within a shorter time, by considering the
* Corresponding author. Department of Communications Management, Ming
Chuan University, 250, Zhong Shan North Road, Section 5, Taipei, Taiwan, ROC.
E-mail address: [email protected] (K.-L. Chang).
Peer review under responsibility of College of Management, National Cheng
Kung University.
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Asia Paci?c Management Review
j ournal homepage: www. el sevi er. com/ l ocat e/ apmrvhttp://dx.doi.org/10.1016/j.apmrv.2014.12.007
1029-3132/© 2015, College of Management, National Cheng Kung University. Production and hosting by Elsevier Taiwan LLC. All rights reserved.
Asia Paci?c Management Review 20 (2015) 49e55
dependence among factors, which distinguishes this study from
others in the literature. We ?rst present a literature review of the
location selection. Next, the ANP and TOPSIS as selection tools are
described. The integrated method within the context of selecting
the optimal location for a Taiwanese service apartment is shown in
Section 5. The conclusion is given in Section 6.
2. Location selection
Many approaches for location selection have been developed.
Cheng, Li, and Yu (2007) used geographic information systems to
select a location for shopping malls. Wu, Lin, and Chen (2007)
used the modi?ed Delphi method, analytic hierarchy process
(AHP), and sensitivity analysis, to select the optimal location for a
regional hospital in Taiwan. Anagnostopoulos, Doukas, and
Psarras (2008) proposed a fuzzy multicriteria algorithm to
solve the distribution center location selection problem. Chou,
Chang, and Shen (2008) present a new fuzzy multiple attri-
butes decision-making method to answer facility location se-
lection problems. Chou et al. (2008) apply fuzzy AHP to select
international tourist hotel locations. Kapoor et al. (2008) used
fuzzy cluster analysis for the location selection problem. Tabari,
Kaboli, Aryanezhad, Shahanaghi, and Siadat (2008) selected the
optimal location based on the concept of fuzzy AHP. Guneri,
Cengiz, and Seker (2009) applied fuzzy ANP to select a suitable
location for a shipyard. Hsu (2010) utilized ANP to select the
optimal location for an international business of?ce center in
China. Kayikci (2010) combined fuzzy AHP and arti?cial neural
networks for location selection. Lin and Tsai (2010) integrated
ANP and TOPSIS to select locations for foreign direct investments
in new hospitals in China.
€
Onüt, Efendigil, and Kara (2010) used
fuzzy AHP and fuzzy TOPSIS to select a shopping center site.
Bottero and Ferretti (2011) applied ANP to rank sites for the
location of a waste incinerator plant for the Province of Torino in
Italy. Li, Liu, and Chen (2011) selected a logistic center location on
the basis of the axiomatic fuzzy set (AFS) clustering approach
and TOPSIS. Athawale, Chatterjee, and Chakraborty (2012)
applied the preference ranking organization method for enrich-
ment evaluation (PROMETHEE II) to solve facility location se-
lection problems. Choudhary and Shankar (2012) used fuzzy AHP
and TOPSIS to select locations for a thermal power plant.
Ishizaka, Nemery, and Lidouh (2013) selected the location of
casinos in the Greater London region using the weighted sum
method, TOPSIS, and PROMETHEE.
Several previous studies treat the selection criteria as inde-
pendent. After discussions with senior executives, we ?nd that
selection criteria are not independent in actual selection situations.
To address this issue, this paper combines ANP with TOPSIS to make
better decisions in selecting optimal locations for Taiwanese service
apartments. ANP, which captures the interdependence, is applied to
generate the weights of the selection criteria. TOPSIS is used to rank
the alternatives.
3. ANP
ANP (Saaty, 1996) is a comprehensive decision-making tech-
nique that captures the outcome of dependency between criteria.
AHP serves as a starting point for ANP. Priorities are established in
the same way that they are in AHP using pairwise comparisons. The
weight assigned to each perspective and criterion may be esti-
mated either from the data, or subjectively by decision makers. It is
desirable to measure the consistency of the decision makers'
judgment. AHP provides a measure through the consistency ratio
(C.R.) which is an indicator of the reliability of the model. This ratio
is designed in such a way that the values of the ratio exceeding 0.1
indicate inconsistent judgment (Saaty, 1980). ANP comprises four
major steps (Saaty, 1996).
