An empirical study on measuring operating efficiency and profitability of bank branches 10 10160377 2217(90)90002 s

282

European Journal of Operational Research 46 (1990) 282-294
North-Holland

Case Study

An empirical study on measuring operating
efficiency and profitability of bank branches
Muhittin O R A L and Reha Y O L A L A N

Sciences de l'Administration, Universitd Laval, Ste-Foy, QuObec, P.Q. G1K 7P4, Canada

Abstract: This paper discusses the methodology of an empirical study that was employed to measure the
operating efficiencies of a set of 20 bank branches of a major Turkish Commercial Bank offering relatively
homogeneous products in a multi-market business environment. The methodology was based on the
concepts and principles of Data Envelopment Analysis (DEA). The results of the study have indicated that
this kind of approach is not only complementary to traditionally used financial ratios but also a useful
bank management tool in reallocating resources between the branches in order to achieve higher
efficiencies. It has been also observed that the service-efficient bank branches were also the most profitable
ones, suggesting the existence of a relationship between service efficiency and profitability.

Keywords: Efficiency, productivity, performance evaluation, banking, mathematical programming

1. Introduction
The primary objective of measuring and
evaluating the operating efficiency of bank
branches in a competitive environment is not only
to position the branches with respect to each other
in terms of their efficiencies but also to gain
insight into the nature of operations so that

managerial measures can be taken to improve
their performance. More specifically, the method
of performance evaluation needs to be somehow
linked with the decision models in order to be able
to associate the results obtained with the decision
(Oral, 1986). This requires analytical techniques
that provide means of identifying the relative
strenghts and weaknesses of bank branches beyond those available from accounting and financial ratios.

Received November 1988; revised May 1989

Banks, especially in industrialized countries,
have been in search of new management tools to
improve their performance. Most frequently, they
have tried to achieve this by improving cash
management and offering new services that attract
additional funds. Management of operations has
been usually a secondary concern, partly because
this is considered, for some reason, to be less
critical to profitability. The importance of operating efficiency has been recently put into evidence
by a study done at Citicorp. According to one of
the findings of this study, a 1% decrease in operating expenses would have resulted in more than 2%
increase in net income and earnings per share
(Sherman and Gold, 1985).
The operating performance of a bank is usually
measured using accounting and financial ratios
such as return on assets, return on investments, or
similar ratios. These ratios of course provide a
great deal of information about a bank's finav_,:ial
performance when compared with prior periods

0377-2217/90/$3.50 © 1990 - Elsevier Science Publishers B.V. (North-Holland)


M. Oral, R. Yolalan / Operating efficiency and profitability of bank branches

and with other banks' performance. There are
however shortcomings of these measures. One is
that financial ratios fail to consider the value of
management's actions and investment decisions
that will affect future as opposed to current performance (Sherman and Gold, 1985). In other
words, financial ratios are short term measures
and therefore may not be appropriate to reflect
the real performance of a bank in the long run,
and they may be seriously misleading. Another
limitation is that financial ratios aggregate many
aspects of performance such as operations,
marketing, and financing. As Sherman and Gold
(1985) stated, a bank may appear to be performing well even if it is poorly managed on certain
of these dimensions, as long as it compensates by
performing particularly well on other dimensions.
It is necessary for management to identify and
develop means of improving branch performance.
For this purpose, other bank management tools
that compensate for the weaknesses in accounting
and financial ratios are needed. It seems that Data
Envelopment Analysis (DEA) is such an approach. The experience gained during this empirical study indicates that DEA can be considered as an alternative bank management tool to
traditional accounting and financial ratios since it
offers means of more comprehensively assessing
the operating efficiency of bank branches.

This paper empirically evaluates the use of the
DEA approach as a bank management tool to
improve the productivity of the branches of a
major Turkish Commercial Bank, and consists of
the following sections. The next section, Section 2,
briefly describes the principal characteristics of
DEA within the context of the banking sector.
Section 3 gives a background of the banking sector in Turkey in order to put the discussion in
perspective. Section 4 describes the procedure used
in applying the DEA method in 20 branches of
the Commercial Bank. Section 5 reports the resuits of the DEA evaluation of the 20 branches.
Finally, Section 6 concludes the paper.

2. The DEA approach in summary
DEA is basically a mathematical programming
technique initially developed by Charnes, Cooper,
and Rhodes (1978, 1979, 1981) to evaluate the
relative efficiency of public sector not-for-profit

283

organisations where accounting and financial
ratios are of little value, multiple outputs are
produced with multiple inputs, and the production
or standard i n p u t - o u t p u t relationships are neither
known nor easily identified. The term 'relative' is
rather important here since an organisation identified by the DEA technique as an efficient unit in a
given set may become an inefficient one when
evaluated in another set of organisations. What
DEA does in fact is this. It compares organisations' observed outputs and inputs, identifies the

relatively 'best practice' units to define the 'efficient frontier' and then measures the degree of the
inefficiency of the other units relative to the efficient frontier thus defined. Different mathematical forms of the DEA model have been suggested
in the literature. The formulation that was used in
this study is based on the following form:
Maximize

EB

E UrBYrB
r=l

=

E ViBX,B
i=1

subject to
E l"lrBYrj

ViBXij

r=l

<~ 1

i

for j = 1, 2 . . . . . N,
UrB, V,B>~e>O

Vr, i,

where
observed quantity of output r produced by
bank branch j,
observed quantity of input i used by bank
Xij
branch j,
UrB : the weight (to be determined) given to output r by the Base Branch B,
UiB : the weight (to be determined) given to input
i by the Base Branch B,
a sufficiently small positive number.
=

The linear fractional programming model above
can be transformed into an ordinary linear programming model by letting ~trB = turB and com =
tV,B, where t -1 =~'.~vmx m. Then the equivalent
DEA model, the DEA Model A henceforth, can
be stated as follows.
DEA Model A
R
Maximize

EB

=

E btrBYrB
r=l

(1)


M. Oral, R. Yolalan / Operating efficiency and profitability of bank branches

284

subject to
1

E ~iBXiB =

(2)

1,

i=1
R

I

~ ~rBY~j- ~ ~°~Bx~j~ 0
r=l

for j = l , 2

. . . . . N,

i~l

(3)
~ r B ' ~iB ~ E • 0

Vr,

i.

