Technical Journal of Engineering and Applied Sciences
Available online at www.tjeas.com
©2014 TJEAS Journal-2014-4-3/124-134
ISSN 2051-0853 ©2014 TJEAS
Locating the bank branches using a hybrid method
Lotfalipour Zainab1 , Naji- Azimi Zahra2, Kazemi Mostafa3
1. MBA student, Management department of Ferdowsi University, Mashhad, Iran
2. Faculty member in department of Management , Ferdowsi University, Mashhad, Iran
3. Faculty member in department of Management ,Ferdowsi University, Mashhad, Iran
Correspondence author email: [email protected]
ABSTRACT: Survival in today's competitive world remains no space for mistakes. In this regard, planning and
optimal decision-making are of the affecting factors in achieving success, and appropriate locating by
organizations. The banks are of the organizations that the right selection of their branches plays a major role in
their success. The purpose of this study is to aid the bank managers in order to select the appropriate location
for establishing new branches and decreasing the risk of decision-making. The Pasargad bank was the case of
this study and the five regions are nominated for establishing the new bank branches using the views of
banking experts. To prioritize and select the appropriate location, the affective factors in locating the branches
were selected with the help of experts and the literature review then, their relative weights was determined
using the AHP method. But, since the paired comparisons of AHP is dependent on personal opinions, we came
to get assistance from the hybrid method of AHP and Monte Carlo simulation in order to decrease the risk of
decision-making, prioritize the locations, and select the best one. Finally, we compared the results statistically
using both the descriptive and inferential statistics.
Keywords: Location problem, Multi Criteria Decision Making, Analytical Hierarchy Process, Monte Carlo
Simulation
INTRODUCTION
Placement and searching for new places has historically been considered by researchers and managers of
different organizations (e.g., Charnetski 1976; Hotelling 1929; Isard 1956). They clearly found that selecting the
right location would prevent many financial problems of the organizations, provide many benefits for them, and
result in their success (Guneri et al. 2009; Kuo et al. 1999). Of the organizations that are closely associated
with the concept of locating, are the banks. Although, the volume of practices and customers' traffic to their
branches has been reduced because of spreading the electronic banking right now, but still the quality of
branches' performance plays a major role in the efficiency of these financial-service enterprises. Therefore, it
should be considered that the locating of branches is performed in such a way that leads to customers'
satisfaction due to enhancing the quality of branches' performance. Few studies could be found related to
locating in the field of banking from which the Min's (1989) article could be mentioned.
From interviewing with managers of branches and investigating the statistics of their performance, it appears
that the decision-makers of these enterprises still have difficulty with selecting a location for establishing a new
branch, because it is a very complex decision-making process. Decision-makers carry out extensive
researches and given the obtained information and their working experiences make a decision about selecting
a location for establishing a new branch. Since many factors are involved in decision-making, there exists a
possibility for personal judgments and making mistake. Furthermore, decision-making is not a responsibility of
only one person and it is difficult to consider the opinions of all the decision-makers. These issues along with
the other limitations such as finding the desired estate and possibility of buying or necessity of renting and
many more, make it difficult to make decision.
Since most of today's decision-makings have taken a mathematical form and many qualitative and quantitative
factors are involved in this process, it seems to be helpful for managers to utilize the multi-criteria decisionmaking methods. Amongst the multi-criteria decision-making methods, the analytical hierarchy process not only
allows you to investigate a wide range of primary and secondary indicators but also to study the association of
these criteria with the desired alternatives. This method has been used in many large organizations like IBM,
British Airway, Ford Motor, and Xerox and has been provided satisfactory results (Saaty 2008). In addition,
Tech J Engin & App Sci., 4 (3): 124-134, 2014
since the decisions about selecting a location for establishing new branches are made by a decision-making
team not an individual, the group analytical hierarchy process sounds to be appropriate, because by using this
method the opinions of all the team members are considered in decision-making process in such a way that
they cannot impose their opinion on the others. Indeed, the group analytical hierarchy process leads to
excellent decisions so that combines all the decisions together and optimal decision includes the opinions of all
members. However, since the criterion to decide in AHP is the comparisons of individuals, the hybrid method of
AHP and Monte Carlo simulation is used in this study in order to decrease the effect of personal opinions.
According to our information, this hybrid method is not used yet in locating the bank branches. Rest of the
paper is consisted of literature review in section two, hybrid method used in section three, and computational
results and conclusion in sections four and five.