Step 1. Construct hierarchy and structure problem
The problem should be clearly stated and hierarchy structure
constructed. The hierarchy can be determined by the decision
makers' opinion via brainstorming or other appropriate methods,
such as literature reviews.
Step 2. Determine the perspectives and criteria weights
In this step, the decision-making committee makes a series of
pairwise comparisons to establish the relative importance of per-
spectives and criteria. In these comparisons, a 1e9 scale is applied to
compare two perspectives or criteria according to the interdepen-
dency of perspectives and criteria. The eigenvector of the observ-
able pairwise comparison matrix provides the perspectives and
criteria weights at this level, which will be used in the supermatrix.
Step 3. Construct and solve the supermatrix
The perspectives and criteria weights derived from Step 2 are
used to obtain the column of the supermatrix. Finally, the super-
matrix will be steady by multiplying the supermatrix by itself until
the row values of the supermatrix converge to the same value for
each column of the matrix. We call that the limiting matrix.
Step 4. Select the best alternative
Based on the limiting matrix and the weights of alternatives
with respect to the criteria, we can aggregate the total weight of
each alternative. We rank the alternatives according to their total
weights.
In the literature on the application of ANP, Ertay, Büyük€ ozkan,
Kahraman, and Ruan (2005) tried to implement quality function
deployment (QFD) under a fuzzy environment. Moreover, ANP is
used to prioritize design requirements. Kahraman, Ertay, and
Büyük€ ozkan (2006) combined ANP and a fuzzy logic approach to
incorporate the customer needs and the product technical re-
quirements systematically into the product design phase in QFD.
Chang, Wey, and Tseng (2009) used the fuzzy Delphi method, ANP,
and zero one goal programming to select revitalization strategy
projects for the historic Alishan forest railway. Chen, Huang, and
Cheng (2009) used ANP and the balanced scorecard (BSC) for
measuring knowledge management (KM) performance. Guneri
et al. (2009) applied fuzzy ANP to select a suitable location for a
shipyard. Hsu and Hu (2009) used ANP to select suppliers by adding
the concept of hazardous substance management. Lee, Tzeng, Guan,
Chien, and Huang (2009) established an investment decision model
based on the Gordon model. ANP is applied to generate the weight
of criteria because of interrelations and self-feedback relationships
among the criteria. Liao and Chang (2009a) used ANP to measure
the performance of hospitals. Liao and Chang (2009b) applied ANP
to select television sportscasters for the Olympic Games. Liao and
Chang (2009c) combined ANP with BSC to select the key capabil-
ities of Taiwanese TV shopping companies. Liao and Chang (2009d)
applied ANP to choose public relations personnel for Taiwanese
hospitals. Lin (2009) combined ANP with fuzzy preference pro-
gramming to select suppliers and then allocated orders among the
selected suppliers using multi-objective linear programming. Oh,
Suh, Hong, and Hwang (2009) applied ANP and BSC to evaluate
the feasibility of a newtelecomservice. They point out that ANP can
obtain more realistic results. Wu, Lin, and Peng (2009) combined
ANP with conjoint analysis to simplify ANP for hospital
K.-L. Chang et al. / Asia Paci?c Management Review 20 (2015) 49e55 50
policymakers making appropriate management policies. Aznar,
Ferrís-O~ nate, and Guijarro (2010) used ANP for property pricing.