(4)

The DEA Model A above has the following
interpretation within the context of commercial
banking. There are N bank branches in the observation set M, each of which producing R different outputs using I different inputs, and we are
interested in determining the relative efficiency E B
of Base Branch B E ~ with respect to all other
branches in the set M. The relative efficiency E B
is nothing but the ratio of weighted outputs (also
termed virtual output) of the Base Branch B to its
weighted inputs (also termed virtual input). Such a
definition of efficiency transforms the multidimensional nature of inputs and outputs into a
single scalar ratio of single virtual output to a
single virtual input. The objective is to assign the
highest possible value to E B by comparing the
observed outputs and inputs of all bank branches
in the set ~ such that none of the bank branches
has an efficiency index greater than 1. This means
that the Base Branch B is allowed to determine the
values of/~B's and ~0~B's, but consistently due to
the constraints in (3), such that the results favour
the Base Branch B most. It is 'most favourable' in
the sense that ~B's and ¢0iB's are optimally determined from the viewpoint of the Base Branch B

and are used to calculate the efficiency of the
other branches in (3). Changing the Base Branch
B of course results in a different set of weights
and efficiency values. Although it is favourable to
the bank branch being evaluated, DEA Model A
still provides a means of consistently obtaining the
values of ~rB's and ~0~'s, which may not correspond to the values that a bank manager would
otherwise assign to outputs and inputs. Another
point to be made here is that E B ~< 1 since the
efficiency of the Base Branch B is also a member
of the constraint set in (3). In summary, the DEA
Model A provides an ex post evaluation of how
efficient the Base Branch B was with the actual
inputs xi~'s used to produce its actual outputs

y~a's without explicit knowledge of the input-output relationships or production function it used.
In this context, the data set consists of x~j's and
yrfs whereas the variable set is formed of #rB's
and ~oiB's. The application of the DEA Model A
requires a careful identification of inputs and outputs that is meaningful and feasible within the
framework of the competitive environment of
commercial banks.
A complete DEA analysis involves the solution
of N such programs as formulated in (1)-(4)
yielding N different (#~j, ~0ij) weight sets. In each
program, the constraints are held the same while
the ratio to be maximized is changed. Such an
analysis provides the following type of information for decision making purposes.
1. Each bank being evaluated will have a value
E B, 0 < E B ~< 1, obtained from the DEA Model A

indicating its efficiency level. If E B < 1, the branch
is inefficient compared to 'best practice' units in
the observation set ~ . If E B = 1, this is a relatively 'best practice' branch and therefore is identified as an efficient one. However, the branch so
identified as an efficient one is not necessarily
efficient in an absolute sense, it is simply not less
efficient than other branches in the observation
set ~ .
2. The DEA Model A will identify, from the
viewpoint of a Base Branch B, the 'efficiency
reference set' ~B or 'efficient frontier' which is a
subset of ~ that includes only those branches
with E = 1 from the observation set ~ . The Base
Branch B is compared against the branches in ~B
to find the sources of its inefficiency, if any. This
allows a bank manager to locate and understand
the nature of the existing inefficiencies by comparing h i s / h e r branch with a select subset of more
efficient branches. It therefore avoids the need to
investigate all branches to understand the existing
inefficiencies, and consequently helps allocate
limited managerial resources to areas where efficiency improvements are most likely to be
achieved.
3. The DEA Model A hence produces information with which managerial measures (reducing
the inputs used, or increasing the outputs produced) can be formulated to make an inefficient
branch relatively efficient.
These points will be more clearly illustrated
when the application of the DEA Model A is
discussed later in the text. The reader is also


M. Oral, R. Yolalan / Operating efficiency and profitability of bank branches

referred to Sherman (1984a, b), Sherman and Gold
(1985), and Parkan (1987) for similar arguments.
It is of great use, as will be seen later while
discussing the empirical results of this study, to
have the dual formulation of the DEA Model A
for formulating managerial measures to be taken.
Using XBj's as the dual variables corresponding to
the constraints in (3), Sr~B and s ~ ' s to the constraints fitrB> E and ~iB > E, respectively, in (4),
and Z a to the constraint in (2), we have the dual
formulation as follows:
Minimize

ZB - e

s[B + ~ s,.~
r=l

(5)

i=1

subject to
N

XB~y. - Y r B - sTB = 0,

r = 1, 2 . . . . . R,

(6)

j=l
N

-- E

~kBjXij -'b ZBXiB -- S~B = O,

i = 1 , 2 . . . . . I,

J=l

XBj>~0, SrB+>0,-/ Sm- >/0

Vj, r, i,

(7)
(8)

Z B unconstrained in sign.
The interpretation of the slack variables s+B
and S,B is as follows. If the optimal s+B* > 0, then
it is possible to increase output r by s+B* without
altering any of the h Bj values and without violating any constraints. Similarly, if s,~* > 0 then we
can reduce the use of input i from XiB to Xm -S,~*, again without altering any of the ?~Bj values
and without violating any constraints. The economic interpretation of the optimal Z~, on the
other hand, is that the Base Branch B must use
less of each input by a quantity that is equal to

