Cross Firm Bank Branch Benchmarking Using Handicapped" Data Envelopment Analysis to Adjust for Corporate Strategic Effects

Transcription

1 Cross Firm Bank Branch Benchmarking Using Handicapped" Data Envelopment Analysis to Adjust for Corporate Strategic Effects Zijiang Yang School of Analytic Studies & Information echnology Atkinson Faculty of Liberal & Professional Studies York University Joseph C. Paradi Centre for Management of echnology and Entrepreneurship University of oronto Abstract In today s economy and society, performance analyses in the services industries attract more and more attention. However, the traditional Data Envelopment Analysis (DEA) approach requires a consistent operating environment that one may deem as the culture. In reality, there is an especially important situation when the units belong to different organizations and the groups of units can not have the same culture. his reality challenges the traditional methods of applying DEA theory to realworld cases. A new technology was developed that allows efficiency evaluation by benchmarking three different banks branches in the city of Mississauga, Canada, using DEA. his new approach overcomes the above limitation by introducing a mathematically handicapped DEA model. Using this development, cultural differences due to corporate management's policies can be adjusted for. Finding a handicapping function which can fairly assess the large Canadian banks managerial and business strategy differences was another contribution of this work.. Introduction In today s highly competitive economy and a society where consumers demand a very high level of service, performance analyses in the services industries attract more attention than ever. Since Sherman and Gold [9] wrote the first significant DEA bank analysis paper, DEA has become a leading approach for performance analysis in the services industry as in [][5][][4]. However, traditionally, DEA analyses require a consistent infrastructure and operating environment which we may deem as the culture in which the entities, appropriately called Decision Making Units (DMUs), operate. In reality there is a need to compare DMUs where some units may have an advantageous environment which the others cannot adopt; hence, the comparisons are not always fair. his reality challenges the traditional methods of applying DEA theory to real-world cases. Although Banker and Morey [3] introduced categorical inputs and outputs, their development rests on the assumption that there is a natural nesting or hierarchy of categories. he same authors [4] had also dealt with the relative technical and scale efficiencies of decision making units when some of the inputs or outputs are exogenously fixed and beyond the discretionary control of the DMU managers. However, these approaches do not cover all of the instances where benchmarking is desirable but the operational issues arising from corporate action and/or policies can not be represented by exogenous variables because realistic situations may not have a natural representation at discrete levels. Cooper at al. [9] introduced a method to do the crosssystem comparisons. hey make use of a mixed integer LP (linear programming) formulation with binary variables to evaluate DMUs in different systems. Furthermore, Lozano-Vivas et al. [3] incorporate environmental variables directly into the basic DEA model since adding variables to the DEA model raises the efficiency s. heir method of adding environmental factors guarantees that only the efficiency s of DMUs with poor environmental conditions can change. his approach /6/$2. (C) 26 IEEE