RESEARCH BACKGROUND
LOCATING
Locating has an extensive theoretical history. Many attempts have been made to solve the locating problems
in which a wide range of objective factors and methodology is applied (Badri 1999). The year 1909 is known as
birthdate of locating theory, because in which this theory was exposed by Weber for the first time (Brandeau &
Chiu1989). He used the locating problem to determine the location of an industrial center in order to minimize
the transportation costs (Tabari et al. 2008).
After him, researchers made some changes in his proposed model and exploited new methods in order to
locating in different sectors of industry. For instance, two years later, Geoffrion used the decomposition method
along with mixed integer linear programming, simulation, and heuristic method in the analysis of locating
problems (Badri 1999). And after him, Aikens (1985) took advantage of another method named mathematical
programming in order to develop the models of facilities locating (Chou et al. 2008). Chen (1996) is of the other
researchers who have focused on locating problem. He used the mathematical programming to offer a model
for selecting the optimal location of distribution centers, and then, offered the fuzzy group decision model trying
to find a suitable location for plant or retailing store (Chen 1999). In addition, Min (1989) combined the fuzzy
goal programming and decision support system in order to locating the bank branches.
Using the metaheuristic methods is also another approach to solve the locating problems. For example, in an
empirical study, a group of researchers investigated the difference among three methods of tabu search,
simulated anealing, and genetic algorithm in locating the facilities (Arostegui JR et al. 2006). Chen (2007) has
also used a hybrid heuristic method in locating of hub. Furthermore, Caballero et al. (2007) have used a
metahuristic method based on tabu for locating. After them, Chen and Ting (2008) combined a Lagrangian
heuristic method and Ant Colony System in order to locating the single source capacitated location problem.
LOCATING AND ANALYTICSAL HIERARCHY PROCESS
In decision-making in the real world, the decision-maker is faced to many important factors and criteria which
judgments about the importance of each of them affect his final decision. In such cases, the multi-criteria
decision-making methods are used by decision-makers. Amongst them, the analytical hierarchy process is one
of the most useful and widely used methods (Triantaphyllou & Mann 1995), because allows the decision-maker
to formulate the decision-making process based on the hierarchical decision tree, consider the various
qualitative and quantitative criteria, and analyze the competing alternatives of decision-making based on paired
comparisons (Saaty 1990).
The AHP method is widely used in various fields. In Turkey, Buyukozkan (2004) applied two methods of fuzzy
analytical hierarchy and fuzzy Delphi in order to determine the best selection for e-market place. Furthermore,
another researcher in the same country conducted the analytical hierarchy process for locating the industrial
plants (Kazancoglu & Ada 2009). In 2011, two other Turkish researchers used the analytical hierarchy process
for locating the gas stations (Semih & Seyhan 2011). In Russia, Lorentz (2008) utilized the AHP method for
identifying and weighting the affective factors in locating the food factories. Selecting the appropriate location for
outsourcing abroad using the analytical hierarchy process is also an issue performed by several American
researchers (Boardman et al., 2008). In another research, locating an emergency logistic center was done with
the aid of AHP method in China (Liu & Xiaohua a 2011). Another study was also performed in the dry port
location selection in the same country using the two methods of Fuzzy-AHP and elimination ET choice
translating reality (Ka 2011). Wei and his colleagues (2011) located the fire stations through the AHP method
along with GIS. Bagum et al. (2012) also investigated the external and internal factors of locating the wind
pumping system in Bangladesh using the Brown-Gibson plant location model and analytical hierarchy process
respectively.
In the field of services, Tzeng et al. (2002) used the analytical hierarchy process in order to specify the
appropriate location for establishing the restaurant. Chou and his colleagues (2008) created a fuzzy multicriteria decision-making using the analytical hierarchy process, Fuzzy, and Ideal and anti-ideal solution, and
used it in locating the international tourism hotels.
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HYBRID METHID OF AHP AND MONTE CARLO SIMULATION IN LOCATING THE BANK BRANCHES
In this paper, prioritizing the regions in order to determine a location for the new branch of Pasargad bank
was performed using the hybrid method of AHP and Monte Carlo simulation, because the Monte Carlo method
decreases the uncertainty of paired comparisons in the AHP (Hsu & Pan 2009). This method leads to more
confidence in the results of decisions and enables the decision-makers to express their priorities with more
flexibility than the AHP method. This method applies a triangular distribution in order to more efficiency when
the distribution is unreliable and considers three states of minimum, maximum, and the most probable (Momani
& Ahmed 2011).