(1 - z ~ )x,~ + s,B*

in order to become efficient. With this observation, the role of ~aj's becomes rather clear. The
'Composite Branch', which is the efficient branch
that the Base Branch B would like to become by
reducing its input usages by quantities of

(1 - Z ~ )X,B + S,~*,
can be defined in terms of the optimal hBy s.
More precisely, the 'Composite Branch' Pc is the
point that is given by

E x%pj,
jEJ#' B

285

where Pj is the point corresponding to the efficient branch j. Then ~ j can be interpreted as the
technical weight given to branch j in defining the
technology of the 'Composite Branch' Pc.
A final remark regarding the application of the
DEA Model A as formulated above is that the
efficiency thus identified (henceforth it will be
termed as " t h e locally most favourable efficiency"
since the reference set is determined by the Base
Branch B itself) will tend to understate, rather
than overstate, the inefficiency present. Any
managerial measure based on the implications of
such an efficiency index may not be sufficient to
completely remove the inefficiency present. A way
of partially avoiding this kind of overestimation is
to compare the efficiency of the Base Branch B

also with the efficiency of the 'global leader', the
bank branch which is identified as efficient by all
or almost all bank branches in the observation set.
Making 'the global leader' a member of the reference set forces the Base Branch B to compare
itself with a better branch while formulating its
managerial measures. The DEA model that will
yield 'the globally most favourable efficiency' can
be formulated as follows.

DEA Model B
R

Maximize

EB

=

E ]IrBYrB

(9)

r=l

subject to
1
E

i=l
R

iDiB :

(lO)

I,
1

E btrBYrj-- E WiBXij<~O
r=l

for j = 1, 2 . . . . . N,

i=1

(11)
R

1

E ~rBYrL -- E £OiBXiL = O,
r=l

(12)

i=1

/XrB, O~iB>/e>0

Vr, i,

(13)

where the subscript " L " denotes 'the global
leader'. The constraint in (12) is introduced simply
to force the Base Branch B to have 'the global
leader' in its reference set. To obtain a solution
from the DEA Model B, one needs to identify 'the
global leader'. In this study, this is done by following the steps below:


286

M. Oral, R. Yolalan / Operating efficiency and profitability of bank branches

Step 1: Find the efficiency reference set for
each and every bank branch using the DEA Model
A yielding the most favourable efficiency.
Step 2: Determine, for each and every bank
branch, the number of their appearances in the
efficiency reference sets.
Step 3: Identify the bank having the highest
number of appearances in the efficiency reference
sets. Suppose that is Bank Branch L. Hence, the
constraint in (12).
In reality, we need both DEA models in order
to determine the corrective actions to be taken
more realistically since the Base Branch B is forced
to compare itself with 'the global leader' as well.
In this empirical study, both of the models were

used in the performance evaluation of the bank
branches and in the formulation of managerial
measures.

3. Banking sector in Turkey: A background
This section addresses itself to a short description of the banking sector in Turkey for the purpose of providing a minimal background in order
to put later discussions in perspective.
From the viewpoint of operating efficiency of
banks, it is perhaps best to discuss the policies
governing the banking sector in Turkey in two
periods:
(i) the period prior to the National New Economic Policy introduced in January 1980, and
(ii) the period after January 1980.
During the period prior to January 1980 the
commercial banks of oligopolistic nature had
hardly faced any competition in terms of collecting funds and giving loans. As a consequence of
this, they had acted almost in a monopolistic
manner in determining the interest rates to be
applied to credits and to deposits. The typical
relationship between the interest rate I c charged to
credits, the interest rate I d paid on deposits and
the inflation rate I was almost always in the form
of ld < Ic < I. The economic implications of this
relationship were, in summary, threefold:
1. There was not much incentive for an average
person to deposit his/her savings in the commercial banks since I d < I. Therefore private savings
were mostly invested in real estate, or in company
shares, or simply in gold. In other words, private
savings were mostly channeled to construction

and industrial firms. The private savings deposited
in the commercial banks were usually short term
deposits to meet daily needs.
2. There was great incentive for industrial firms
to borrow since the inflation rate was always
considerably higher than the interest rate paid on
loans; that is, I > I c. Having revenue based on the
inflation rate and financial cost based on a lower
interest rate had only helped industrial firms improve their financial positions, without much need
to increase their capital. It was common practice
for any business-minded person to 'borrow and
invest' in industrial activities. This favourable
position of the industrial firms was further reinforced by the protectionist 'import-substitution'
policies of the governments of different economic
positions and by relatively large domestic demand
for industrial products.
3. The large difference I c - I d , compared with
those in industrialized countries, secured rather
handsome profits for the commercial banks in the
country, and hence gave confidence, perhaps overconfidence, to the banking sector. High profits
were attributed, without feeling much need for a
careful analysis, to the assumed skill of top level
bank managers. Not acknowledging the politicaleconomic context in which these handsome profits
were made did not help the commercial banks
very much to improve their productivity.
The new economic policies adopted in January
1980, which introduced the spirit of a free market
economy and competition, have not only had a
considerable impact on restructuring the national
economy but also on the way business is conducted in the banking sector. Like industrial firms,

the existing traditional commercial banks have
suddenly found themselves in fierce competition
not only with foreign banks but also with thousands of local financial firms of different sizes.
These local financial firms, although many of them
petitioned for bankruptcy shortly after coming
into existence, have successfully competed against
the traditional commercial banks by offering interest rates on deposits higher than the inflation
rate, which was something that never happened in
the recent economic history of Turkey. The impact
of this on the banking sector can be summarized
as follows:
1. The traditional commercial banks had to
offer competitive interest rates on savings accounts
in order to attract and maintain their clients