2 has a pre-requisite: they must know in advance the type of influence each environmental variable has on the efficiency s. In other words, each uncontrolled factor must have an influence of known orientation. his paper provides an alternative way to adjust the input and/or output levels of a group of DMUs and bring them to a level which resembles a common corporate environment before benchmarking them. We named this the Handicapping Function to signal that its purpose is to set all players in an operational framework where their head office policies are neutralized and the operating units are compared solely on a basis that would exist if they all belonged to the same firm. For more clarity, after the handicapping function is applied, all DMUs should be comparable only on their actual performance without corporate policy issues obscuring managerial performance. he banking industry is of great importance to every one of us, but it is not independent of the economy and society surrounding it. All the economic, political and social changes we experience exert important influences on the banks. Canadians enjoy services from 49 banks, domestic and 38 foreign bank subsidiaries, which manage over $.4 trillion (CAD) in assets. hey serve Canadians with 222, employees, 8,4 branches and 6,6 ABMs [6]. Banks are very heavily regulated in Canada. he Bank Act, first enacted in 87 and is renewed every years, defines what the banks can and cannot do. Moreover, the Office of the Superintendent of Financial Institutions (OSFI), Canada s federal financial supervisor, monitors the banks operations. Subject to the regulations, each bank can adopt any strategy it deems appropriate to maximize their profits. With the availability of new technology and the Internet, more and more organizations are entering some aspect of the banking business and this has resulted in intense competition in the financial services markets. Major domestic banks continue to pursue all the opportunities available to them to enhance their competitiveness. Consequently, performance analysis in the banking industry has become and integral part of their management practices. op bank management wants to identify and eliminate the underlying causes of inefficiencies, thus helping their firms to gain competitive advantage, or, at least, meet the competitive challenges from others. Although the largest 5 Canadian banks control the banking scene in Canada and at times are said to be acting as an oligopoly, they do compete vigorously with each other and everyone else. While they all do many similar things and therefore, from a retail client's point of view, there is not a lot to choose between them, their corporate policies do affect the branches. For example, ScotiaBank is a prominent multinational bank operating in 45 Countries; D Financial Group operates the second largest discount securities broker in the world; and BMO Financial Group carries on a significant U.S. banking business. hese strategies (and others like them) do effect how their branches operate since the branches either benefit from or suffer from some business opportunity/difficulty offered/caused by their head office strategies. Unfortunately, these activities are essentially impossible to represent as exogenous variables which could serve to level the playing field. So we embarked on a different approach to enable us to benchmark branch performance across there branch networks. his paper presents an evaluation of the Mississauga, Ontario (a city of 5, people adjacent to oronto) based branches of three of the five large Canadian banks using DEA. his evaluation shows a cross-bank comparison where the traditional DEA analysis would not result in a satisfactory analysis. In fact, the city of Mississauga was chosen to provide a uniform market environment for this work so that the regional and demographic differences were not a factor. For more clarity, we had eliminated the usual regional and local issues most studies are concerned with by this geographical limitation. his left us with the need to identify how bank Head Office policies and operating practices affects the branches productivity. In proposing to achieve this objective, a mathematically handicapped DEA formulation is developed in order to incorporate strategic differences into a handicapping function, constructed in a manner similar to some reported in the literature. his should allow us to fairly assess the three branch networks on the same basis without Head Office caused beneficial or detrimental influences. he handicapping approach ensures that the bank branch s ability to produce results at the customer level is the same for all of them. Furthermore, using the handicapping function a DEA based bank production model is developed to facilitate bank branch efficiency examination. he rest of the paper is organized as follows. Section 2 presents a brief description of DEA basics and the mathematical formulation of the handicapped DEA methodology. Section 3 discusses the sample data and the model. Section 4 summarizes the sample and Section 5 gives the handicapping function developed here. Section 6 shows the results while Section 7 discusses the potential use of the results and the potential application areas of this new DEA methodology. Finally Section 8 concludes the paper. 2

3 2. echnical Development 2.. DEA Basics Data Envelopment Analysis (DEA) is used to establish a best practice group of units and to determine which units are inefficient compared to best practice groups as well as to show the magnitude of the inefficiencies present. Consider n DMUs to be evaluated, DMU j (j=,2 n) which consumes amounts X j ={x ij } of inputs (i=, 2,, m) and produces amounts Y j ={y rj } of outputs (r=,, s ). he efficiency of a particular DMU can be obtained from the following linear programs (input-oriented BCC model [2]). s. t. min θ, λ, s +, s θx z + = θ ε s ε s Yλ - s + = Y Xλ s = λ = λ, s +, s (2.) In Equation 2., the variable θ is the proportional input contraction factor applied simultaneously to the DMU s (the DMU being evaluated) inputs to improve its efficiency. his proportional reduction translates into a radial movement of all inputs toward the envelopment surface and ranges between values from to. he slack variables (s + and s - ) are variables added to the linear programming model in order to convert inequality constraints to equality constraints. heoretically, the presence of the non- Archimedean ε in the primal objective function effectively allows the minimization over θ to preempt the optimization involving the slacks. A DMU is termed efficient if and only if the optimal value θ* is equal to and all the slack variables are zero. he output constraint states that outputs of the observed unit, i.e., y, cannot exceed those of the efficient units in its reference set. Furthermore, the input constraint maintains that the efficient units can never employ more than θ x inputs, where x denotes the inputs of the unit under observation. In this paper, each DMU is a bank branch in the sample. θ is the efficiency for each bank branch. Performing a DEA analysis actually requires the solution of n linear programming problems of the above form, one for each DMU. his model allows variable returns to scale. he dual program of the above formulation is illustrated by: max μ, ν s. t. w = μ Y μ Y v + u v X = X + u - μ ε v ε u free (2.2) In Equation 2.2, variables μ and v represent the sets of input and output weights or multipliers, respectively, whereas u is equivalent to the returns-toscale indicator in the presence of unique optimal solutions. he value for u is unrestricted because it may be either positive or negative. If the convexity constraint ( λ = ) in (2.) and the variable u in (2.2) are removed, the feasible production region is enlarged, which results in the reduction in the number of efficient DMUs, and it is assumed that all DMUs are operating at constant returns to scale. he resulting model is referred to as CCR model [7]. For a thorough understanding of DEA the reader is referred to the textbook by Cooper et al. [9] Handicapped DEA Model he typical DEA methodology does performance analysis for units assumed to be operating under similar environments, or culture. As mentioned earlier, this paper introduces a new concept called the handicapped DEA model. he purpose of the handicapped DEA model is to balance the corporate head office created differences for the DMUs under examination; hence, it yields a fair and equitable cross-bank comparison for bank branches (DMUs) that belong to different banks. Before we use the handicapped DEA models, we need to define a handicapping function that can compensate for the different corporate strategies under which the DMUs operate. he handicapping factor applied to each DMU, derived from the handicapping function, can be either deterministic or stochastic. he methodology we decided on involves the manipulation of the inputs and outputs of a unit in a systematic way. More specifically, the DMUs which turn out to be disadvantaged in some measure will be compensated by reducing their inputs (or increasing their outputs) while the advantaged DMUs may be handicapped by 3