In this study, the following stages will be done in order to locate the bank branches using the hybrid method of
analytical hierarchy process and Monte Carlo simulation:
Modeling
Simulating and carrying out the paired
comparisons using the AHP method
Prioritizing the branches
Writing down the results
No
Is it time to
check out the
simulation?
Yes
Conclusion
Figure 1. Stages of the hybrid method of AHP and Monte Carlo simulation
MODELING
The analytical hierarchy process needs to break a problem with several indicators down to a hierarchy of levels
(Abu Dabous & Alkass 2008). In this study, we extracted the major locating criteria and sub-criteria after a
survey of the heads, associates, and experts of the Pasargad bank and reviewing the literature, and selected
five candidate locations for establishing the new branch via the opinions of banking specialists. Figure 2
indicates the hierarchical structure of locating for branches of the Pasargad bank in which the highest level
represents for the main objective and the lowest level represents for the decision options. The middle levels
belong to major criteria and sub-criteria. As it can be seen in this figure, the first criterion is the place position
indicating the effect of proximity with the wealthy residential areas (Min 1989; Tzeng et al. 2002; Okeahalam
2009), commercial areas and markets (Meidan 1993; Boufounou, 1995; Tzeng et al. 2002), plants and huge
economic organizations (Boufounou 1995), and industrial towns. The branches distance towards one another is
also considered in this criterion (Min 1989). The next one is the economic criterion, which indicates that to what
extent each branch candidate increases the bank reserves (Tzeng et al. 2002) and the potential and capacity of
branch itself (Cheng et al. 2005). The third one is related to safety (Chou et al. 2008). The accessibility is the
fourth criterion (Cheng et al. 2005) related to factors such as locating at the site of traffic plans, existing the
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public transportation, and access to parking (Tzeng et al. 2002; Chou et al. 2008). The last one is the
competition criterion (Cheng et al. 2005). The existence of branches from the other banks (Min 1989;
Boufounou 1995; Tzeng et al. 2002; Chou et al. 2008) as well as the awareness of their reserves is considered
in this criterion.
Locating the bank branches

Competitive
 Existence of the
competitors
 Financial
recourses of the
other banks
Accessibility
 Locating in traffic
zones
 Access to parking
Ghasemabad
Forudgah
Economic
Security

Environmental
security


Emamreza
Financial
recourses of the
bank
Branch's potential
and capacity
Hefdahshahrivar
Positional
 Closeness to
business centers
 Proximity to
wealthy
residential areas
 Proximity to
large economic
organizations
 Closeness to
industrial towns
 Geographical
distribution of the
bank branches
Tolab
Figure 2. Hierarchical structure of bank locating
PAIRED COMPARISONS
In this stage, the paired comparison questionnaires were prepared and given to some experts of Pasargad
bank, and then, the paird comparisons were made based on the Saaty scaling table (Saaty 2008).
Nevertheless, one of the shortcomings of AHP method is to force the decision-makers to choose only one
number in paired comparisons (Banuelas & Antony 2004). To cover this weakness, we located the bank
branches with the help of complementary method of Monte Carlo simulation, which has not been used for
locating in the literature so far. Monte Carlo simulation is a technique through which the uncertainties resulting
from the variance of values in input variables that affect the model output are simulated via the random
numbers. In this regard, we consider each component of paired comparisons as a random variable with
triangular distribution function, which its amounts are shown through an ordinal ternary by the first, second, and
third numbers are respectively representing for the least, the most probable, and the most possible values. In
other words, the managers and experts allocate a ternary rather than a single number to each paired
comparison, which its components are extracted from the following table.
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Table 1. The fundamental scale of absolute numbers (saati 2008)
Intensity of importance
Definition
Explanation
1
Equal Importance
Two activities contribute equally
to the objective
2
Weak or slight
3
Moderate importance
Experience and judgement
slightly favour one activity over
another
4
Moderate plus
5
Strong importance
Experience and judgement
strongly favour one activity over
another
6
Strong plus
7
Very strong or
An activity is favoured very
demonstrated importance
strongly over another; its
dominance demonstrated in
practice
8
Very, very strong
9
Extreme importance
The evidence favouring one
activity over another is of the
highest possible order of
affirmation
If activity i has one of the
Reciprocals
above non-zero numbers
A reasonable assumption
of above
assigned to it when
compared with activity j,
then j has the reciprocal
value when compared
with i
May be difficult to assign the best
1.1–1.9
value but when compared with
If the activities are very
other contrasting activities the
close
size of the small numbers would
not be too noticeable, yet they
can still indicate the relative
importance of the activities.