M. Oral, R. Yolalan / Operating efficiency and profitability of bank branches

against the new local financial firms. This competition has increased the cost of funds for the banks
and financial firms.
2. To maintain their usual level of profits, the
commercial banks had no alternative but to charge
higher interest rates to their industrial customers
which have been accustomed to use inexpensive
credits rather than their own financial resources.
Faced with paying high interest rates on credits,
even higher than the inflation rate for the first
time, industrial firms have not only tried to reduce
their financing costs by decreasing credit requests
from the banks but also increased their capital by

issuing new shares to the public with very favourable payment plans, thus becoming serious competitors of banks and financial firms in collecting
funds.
3. The new economic policies seem to serve the
average person with savings rather well by offering several attractive alternatives for investment.
Even the trend to invest in real estate has been
considerably reversed during this period in favour
of deposits. The commercial banks, on the other
hand, seem to suffer, at least temporally, from the
new economic system, especially in maintaining
their accustomed level of profits since the rate of
increase for credit applications has dropped, thus
cutting down the revenue sources of commercial
banks.
The points discussed above can also be observed from the relevant statistics. The annual
percentage increase in credit applications shows
first a sharp decline starting in 1981, from 66.6%
to 39.2%, and continues to decrease down to the
level of 29.4% in 1984. This is mainly due to the
reluctance of industrial firms to borrow money
from the commercial banks because of t h e high
interest rates charged on loans. Having less than
usual credit applications has resulted in a profit
squeeze for the commercial banks. The profit increase rate in constant prices suddenly dropped
from 267% in 1980 down to 70% in 1981. Even
negative profit increase rates (meaning profit decreases in constant prices) were observed in 1982
and in 1983.
In order to improve their weakened positions
the commercial banks have tried to make their
services accessible to customers even in remote
regions in the country by rapidly increasing the

number of their branches. The commercial banks
increased their branches from 2862 in 1976 to

287

3351 in 1986, meaning at least 489 new branches
in a decade. This has certainly contributed to
increases in deposits, but at the cost of paying
higher interest rates due to the competition and at
the cost of investing in new branches. Also realized during this period was the importance of
operating efficiency of bank branches, an aspect
constantly overlooked before.

4. The field study
The Commercial Bank (henceforth simply "The
Bank") for which this study was done is one of the
major national banks operating in Turkey and
employs around 9500 personnel in its 583 branches
of different sizes. The executives of The Bank have
distinguished themselves, through the years, as
managers most receptive to new banking technology and management tools. They have initiated
many studies, especially after the introduction of
the National New Economic Policy in January
1980, in order to improve the performance of the
branches and provide high levels of service to their
client. The DEA study being reported here is one
of the studies initiated in that epoch.
Before going into the discussion of the empirical study done, it may be most appropriate to
comment on the nature of the previous applications of the DEA models. Initially, DEA models
were used to assess the relative efficiency of notfor-profit organisations such as schools (Bessent

and Bessent, 1980, Bessent et al., 1982, Bessent et
al., 1983), hospitals (Nunamaker, 1983, Banker,
Conrad and Strauss, 1986, Sherman, 1984a, b),
courts (Lewin, Morey and Cook, 1982), public
projects and programs (Charnes, Cooper and
Rhodes, 1981), the military (Bowlin, 1987), etc.
Through time, however, the application of DEA
models has been extended to cover for-profit
organisations as well. The most noticeable among
these application studies are the ones reported by
Byrnes, F~ire and Grosskopf (1984), Sherman and
Gold (1985), Parkan (1987), and Byrnes and Fare
(1987). In all these applications, the DEA models
used were basically some versions of the type A
given in (1)-(4). This study, on the other hand,
employed both the DEA Model A and the DEA
Model B in order to suggest more realistic measures by comparing the performance of the base
branch with those of 'the local leaders' (DEA


M. Oral, R. Yolalan / Operating efficiency and profitability of bank branches

288

Model A) and 'the global leader' (DEA Model B).
Moreover, the possible relationship between
service efficiency and profitability of bank
branches was also investigated. This was done by
considering different combinations of inputs and
outputs.

The steps followed in conducting the field study
and their brief descriptions are given below.

Step 1. Selection of Bank Branches for the Study:
It seems that the DEA models are most meaningful when they are applied to observation sets of
units or organisations providing similar services
and using similar resources. By the same argument, it makes little sense to compare very large
bank branches to very small ones since there will
be rather considerable differences in the services
rendered and the resources used. The homogeneity
requirement was taken into consideration while
forming the observation set of this study. The first
20 bank branches (all in Istanbul) having a ranking score S between 61-80 were selected to form
the observation set ~ for this study. The ranking
score Sj, 0 ~< Sj ~< 100, of bank branch j is given
by
sj = wDDj + wL/ j +

+ wK/(j + wMMj,

where

W.

the points assigned to bank branch j using
a predetermined function mapping the
amount of money deposited in the bank
branch on a scale of 0-100,
the points assigned to bank branch j using
a predetermined function mapping the

amount of loans given to clients in the bank
branch on a scale of 0-100,
= the points assigned to bank branch j using
a predetermined function mapping the
amount of foreign exchange transactions in
the bank branch on a scale of 0-100.
= the points assigned to bank branch j using
a predetermined function mapping the
amount of profit made in the branch on a
scale of 0-100,
= the points assigned to bank branch j using
a predetermined function mapping the number of personnel in the bank branch on a
scale of 0-100,
the positive weights, the sum of which is
equal to unity, given to the above factors.