Chen and Chen (2010) applied decision-making trial and evaluation
laboratory (DEMATEL), fuzzy ANP, and TOPSIS to develop a new
innovation support system. Da gdeviren (2010) employed ANP and
modi?ed TOPSIS to select personnel. Hsu (2010) utilized ANP to
select optimal location for an international business of?ce center in
China. Liao and Chang (2010) combined ANP with BSC for
measuring the managerial performance of TV companies. Liao,
Chang, and Tseng (2010) selected program suppliers for TV com-
panies using ANP. Lin and Tsai (2010) integrated ANP and TOPSIS to
select locations for foreign direct investments in new hospitals in
China. Tseng (2010) used ANP, DEMATEL, and fuzzy set theory to
obtain the relative weight of BSC factors for a university perfor-
mance measurement. Yang, Hui, Leung, and Chen (2010) applied
ANP to select logistics service providers for air cargo. Yüksel and
Da gdeviren (2010) integrated fuzzy ANP and BSC to measure the
performance of a manufacturing ?rminTurkey. Bottero and Ferretti
(2011) applied ANP to rank sites for the location of a waste incin-
erator plant for the Province of Torino in Italy. Ertay, Akyol, and Araz
(2011) applied fuzzy ANP to rank engineering characteristics for
implementing QFD. Liao, Chen, Chang, and Tseng (2011) used ANP
and TOPSIS for assessing the performance of Taiwanese tour guides.
Fazli and Jafari (2012) applied DEMATEL, ANP, and VlseKriter-
ijumska Optimizacija I Kompromisno Resenje (VIKOR) to select the
best alternative for investment in stock exchange. Hu, Wang, and
Hung (2012a) utilized ANP to evaluate e-service quality of micro-
blogging. Hu, Wang, and Wang (2012b) used ANP to evaluate the
performance of Taiwan homestay industry.
ANP, widely applied in decision making, is more accurate and
feasible under interdependent situations. However, after discus-
sions with senior executives, we found that the selection criteria for
locations are interrelated. ANP, which captures the interdepen-
dence, appears to be one of the more feasible and accurate solu-
tions for generating the weights of the selection criteria.
4. TOPSIS
TOPSIS, proposed by Hwang and Yoon (1981), enables decision
makers to determine the positive ideal solution (A
*
) and negative
ideal solution (A
À
). On the basis of TOPSIS, the chosen alternative
should have the shortest distance from the positive ideal solution
and the farthest from the negative ideal solution. The computing
process is presented as follows.
Step 1. Construct the standardized appraisal matrix
r
ij
¼
x
ij
????????????????
m
i¼1
x
2
ij
_ (1)
where i indicates the alternatives, j denotes the selection criteria,
and x
ij
means the i alternative under the j criterion to be assessed.
Step 2. Construct the weighted standardized appraisal matrix
Weights of selection criteria, w ¼ ðw
1
; w
2
; :::; w
n
Þ, multiplied by
the standardized appraisal matrix, may be expressed as:
v ¼
_
¸
¸
_
v
11
v
12
… v
1n
v
21
v
22
… v
2n
« « / «
v
m1
v
m2
/ v
nm
_
¸
¸
_
¼
_
¸
¸
_
w
1
r
11
w
2
r
12
… w
n
r
1n
w
1
r
21
w
2
r
22
… w
n
r
2n
« « / «
w
1
r
m1
w
2
r
m2
/ w
n
r
mn
_
¸
¸
_
(2)
Step 3. Identify the positive ideal solution and negative ideal
solution
A
*
¼
_
v
*
1
; v
*
2
; :::; v
*
j
; :::; v
*
n
_
¼
__
max
i
v
ij
jj2J
_
ji ¼ 1; :::; m
_
; (3)
A
À
¼
_
v
À
1
; v
À
2
; :::; v
À
j
; :::; v
À
n
_
¼
__
min
i
v
ij
jj2J
_
ji ¼ 1; :::; m
_
:
Step 4. Calculate the Euclidean distance between the positive ideal
solution (S
*
i
) and negative ideal solution (S
À
i
) for each alternative
S
*
i
¼
???????????????????????????????
n
j¼1
_
v
ij
À v
*
i
_
2
¸
¸
¸
_
; i ¼ 1; :::; m; (4)
S
À
i
¼
????????????????????????????????
n
j¼1
_
v
ij
À v
À
i
_
2
¸
¸
¸
_
; i ¼ 1; :::; m:
Step 5. Calculate the relative closeness to the positive ideal solution
for each alternative
C
*
i
¼
S
À
i
S
*
i
þ S
À
i
(5)
An alternative A
i
is closer to A
*
and farther from A
À
asC
*
i
approaches 1.