4 increasing their inputs (or decreasing their outputs) in order to reach a stage where they can be compared as if they were all from the same firm. Compared to the normal DEA methodology, handicapped DEA models include a handicapping function denoted by h and this can be used to handicap either inputs or outputs. Assume h j is the handicapping factor to handicap input measures and ĥ j handicaps output measures. he mathematical formulation is presented as follows: Input-Oriented BCC Dual s max w u hˆ = r ( yr) + u u, ν r= m s. t. vi ( h xi) = i= s m ur ( hˆ j yrj ) vi ( h j xij ) + u r= i= ur, vi u free j =,..., n (2.4) Input-Oriented BCC Primal m s + min z = θ ε s + + i sr θ, λ, s, s i= r= n.. ( ˆ s t ) = ( ˆ hj yrj λ j sr h j yr) r =,..., s j= n + θ ( h xi ) ( h j xij ) λ j si = j= n λ j = j= + λ j, si, sr i =,..., m (2.3) Equation 2.3 is built based on Equation 2.. Equation 2.3 considers h j x ij as the adjusted input and ĥ y j rj as the adjusted output. Hence, we penalize the DMUs with the advantaged environment more by the higher input-handicapping measure h and (or) the lower output-handicapping measure ĥ j, thus, the inputs of these DMUs are relatively increased and (or) their outputs are relatively decreased, either or both of which makes the DMUs less efficient. On the other hand, we compensate those DMUs with the disadvantaged environment by assigning a lower input-handicapping measure h and (or) a higher output-handicapping measure ĥ, which enables these j DMUs to reach the efficient frontier sooner. In this paper, h is calculated by the index number approach. he (scalar) variable θ is the proportional reduction to be applied to all inputs of DMU (the DMU being evaluated) to move it onto the frontier. he vector λ indicates the contribution of the efficient DMUs to the peer group that forms the reference set for the DMU under evaluation. heir magnitude indicates the degree to which the characteristics of the efficient DMUs are used to construct the virtual DMU on the frontier to which the inefficient one is projected. he dual problem 2.4 yields an alternative geometric interpretation. In the dual form, ν and μ are the vectors of input and output weights. Efficiency is measured as a function of these weights. Each DMU is then allowed to choose weights that maximize its efficiency, provided that the set of weights yield efficiency s that do not exceed unity, for all DMUs. he variable u is the measure of scale efficiency. his model can be restricted to constant returns to scale by removing the convexity constraint in the primal form and u from the dual form. he handicapped DEA model reduces multiple non-controllable environmental variables into a single handicapping measure without complicating the analysis, and this substantially improves the discriminatory power of DEA. Finally, this methodology ensures that the deviation from the frontier comes from pure operational inefficiency, not a combination of inefficiency and the cultural disadvantage imposed by the environment. In all, the handicapped DEA model provides an unbiased comparison for the DMUs under study. he limitation of this methodology is that there is no general form for the handicapping function and users need to find their own handicapping system for each application domain, which obviously depends on the different situations. 3. DEA Model and Methodology his paper develops comprehensive DEA models to measure the efficiency and productivity for Canadian bank branches when these branches do not belong to the same bank. It introduces an operational efficiency model that adopts a production approach. his model examines how well different branches combine their resources to support the largest possible output of services. he emphasis is placed on how bank culture affects its branches efficiency. 4