Step 2. Identification of Input and Output Sets:
As mentioned earlier this study addressed itself
not only to assess the service efficiency of bank
branches but also to analyse their profitability.
Therefore, two sets of inputs and outputs were
needed; one set for service efficiency assessment,
and one for profitability analysis.
The input set for service efficiency assessment
consisted of five elements:
xa =
x2 =
x3 =
x4 =
x 5=

the
the
the
the
the

number
number
number
number
number

of
of
of
of
of

personnel,
on-fine terminals,
commercial accounts,
saving accounts,
credit applications.

The first two items, usually under the direct
control of bank managers in the short run as well
as in the long run, are widely used factors as
inputs in most DEA applications in banking sector. The last three items, which are usually influenced in the long run, are also frequently used
factors, but as outputs rather than inputs. The

reason for using them as inputs in this study is to
reflect the steady state market conditions which
have been established through years. In other
words, the equilibrium state achieved (or the cliental infrastructure developed) i n the market as a
result of the previous efforts and achievements in
obtaining and maintaining clients was considered
to be the market structure or environment provided to the bank branch, and hence an input to
the current operations.
On the output side of service efficiency assessment, although 11 different outputs were initially
identified, a set of only four outputs was considered; namely,
y~ = the amount of time spent on general service
transactions (accounting, control, information, transfers, payments),
Y2 = the amount of time spent on credit transactions (contracts, guarantees, credit and risk
related procedures),
Y3 = the amount of time spent on deposit transactions (commercial accounts, saving accounts),
Y4 = the amount of time spent on foreign exchange
transactions.
Observe that the outputs above are measured in

time units. Traditionally, it is the number of transactions that is used in DEA applications. There
were two reasons for quantifying outputs in time


M. Oral, R. Yolalan / Operating efficiency and profitability o f bank branches

units. First, the results of this D E A analysis were
to be compared with those obtained from The
Performance Evaluation Model (referred to as
PEM henceforth), a model already in use in The
Bank and its outputs are measured in time units.

Second, it was observed that there is a strong
relationship between the annual number of transactions of a particular type and the annual total
time spent on these transactions.
Given the fact that the commercial banks are in
business also for profit, it is quite legitimate to ask
whether achieving a high level of service efficiency
implies a high level of profitability as well. To
investigate this, the DEA Models A and B were
used, this time with a different set of inputs and
outputs in monetary units. The input set for profitability assessment consisted of four main items:
xI =
x 2=
x 3=
x4=

personnel expenses,
administrative expenses,
depreciation,
interests paid on deposits.

Note that the inputs above correspond to major
cost items of bank operations. The output set of
profitability assessment, on the other hand, included only two items which accounted for a
sufficiently large part of total income of a bank
branch; namely,
y~ = interests earned on loans,
Y2 = non-interest income.
With the above sets of inputs and outputs for
profitability assessment, it is clear that the ratio
Table 1

Input-output

combinations

for service efficiency assessment

Inputs and outputs

Combinations

a

(1)

(2)

(3)

(4)

(5)

xl = number of personnel

+

+

+

+

+

x 2 = number of terminals

+

+

+

+

+

x 3 = number of commercial accounts

+

+

-

x 4 = number of saving accounts

+

+

-

x 5 = number of credit applications

+

+

+

+

+

x6 = x3+ x4

--

+

+

--

+

+

y~ = t i m e o n g e n e r a l s e r v i c e s

+

Y2 = t i m e o n c r e d i t s

+

+

+

Y3 = t i m e o n d e p o s i t s

+

+

+

Y4 = t i m e o n f o r e i g n e x c h a n g e

+

+

y s = yl + y4
y6=y~+y2+Y3+y4

289

Table 2

Input-output

combinations

Inputs and outputs

for profitability assessment
Combinations

a

(1)

(2)

x~ = p e r s o n n e l e x p e n s e s

+

+

(3)
+

x 2 = administrative expenses

+

+

-

x 3 = depreciation

+

+

-

x 4 = interests paid

+

+

+

X 5 =

--

_

+

Yl = i n t e r e s t s e a r n e d

+

-

+

Y2 = n o n - i n t e r e s t i n c o m e

+

-

+

y 3 = yl + y2

--

+

-

a

+

X 2 +

(_)

x 3

implies the inclusion (exclusion) of the variable.

appearing in the objective functions of DEA models is nothing but the ratio of weighted sum of
revenues to weighted sum of expenses, hence an
index of profitability.
Step 3. Calculation of Efficiencies: Two series of
calculations were made, one for service efficiency
and one for profitability. In each case, different
combinations of inputs and outputs were used in
order to investigate their possible impact on efficiency index. The i n p u t - o u t p u t combinations
that were considered are given in Tables 1 and 2.
The different combinations of inputs-outputs
allowed us to investigate how much the efficient
frontiers differed from one another. This was
needed to have a reasonable level of confidence in
the managerial suggestions to be made later based
on these results.

Step 4. Identification of the Sources of Inefficiencies: Based on the efficiency calculations and
efficiency reference sets, the weaknesses of the
inefficient bank branches were identified, albeit in
general terms. This was done with respect to service
efficiency and profitability.
Step 5. Formulation of Suggestions: As a final
step of the study, a set of managerial suggestions,
thought to be most likely to improve the performance of the inefficient bank branches, was formulated.

5. Empirical results

+

+

a + ( _ ) implies the inclusion (exclusion) of the variable.

+

This section includes not only a discussion and
interpretation of the computational results but
also some observations and comments on the
methodology employed in this empirical study.


M. Oral, R. Yolalan / Operating efficiency and profitability of bank branches

290

First, we shall present the general observations
and findings and then the managerial implications
of the computational results.