Step 6. Rank the preference order by C
*
i
According to C
*
i
, larger index values indicate better performance
of the alternatives.
TOPSIS has been widely explored in the literature. Da gdeviren,
Yavuz, and K?l?nç (2009) used AHP and fuzzy TOPSIS to select
weapons. Gumus (2009) employed fuzzy AHP and TOPSIS to eval-
uate hazardous transportation ?rms. Saremi, Mousavi, and Sanayei
(2009) applied fuzzy TOPSIS to select an external total quality
management (TQM) consultant. Sun and Lin (2009) used fuzzy
TOPSIS to generate the weight of each criterion and rank four
shopping websites. Wang, Cheng, and Huang (2009) developed a
fuzzy hierarchical TOPSIS that improves the idea of Chen (2000) for
selecting a lithium-ion battery protection integrated circuit (LI-
BPIC) supplier. Chen and Chen (2010) applied DEMATEL, fuzzy ANP,
and TOPSIS to develop a new innovation support system for
Taiwanese higher education. Da gdeviren (2010) employed ANP and
modi?edTOPSIStoselect personnel. Kelemenis andAskounis (2010)
proposed a new approach on the basis of fuzzy TOPSIS to select in-
formation technology professionals. Lin and Tsai (2010) integrated
ANP and TOPSIS to select locations for foreign direct investments in
new hospitals in China.
€
Onüt et al. (2010) used fuzzy AHP and fuzzy
TOPSIS to select a shopping center site. Liao et al. (2011) used ANP
and TOPSIS for assessing the performance of Taiwanese tour guides.
Li et al. (2011) selected a logistic center location based on the AFS
clustering approach and TOPSIS. Choudhary and Shankar (2012)
used fuzzy AHP and TOPSIS to select locations for thermal power
plants. Ishizaka et al. (2013) selected the location of a casino in the
Greater Londonregionusing the weightedsummethod, TOPSIS, and
PROMETHEE. The authors foundthat PROMETHEE and the weighted
sum method are more suitable than TOPSIS.
Although TOPSIS is comprehensible and the computations are
uncomplicated, it suffers from the inherent problem of assigning
reliable subjective preferences to criteria (Shyur, 2006). Due to the
K.-L. Chang et al. / Asia Paci?c Management Review 20 (2015) 49e55 51
interdependent criteria, ANP is applied in this paper to generate the
weights for the selection criteria. TOPSIS is used to rank the
alternatives.
5. A case study
We employ the fuzzy Delphi method, ANP, and TOPSIS in a case
study of a real-life ?rm to select optimal locations. The company is
the ?rst electronic business platform in Taipei established to pro-
vide professional service apartment chain services. It has several
service apartments in Taipei City, Taiwan, which are all located in
well-to-do residential communities. In addition to modern room
facilities, professional housekeeping services, and a secure and
comfortable residence environment, all services can be customized
according to customers' requirements. The decision committee
includes two managers. There are three locations as alternatives.
We depict the selection process as follows.
Step 1. Construct hierarchy and structure problem
The fuzzy Delphi method can create better criteria selection
(Ma et al., 2011). We apply the concept of the fuzzy Delphi method to
revise the hierarchy of Chou et al. (2008) and select optimal locations
for service apartments. Firstly, basedonChouet al. (2008b), we obtain
the selection criteria. Then, questionnaires based on a 9-point Likert
scale, with 1 as the most unimportant and 9 as the most important,
are sent to 31 senior executives to obtain their opinions about the
importance of the criteria. In this paper, the geometric mean of each
criterion is used to denote the consensus of the experts' evaluation
value of the criteria. According to the geometric mean, we retain the
top 12 criteria as shown in Table 1 to structure the hierarchy for
Taiwanese service apartment location selection (Fig. 1).
Step 2. Determine the perspectives and criteria weights
In this step, the decision-making committee makes a series of
pairwise comparisons to establish the relative importance of per-
spectives. Inthesecomparisons, a 1e9scale is appliedtocompare the
two perspectives. The pairwise comparison matrix and the devel-
opment of each perspective priority weight are shown in Table 2.