In the present study, which does not exist one decision-maker but there exists a group of decision-makers; the
opinions of these individuals should be merged somehow. The first solution is that the members of decisionmaking group come together and reach to a single opinion. But, this procedure was not used here because
aggregating the experts and managers together in a meeting was impossible.
On the other hand, since prioritizing the branches is being performed in this paper using the AHP method as
well as the hybrid method of AHP and Monte Carlo simulation separately, it should be determined how to
combine the opinions in either AHP or Hybrid method. According to what was stated, the geometric mean is
used in the first method in which prioritizing the alternatives is carried out only using the AHP method. How to
combine the opinions in the hybrid method will be mentioned in the next section.
SIMULATION AND PRIORITIZING
As previously mentioned, in this problem we have a random variable with a triangular distribution function per
each component of paired comparisons, which the minimum, maximum, and most probable values are identified
by experts. In other words, there exists an interval per each paired comparison in the simulation and every time
a random number with a triangular distribution function is elected from this interval as a number relating to
comparison. Given the high capabilities of Excel software, this stage and the next ones is done using the
simtools tab in this software.
Since there exists a group of decision-makers rather than a single decision-maker in this study and the random
selection is very important as well, the opinion tables of all the decision-makers are integrated at first. In this
case, the minimum, mean, and maximum values of experts' opinions for each component are listed in the
relevant table. Then, one number in each interval is selected randomly using the Monte Carlo simulation and
considering the triangular probability distribution, and after creating all the required matrices, AHP will continue
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as usual and the regions are prioritized based on obtained scores. Then, the whole process is repeated 1000
times, and each time the results are recorded.
It should be noted that after generating random numbers, the consistency of tables are also investigated and if
the consistency of matrix is greater than .10, another random number is generated so that, we have a total of
1000 iterations of the consistent simulation matrix.
COMPUTATIONAL RESULTS OF CASE STUDY
Analytical hierarchy process
In the first method of the present study, branches have been prioritized solely based on the analytical hierarchy
process. As it can be seen in table 2, the branch of Emamreza Street has gained the most score using the AHP
method. Furthermore, the prioritization results of the other regions based on this method are provided in the
table.
Table2. Ranking of candidate places using AHP
Place of branch
Score
Emamreza
0.229
Forudgah
0.199
Tolab
0.198
Ghasemabad
0.190
Hefdahshahrivar
0.185
As it can be seen, the branches are rated closely and it is difficult to give a preference to one over another. For
example, if we investigate the table scores with the precision of a one-digit decimal, there is no difference
between the branches of Forudgah, Tolab, and Ghasemabad. For this reason, another method is needed to
compensate this deficiency and create further certainty in decision-making.
Hybrid method of analytical hierarchy process and Monte Carlo simulation
In this section, the results of 1000 iteration of the hybrid process of AHP and Monte Carlo simulation was
investigated via the STATISTICA software.
Figure 3 plots the frequency charts for each region and table 3 indicates the statistical information relating to the
five branches of Tolab, Hefdahshahrivar, Emamreza, and Ghasemabad. As it can be seen in table 3,
Emamreza branch is in the first rank than the other locations in terms of score means. In these charts, the
horizontal axis represents for obtained scores and vertical axis for score frequency of each branch in 1000
iteration of the process.
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Figure 3. Frequency charts of branches in the hybrid method of AHP & Monte Carlo
De scri ptives
Table
3. Statistical information of the five branches based on the hybrid method of AHP & Monte Carlo
Sc ore2
Tolab
Hefdahshahrivar
Emamreza
Forudgah
Ghasemabad
Total
N
1000
1000
1000
1000
1000
5000
Mean
.28302
.21300
.23113
.14177
.13107
.20000
St d. Deviat ion St d. Error
.095701
.003026
.026735
.000845
.030017
.000949
.034677
.001097
.059911
.001895
.079660
.001127
95% Confidenc e Int erval for
Mean
Lower Bound Upper Bound
.27708
.28896
.21135
.21466
.22927
.23300
.13962
.14393
.12735
.13479
.19779
.20221
Minimum
.149
.151
.178
.097
.061
.061
Maximum
.415
.274
.328
.215
.251
.415
Furthermore, according to information obtained from the 1000 iteration of the simulation, Emamreza branch
495 times, Tolab branch 492 times, Qasemabad branch 11 times, and Hefdah Shahrivar branch 2 times has
earned the first place. According to this method, the Forudgah branch could not win the first place in 1000
iteration. The following figure shows the ranking frequency of branches. The horizontal axis represents for
braches' ranks and the vertical axis for frequency of ranks in 1000 iteration of the process.