5.1. General observations and findings
The DEA models used in this study were instrumental in reaching the following conclusions:
1. Although there are suggestions in the pertinent literature as to which input-output combinations should preferably be used in measuring the
operating efficiency of bank branches, it is not
very evident that these are the ones always to be
used regardless of the competitive environment
and organisational nature of bank branches. In
this study, therefore, different input-output combinations were considered to find out the most
meaningful one. From Table 3, it can be observed
that Combination (5) seems to have the capacity

to better discriminate the bank branches according to service efficiency assessment. Observe that
only 4 efficient bank branches were identified with
Combination (5) opposed to 11, 10, 9, and 5
efficient bank branches with the Combinations
(1), (2), (3), and (4), respectively. Having 10-11
efficient bank branches, as in the cases of Combi-

nations (1) and (2), in a set of 20 members is not
of much help in comparing and contrasting the
efficiencies of the bank branches since almost
every bank branch has a perfect or near perfect
efficiency score. As a result of this observation,
Combination (5) was chosen as the input-output
combination to analyze the service efficiency of
bank branches. A similar approach was also used
in determining the i n p u t - o u t p u t combination for
profitability analysis and Combination (1) was
chosen for this purpose.
2. As can be easily observed from Table 6,
according to service efficiency assessment the bank
branches 12, 16, 17 and 20 consistently appear in
the efficiency reference sets, implying that all the
branches seem to have agreed that these four
branches are the efficient ones. Similarly, the most
efficient branches according to profitability assessment are 11, 12, 16 and 20.
3. As mentioned earlier both DEA Model A
and DEA Model B were used in this study. For
service efficiency assessment Model B was based
on Bank Branch 16, 'the global leader', since it
has appeared 17 times in the efficient reference

sets, implying that 17 bank branches out of 20
identified it as efficient for service efficiency (see

Table 3
The DEA efficiency results
Bank
branches

(1)

Service efficiency combinations
(2)

(3)

(4)

(5)

(1)

Profitability combinations
(2)

(3)

1
2
3
4

5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20

1.00
0.71
1.00
0.98
1.00
0.96
0.87
1.00
0.70
0.88
1.00
1.00
1.00

1.00
0.99
1.00
1.00
0.78
0.80
1.00

1.00
0.71
1.00
0.99
0.97
0.96
0.87
0.87
0.66
0.88
1.00
1.00
1.00
1.00
1.00
1.00
1.00
0.78
0.80
1.00

1.00

0.71
0.96
0.98
0.97
0.96
0.84
0.82
0.65
0.88
1.00
1.00
1.00
1.00
1.00
1.00
1.00
0.78
0.80
1.00

0.93
0.64
0.88
0.90
0.81
0.77
0.83
0.77
0.66
0.75

0.93
1.00
0.97
1.00
0.89
1.00
1.00
0.73
0.61
1.00

0.93
0.64
0.88
0.90
0.81
0.77
0.83
0.92
0.64
0.75
0.93
1.00
0.93
0.99
0.89
1.00
1.00
0.73
0.61

1.00

0.32
0.56
0.20
0.50
0.19
0.36
0.44
0.35
0.73
0.35
1.00
1.00
0.34
0.46
0.62
0.98
0.62
0.23
0.31
1.00

0.11
0.41
0.15
0.27
0.12
0.34
0.19

0.20
0.55
0.24
1.00
1.00
0.22
0.43
0.60
0.50
0.56
0.15
0.27
0.60

0.31
0.53
0.20
0.44
0.18
0.36
0.37
0.32
0.64
0.33
1.00
1.00
0.31
0.46
0.79
0.79

0.62
0.22
0.30
1.00


M. Oral, R. Yolalan / Operating efficiency and profitability of bank branches

Table 6). As for profitability, Bank Branch 11,
which has appeared 17 times in the efficiency
reference sets, was chosen as 'the global leader'
for the DEA Model B. It has been observed that
the /~r*~
A and c0*BA values obtained from DEA
Model A were sufficiently close to the ~rB
,B and
~o*BB values, respectively, obtained from DEA
Model B, indicating that the Base Branch B was
quite realistic and not favouring itself very much
in estimating the weights to be assigned to inputs
and outputs. Or, equivalently, the differences/~rB*A
.B
-/LrB and ¢0"~A -~0*BB were too small to make a
distinction between DEA Model A and DEA
Model B. Although in this particular empirical
study two DEA models are not, for practical purposes, distinguishable from one another, this might
not be the case in all real life settings, and therefore it is always wise to consider the DEA Model
B in applications in order to find out whether one
has the tendency to overstate its own efficiency
compared to the one of the 'the global leader'.

This kind of precaution will only help to formulate more realistic managerial measures.
4. It has been also observed that there seems to
be a close relationship between the service efficiency and profitability of a bank branch. In
general, a bank branch realizing lower profit may
not be necessarily performing less efficiently than
the ones with high profits. In other words, the
bank branches may not be very efficient in transaction activities but may be quite profitable, or
vice versa. The results of this study however show
that the service-efficient branches are also profitable. Having such a relation between service efficiency and profitability has increased the confidence of The Bank managers in the DEA models
used.

5.2. Computational results
In the light of the general observations and
comments made above, we will present the computational results obtained from the DEA Model
A using Combination (5) (inputs xl, x2, x 5 and
x 6 and output Y6) for service efficiency, and Combination (1) (inputs x 1, x 2, x 5 and x 6, and output
Y6) for service efficiency, and Combination (1)
(inputs Xl, x 2, x 3, x 4 and outputs Yl, Y2) for
profitability and their managerial implications.