Based on the interdependency of criteria, we apply pairwise
comparisons again to establish the criteria relationships within
each perspective. The eigenvector of the observable pairwise
comparison matrix provide the criteria weights at this level, which
will be used in the supermatrix. With respect to airport, for
example, a pairwise comparison within the traf?c perspective can
be shown in Table 3. In this way, we can derive the weight of each
criterion to obtain the supermatrix.
Step 3. Construct and solve the supermatrix
The criteria weights derived in Step 2 are used to obtain the
column of the supermatrix as shown in Table 4. Finally, the system
solution is derived by multiplying the supermatrix of model vari-
ables by itself, which accounts for the variable interaction, until the
system's row values converge to the same value for each column of
the matrix, as shown in Table 5. According toTables 2 and 5, we can
aggregate the total weight of each criterion, as shown in Table 6.
Step 4. Construct the standardized and weighted standardized
appraisal matrix.
The decision-making committee is asked to establish the
appraisal matrix by comparing three alternatives with respect to
each criterion. After the appraisal matrix Eq. (1) is used to obtain
Figure 1. Hierarchy for Taiwanese service apartments to select optimal locations.
Table 1
Descriptions of the selection criteria.
Criteria De?nition
Public facilities Distance to public facilities
Competitiveness Regional competitiveness
Security Regional public security
Airport Distance to the airport
Downtown Distance to the downtown
Traf?c facilities Easy to travel main traf?c facilities
Traf?c routes Extensiveness of traf?c routes
Indoor facilities Variety of indoor facilities
Human resources Suf?cient human resources
Quality Quality of manpower
Cost Rent cost
Regulations Regulation restrictions
K.-L. Chang et al. / Asia Paci?c Management Review 20 (2015) 49e55 52
the standardized appraisal matrix, shown in Table 7. The criteria
weights derived from ANP shown in Table 6 are multiplied by the
standardized appraisal matrix to obtain the weighted standardized
appraisal matrix.
Step 5. Identify the positive ideal solution and negative ideal
solution
The positive ideal solution and negative ideal solution are
de?ned according to Eq. (3) as:
A
*
¼(0.0666, 0.0168, 0.0679, 0.0299, 0.0358, 0.0558, 0.0587, 0.0734,
0.0374, 0.0362, 0.0357, 0.0481),
A
À
¼ (0.0822, 0.0756, 0.0485, 0.0399, 0.0413, 0.0372, 0.0367,
0.0315, 0.0321, 0.0271, 0.0667, 0.0481).
Step 6. Calculate the Euclidean distance between the positive ideal
solution and negative ideal solution for each alternative
The Euclidean distance between the positive ideal solution and
negative ideal solution for each alternative can be measured by Eq.
(4).
Step 7. Calculate the relative closeness to the positive ideal solution
for each alternative
The C
*
i
value of each alternative can be obtained by Eq. (5).
Table 2
The pairwise comparisons of perspectives.
Geography Traf?c Management Priority weights
l
max
¼ 3.0536 C.R. ¼ 0.0406
Geography 1.0000 1.4142 0.7071 0.3319
Traf?c 0.7071 1.0000 1.0000 0.2956
Management 1.4142 1.0000 1.0000 0.3725
C.R. ¼ consistency ratio.
Table 3
The pairwise comparisons within traf?c perspective with respect to airport.
Downtown Traf?c facilities Traf?c
routes
Priority
weights
l
max
¼ 3.0377 C.R. ¼ 0.0286
Downtown 1.0000 1.4142 1.1180 0.3853
Traf?c facilities 0.7071 1.0000 1.4142 0.3308
Traf?c routes 0.8944 0.7071 1.0000 0.2839
C.R. ¼ consistency ratio.
Table 4
The supermatrix prior to convergence.
