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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 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 gives a background of the banking sector in Turkey in order to put the discussion in perspective Section describes the procedure used in applying the DEA method in 20 branches of the Commercial Bank Section reports the resuits of the DEA evaluation of the 20 branches Finally, Section concludes the paper 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 ~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 E ~iBXiB = (2) 1, i=1 R I ~ ~rBY~j- ~ ~°~Bx~j~ r=l for j = l , N, i~l (3) ~ r B ' ~iB ~ E • 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 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 ~< 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 Each bank being evaluated will have a value E B, < 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 ~ 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 = 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 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, R, (6) j=l N E ~kBjXij -'b ZBXiB S~B = O, i = , 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,~* > 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 E i=l R iDiB : (lO) I, E btrBYrj E WiBXij/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 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: 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 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 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: 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 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 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 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 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, ~< 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 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 Input-output combinations for service efficiency assessment Inputs and outputs Combinations a (1) (2) (3) (4) (5) xl = number of personnel + + + + + x = number of terminals + + + + + x = number of commercial accounts + + - x = number of saving accounts + + - x = 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 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 = administrative expenses + + - x = depreciation + + - x = interests paid + + + X = _ + 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 = yl + y2 + - a + X + (_) x 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 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 and 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 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 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 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: 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 efficient bank branches were identified with Combination (5) opposed to 11, 10, 9, and 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 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 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 The DEA efficiency results Bank branches (1) Service efficiency combinations (2) (3) (4) (5) (1) Profitability combinations (2) (3) 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 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 and x and output Y6) for service efficiency, and Combination (1) (inputs x 1, x 2, x and x 6, and output Y6) for service efficiency, and Combination (1) (inputs Xl, x 2, x 3, x 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 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: 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 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 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: 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 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 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 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 = ( ) (22.0) + ( ) (24.0) = x2c = (0.018) (9.0) + (0.569) (6.0) = 3.6, = 52.0, X c = ( ) (225.0) + ( ) (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 is prepared by using the formulas in (14) with X~l = 0.018 and ~ ~ -0.569 It is clear from the third colunm of Table 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 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 The Composite Branch, which is the combination of Bank Branches 11, 12, and 20 with the values k~n = 0.096, k~l = 0.120 and k~20 = 0.0027, indicates that Bank Branch 19 is over spending for Table Excess use of funds by Bank Branch 19 (profitability assessment) Inputs Composite branch (TL 106) (1) x = personnel expenses 10.2 x = administrative expenses 4.5 x = depreciation 1.9 x = 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 Bank Service efficiency Profitability branches Combination(5) Combination (1) Ea Reference set En Reference set 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 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 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