291

The analysis of the findings will be presented in
two groups:
(i) global analysis,
(ii) detailed analysis.
(i) Global analysis: From Table 3 above it is
clear that Bank Branches 12, 16, 17, and 20 are the
service-efficient ones whereas Bank Branches 19,
2, 9, and 18 are the most inefficient four. A

comparison of the characteristics of the group of
efficient branches with those of most inefficient
ones has revealed the following:
1. The efficient branches turned out to be relatively new compared to the inefficient ones. The
average age of an efficient branch is 15 years,
compared with 23 years in the case of inefficient
ones. This is perhaps partially due to the dynamics
of the national economy in general and to the high
rate of urbanization process in particular, which
imply the demand for banking services is not only
increasing but also shifting from one location to
another. The latter forces commercial banks to
open new branches in newly urbanized sections of
the cities and towns to increase or maintain their
market shares.
2. The efficient branches employ, on the average, less personnel than the inefficient ones, 20
personnel opposed to 25.5. This is also true for the
average number of on-line terminals used, 6.25
against 7.25 in favour of the efficient branches.
3. In terms of the factors shaping the steady
state market conditions (the number of saving and
commercial accounts, and the number of credit
applications), an efficient branch, on the average,
has less accounts (3714) compared to an inefficient one (5962). This result is quite normal since
the efficient branches are relatively new and therefore they have not been in the market long enough
to capture as many accounts as the inefficient
ones have, which are relatively older. Although the
average number of accounts seems to be lower for
an efficient branch (3714 vs. 5962), the number of
transactions per account, on the other hand, is

much higher (25.3 vs. 15.2). Even though efficient
and inefficient branches have approximately the
same level of deposit in monetary units, the average amount of deposits per account is 1.80 times
higher in the efficient branches. In other words,
the efficient branches have accounts which are
'active', meaning there is a spatial shift in demand
for banking services. This in fact is in agreement
with the above observation regarding economic


292

M. Oral, R. Yolalan / Operating efficiency and profitability of bank branches

and urbanization dynamics prevailing in the country. Similar arguments are also valid for the number of credit applications.
With respect to profitability, again from Table
3, it can be seen that Bank Branches 11, 12, 16,
and 20 are relatively the most profitable ones
whereas Bank Branches 5, 3, 18, and 19 are the
least profitable four. A comparison of the characteristics of the group of efficient branches with
those of least profitable ones has revealed the
following:
1. The relatively most profitable branches were
able to make less revenue (on the average 48%
less) compared to the inefficient ones, on foreign
exchange transactions. This again, as in the case of
service efficiency, may be attributed to the age
differences between relatively more profitable and
less profitable branches. In other words, although
the older branches are in better position to attract

foreign transactions, the newer ones are still capable of making more profits.
2. As for the administrative expenses, the relatively most profitable branches spend more (18%
more on the average) compared to the least profitable ones. This disadvantageous position of the
relatively most profitable branches seems to be
recovered by their high level of service operations.
3. However, in the end analysis, the relatively
most profitable bank branches are, on the average,
three times more profitable.
(ii) Detailed branch analysis: To show a detailed branch analysis can be performed, we will
focus on the case of Bank Branch 19 which is
identified as inefficient, with E ~ = 0.610 service
efficiency and with E ~ = 0.309 profitabihty. As
can be seen from Table 6, the efficiency reference
set of Bank Branch 19 consists of Bank Branch 12
and Bank Branch 16 for service efficiency. The
'Composite Branch', which is the hypothetical efficient branch that Bank Branch 19 would like to
become, can be defined in terms of these two
efficient branches. Recalling that the Composite
Branch is a linear combination, in which the coefficients are the dual variables X~j, of the members
of the efficiency reference set, we can write
XiC =

~BI2Xi12 -I- hB16Xil6

(14)

for input i, where X~c is the amount of input i
needed at the Composite Branch C. Put differently, X,c'S are the amounts of inputs that Bank

Table 4

Excess use of inputs by Bank Branch 19 (service efficiency
assessment)
Inputs

Composite
branch
(1)

Branch 19 Excess use
actual
of inputs
(2)
(2)-(1)

x1=
x2=
x5=
x6 =

14.0
3.6
52.0
2485.0

23.0
6.0
85.0
6260.0

personnel

terminals
credit applications
accounts

9.0
2.4
33.0
3775.0

Branch 19 should have been using to produce the
same amounts of outputs currently being produced in order to be considered as efficient. More
specifically, the amounts of input Bank Branch 19
should have been using are
X l c = ( 0 . 0 1 8 ) (22.0)

+ ( 0 . 5 6 9 ) (24.0)

=

x2c = (0.018) (9.0)

+ (0.569) (6.0)

=

3.6,

=

52.0,

X 5 c = ( 0 . 0 1 8 ) (225.0) + ( 0 . 5 6 9 ) (84.0)

14.0,

X6c = (0.018) (2961.0) + (0.569) (4271.0) = 2485.0.