C
1
C
2
C
3
C
4
C
5
C
6
C
7
C
8
C
9
C
10
C
11
C
12
C
1
0.0000 0.6667 0.5858
C
2
0.4142 0.0000 0.4142
C
3
0.5858 0.3333 0.0000
C
4
0.0000 0.2679 0.2997 0.2128
C
5
0.3853 0.0000 0.2379 0.2556
C
6
0.3308 0.2679 0.0000 0.5316
C
7
0.2839 0.4641 0.4624 0.0000
C
8
0.0000 0.2210 0.1927 0.3028 0.4234
C
9
0.3141 0.0000 0.1344 0.1547 0.1475
C
10
0.1078 0.1233 0.0000 0.2879 0.1585
C
11
0.3141 0.3100 0.3557 0.0000 0.2705
C
12
0.2641 0.3458 0.3172 0.2546 0.0000
Table 5
The supermatrix after convergence.
C
1
C
2
C
3
C
4
C
5
C
6
C
7
C
8
C
9
C
10
C
11
C
12
C
1
0.3843 0.3843 0.3843
C
2
0.2929 0.2929 0.2929
C
3
0.3228 0.3228 0.3228
C
4
0.2057 0.2057 0.2057 0.2057
C
5
0.2208 0.2208 0.2208 0.2208
C
6
0.2821 0.2821 0.2821 0.2821
C
7
0.2914 0.2914 0.2914 0.2914
C
8
0.2305 0.2305 0.2305 0.2305 0.2305
C
9
0.1618 0.1618 0.1618 0.1618 0.1618
C
10
0.1481 0.1481 0.1481 0.1481 0.1481
C
11
0.2358 0.2358 0.2358 0.2358 0.2358
C
12
0.2238 0.2238 0.2238 0.2238 0.2238
Table 6
The total weight of each criterion.
Weights from
perspectives
Weights from supermatrix
after convergence
Total weights
of criteria
C
1
0.3319 0.3843 0.1275
C
2
0.3319 0.2929 0.0972
C
3
0.3319 0.3228 0.1071
C
4
0.2956 0.2057 0.0608
C
5
0.2956 0.2208 0.0653
C
6
0.2956 0.2821 0.0834
C
7
0.2956 0.2914 0.0861
C
8
0.3725 0.2305 0.0858
C
9
0.3725 0.1618 0.0603
C
10
0.3725 0.1481 0.0552
C
11
0.3725 0.2358 0.0878
C
12
0.3725 0.2238 0.0834
K.-L. Chang et al. / Asia Paci?c Management Review 20 (2015) 49e55 53
Step 8. Rank the alternatives
According to Table 8, the optimal location is selected. Therefore,
it is obvious that the ranking for the optimal locations is Alternative
2, Alternative 1, and Alternative 3.
The case company takes this result to operate service apart-
ments in Alternative 1 and Alternative 2. After interviewing the two
managers, they point out that a service apartment operated in
Alternative 2 is better based on their survey and annual perfor-
mance evaluation data.
6. Conclusion
This study presents an effective framework applying the fuzzy
Delphi method, ANP, and TOPSIS to select the optimal locations for
Taiwanese service apartments. The fuzzy Delphi method is used to
revise the work of previous studies and construct a hierarchy.
Questionnaires based on a 9-point Likert scale are sent to 31 senior
executives to obtain their rankings of the importance of the criteria.
The top 12 criteria are selected and taken into three perspectives,
namely, geography, traf?c, and management, to structure the hi-
erarchy for selecting the optimal locations. To solve the problem of
selection criteria interdependency, ANP is used to obtain the
weights of the criteria. To prevent excessive calculation and addi-
tional pairwise comparisons of ANP, TOPSIS is used to rank the
locations. By combining the fuzzy Delphi method, ANP, and TOPSIS,
this study can make better decisions in selecting the optimal lo-
cations for Taiwanese service apartments. The proposed framework
has increased the ef?ciency of the decision-making process in
location selection. The fuzzy Delphi method can create a better
criteria selection. TOPSIS eliminates many procedures that are
performed in ANP and enables the systemto reach a conclusion in a
shorter time. Additionally, this model can assist managers of
Taiwanese service apartments in performing similar multiple
criteria tasks objectively and systematically during optimal location
selection. In this paper, the C.R. of each pairwise comparison is