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Figure 4. Frequency charts of the branches ranks
According to frequency charts, these tables are not lonely enough to decide on the best location. Thus, we
conducted an analysis of variance in order to find out whether the differences among the branches' score
ANOVA
means are statistically significant. Results for this test are provided in table 4.
Table 4. Analysis of variance test
Sc ore2
Sum of
Squares
Between Groups
16.172
W ithin Groups
15.551
Total
31.722
df
4
4995
4999
Mean Square
4.043
.003
F
1298.611
Sig.
.000
According to results of the one-way analysis of variance, the assumption of equity for score means of branches
is strongly rejected, because the resulting P-value is much smaller than the significance level of the test i.e. .05
(p-value = .000 < α = .05). Therefore, it can be concluded with the confidence coefficient of 95% that there are
significant differences among the relative score means of the five branches.
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After awareness of the significant difference among the score means of branches, it was determined that the
difference there exists between which one of the branches using the Duncan paired comparison test. Carmer
and Swanson (1973) indicated that the Duncan multiple range test is highly effective in revealing the real
difference between the means when we use the Monte Carlo simulation. Table 5 shows the results of this test.
Table 5. Duncan test result
Score 2
a
Duncan
Group
Ghasemabad
Forudgah
Hefdahshahrivar
Emamreza
Tolab
Sig.
N
1000
1000
1000
1000
1000
1
.13107
Subset for alpha = .05
2
3
4
5
.14177
.21300
.23113
1.000
1.000
1.000
1.000
.28302
1.000
Means for groups in homogeneous subsets are displayed.
a. Us es Harmonic Mean Sample Size = 1000.000.
As it can be seen, the results of Duncan test reveal that all the relative score means are
significantly different and each of them is classified in one distinct category. According to this test, Tolab branch
has the highest level with an average of .283 and Ghasemabad branch has the lowest level with an average of
.131. The box plot, which is shown in figure 5 obviously indicates the difference among the relative score
means of branches.
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Categ. Box & Whisker Plot
0.30
‫م يزان اه م ي ت ي ا وزن ن س ب ي در روش دو م‬
0.28
0.26
0.24
0.22
0.20
0.18
0.16
0.14
0.12
0.10
Tolab
Ghasemabad
Emamreza
Forudgah
Hefdahshahrivar
Mean
Mean±SE
Mean±1.96*SE
Figure 5. Box plot for comparing the importance of the five branches
DISCUSSION AND CONCLUSION
This study tried to identify the affective criteria in locating the bank branches. This was accomplished through
the literature review as well as interviewing with the heads, associates, and experts of Pasargad bank in
Mashhad. Obtained results indicated five main criteria including economic, place position, safety, accessibility,
and competition criterion. Each of these criteria, which include several sub-criteria are also discussed in detail
and can be seen in figure 1.
Another objective was to prioritize the location of new branches based on the obtained indicators. Obtained
criteria as well as the five candidate regions of Tolab, Hefdahshahrivar, Emamreza, Forudgah, and Qasemabad
were prioritized using the analytical hierarchy process and the best one was selected. Then, the Monte Carlo
simulation method was used as a complementary method in order to decrease errors, due to the large amount
of indicators and uncertainty in decision-making. By the group analytical hierarchy process, the branches'
scores were close to each other, which hardens the decision-making process, although the Tolab branch was
selected as the best, according to the both two methods. But, it is not so in the hybrid method as the conducted
statistical tests revealed a significant difference among the branches' scores.
This study focused on the banking industry in a limited scale. Time restrictions, lack of access to decisionmakers (headquarters unit), and lack of access to needed information impeded the comparing and scoring
processes. Besides this information, using the more precise information obtained from the GIS certainly will
result in the more accurate results. Furthermore, the above method can be utilized in the other sections of
banking and in the other industries. It is also proposed to use the other locating methods such as goal
programming, and the other multi-criteria methods, and to compare these methods in order to reach the most
practical method in locating of bank branches.
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