To clearly see the sources of the service inefficiency of Bank Branch 19, Table 4 is prepared
by using the formulas in (14) with X~l 2 = 0.018
and ~ 1 6 ~---0.569.
It is clear from the third colunm of Table 4 that
Bank Branch 19 is currently using more of every
kind of input compared to the Composite Branch.
Take, for instance, the number of personnel actually used and the number of personnel suggested
by the DEA model. The difference of 9 persons
being identified as excess personnel in a branch of
23 persons is rather significant by any standards.
Even The Bank's own performance study, the
PEM, indicates that the number of personnel
needed in Bank Branch 19 is to be reduced from
23 to 19. Although the PEM number is larger than
the one suggested by the DEA model, the managers
argued that the 'excess' personnel so defined can
be used for marketing activities. Consequently, 19
persons were assigned to Bank Branch 19 for the
following year.
In fact, the comparison of the PEM results with
those of the DEA model was not only made for
Bank Branch 19, but for every single one of the 20
branches selected for the study. It has been observed that the DEA results almost always suggested less personnel than the PEM study. Although there were differences between the numbers given by the two methods, the suggestions

M. Oral, R. Yolalan / Operating efficiency and profitability of bank branches

made were in the same directions in the sense that
one method did not propose an increase while the
other was indicating a decrease in the use Of
personnel, or vice versa. In other words, the two
methods agreed in general suggestions, but deviated in specific recommendations. This observation
was quite useful in making final decisions regarding the number of personnel to be assigned to
each branch. As a general policy, which is the end
product of the PEM and the DEA model, it has
been suggested that the number of personnel in
efficient branches is to be increased while it is to
be decreased in inefficient ones. This is to be done
however by transferring personnel from inefficient
branches to efficient ones within the constraints of
the collective bargaining.
A similar argument was used in determining
the number of on-line terminals to be put in each
branch. The other remaining inputs, the number
of accounts and credit applications, are the kind
of inputs no bank would ever like to see decreased. The meaning of the excess use of bank
accounts in the context of this study is simply that
there are too many dormant accounts in Bank
Branch 19 and these accounts are to be made
more active. It is possible that the owners of these
accounts are using other banks as well. This is
why the 'excess' personnel was suggested to be
used to improve the relations with the clients in

the hope of making the dormant accounts active
again.
The performance evaluation of Bank Branch 19
was also done with respect to profitability. The
results of this analysis are given in Table 5. The
Composite Branch, which is the combination of
Bank Branches 11, 12, and 20 with the values
k~n = 0.096, k~l 2 = 0.120 and k~20 = 0.0027, indicates that Bank Branch 19 is over spending for
Table 5
Excess use of funds by Bank Branch 19 (profitability assessment)
Inputs

Composite
branch
(TL 106)
(1)

x 1 = personnel expenses 10.2
x 2 = administrative
expenses
4.5
x 3 = depreciation
1.9
x 4 = interests paid
60.4

Branch 19
actual
(TL 106)
(2)

Excess use
ofinputs
(TL 106)
(2)-(1)

42.8

32.6

14.4
6.7
195.4

9.9
4.8
135.0

293

Table 6
Bank

Service efficiency

Profitability

branches

Combination(5)

Combination
(1)

Ea

Reference set

En

Reference set

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18

19

0.93
0.64
0.88
0.90
0.81
0.77
0.83
0.92
0.64
0.75
0.93
1.00
0.93
0.99
0.89
1.00
1.00
0.73
0.61

{16, 20}
(12,16}
(12,16}
{12,16}
{12,16}
{12,16}
{16,20)
{12,16}

{12,16,17}
{12,16}
(12,16}
{12}
{16, 20}
{12,16}
{12,16}
{16}
{17}
{12,16}
{12,16}

0.32
0.56
0.20
0.50
0.19
0.36
0.44
0.35
0.73
0.35
1.00
1.00
0.34
0.46
0.62
0.98
0.62
0.23

0.31

{12, 20}
{11,12,20}
{11,20}
{11,12,20}
{11,12, 20}
{11,12}
{11,12,20}
{11,12,20}
(11,12,20}
{11, 20}
{11}
{12}
{11,20}
{11,12}
{11,12}
{11,12,20}
(11,'12}
{11,12, 20}
{11,12, 20}

20

1.00

{20}

1.00

{20}

its level of profitability. More specifically, for the
level of profit currently being made, Bank Branch
19 needs to cut its personnel expenses by 76%, the
administrative expenses by 69%, the depreciation
by 72%, and the interests paid by 70% in order to
become efficient. These imply, as in the case of
service efficiency assessment, reductions to be
made in personnel and banking equipment.

6. Discussion and conclusion

The DEA methodology used in this empirical
study seems to have increased the chances of
implementing the findings. One indication of this
is the fact that The Bank has decided to enlarge
the scope of the study by increasing the number of
branches from 20 to 44 to be included in the next
study. The results of this new study will be reported in the future.
It has turned out to be rather meaningful and
useful to consider different combinations of inputs
and outputs in evaluating the efficiencies of the
bank branches. First, it led to a combination that
was most discriminative in assigning efficiency
values to the bank branches. This greatly helped
to clearly identify the efficient bank branches from


294

M. Oral, R. Yolalan / Operating efficiency and profitability of bank branches

the inefficient ones. Second, having considered
different input-output combinations, the managers of The Bank felt more comfortable with the
way the study was conducted and had more confidence in the results.
Although the DEA Model A and DEA Model
B were not, for practical purposes of this empirical
study, distinguishable from one another, it was
decided to use again both of them in the next
study covering 44 bank branches in order to find
out whether there is a tendency among the member branches to overstate their efficiencies.
As a conclusion, it can be claimed that the
DEA approach is not only complementary to
traditionally used financial ratios to evaluate performance but also a useful bank management tool
in reallocating the resources between the branches
in order to achieve higher operating efficiencies.

Acknowledgements
The authors wish to express their gratitude to
Mr. S. Altun, Mr. O. Emirdag, and Dr. I. Pekarun,
Vice-Presidents of the Yapi ve Kredi Bankasi, for
their continuous support and encouragement
throughout the study. Special thanks are also due
to Mr. S. YSriik of the same bank and to Dr. M.
Karayel of the US International Leasing Co.,
Richmond, CA, for their help and suggestions in
formulating the DEA models and interpreting the
result obtained therefrom.

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