5 3.. Production Model Generally speaking, the inputs are the resources that the DMU employs to conduct its operations and the outputs are the services provided by the bank branches. his model includes three types of resources as inputs: labour, premises and I expenses, and other non-interest expenses. All resources are measured in dollars. he resources are devoted to providing four kinds of services: deposits, loans, securities and operating services, the activities from which the branch produces the revenue. hus, we use loan balances, deposit balances, securities balances and gross revenue to measure the contributions a bank branch makes. Inputs FE in dollars Premise/I expenses Other Expenses Figure. DEA model Bank Branch Outputs Loan Deposit Securities Gross Revenue Input orientation is chosen for this model since the branches have little direct control over the services required by their customers. Hence, it is a natural choice for bank managers to improve their staff performance while maintaining the current level of service. he analysis in this paper can be divided into three stages. In the first stage, we are going to run separate DEA analyses for each bank and examine the results. In the second stage, the branches from different banks will be aggregated and the normal DEA models without the handicapping factor will be run. In this way, we treat all the bank branches equally, ignoring the cultural differences imposed by the different banks. In the third stage, we will incorporate the handicapping function into the DEA models and run the models again. he handicapped DEA results will be compared to normal DEA results and individual bank result to investigate how the handicapping function affects the bank branches efficiency and further analysis will be carried out based on handicapped DEA efficiency, for example detecting outliers. Figure 2 shows the three stages. First Stage Run the normal DEA model based on the branch data without handicapping function Figure 2. hree stages 4. Sample See how the handicapping function affects the banks branches ranking and then carry out further analysis hird Stage Second Stage Incorporate the handicapping function into the DEA model and run the model again he sample consists of 7 branches in Mississauga, Ontario, Canada, operated by three big Canadian banks. We had deliberately chosen a very homogeneous community (so we did not have to be concerned with the usual "cultural" differences due to regional issues) that was large enough to have a good selection of branches for each of the three banks we examined. All these branches focus on personal banking. he dataset has been carefully prepared such that all possible outliers (branches due to their different class of business) are removed from the analysis. For example, some branches, which were closed by the bank in the middle of the year, have been removed. Several branches with zero FE were also removed due to incomplete data. In addition, one branch has been identified as the main branch in the area and it hires a lot more people to deal with the business for the whole area. he remaining seventy branches are comparable based on their size and business activities. Of course, in this process we had obtained a branch sample that had a very homogeneous business mix, 5

6 demographics and location. So if they were from the same bank, we would expect that their performance would be very consistent - a situation we see in many Canadian bank studies [8], [6], [8], and [7]. he annual data for the fiscal year 2 are used in this paper. able summarizes the statistics of the raw data. able. Statistics on raw data Standard Max Median Min Average Deviation Inputs (in dollar) FE,394,46 468,553 55,93 545,279 26,498 Premises/ I Expenses,33,433 27,467 42,75 39,73 29,762 Other Expenses,6,86 385,92 22, ,228 28,884 Outputs (in dollar) Deposit ($ s) 4,464 47, ,2 34,537 Loan ($ s) 356,847 78,75 23, 96,95 66,32 Security ($ s) 96,796 8, ,72 9,484 Gross Revenue 6,642,668 2,75,473 44,427 2,38,524,798,42 5. An Index Number Approach to the Handicapping Function in the Canadian Banking Industry Banks are profit-maximizing entities that provide many services, including intermediary services between borrowers and lenders. hey make use of physical goods and services such as labour and materials (stationery, telephone, etc.) to produce financial services such as deposits and loans. During this process, they must conform to a host of regulations such as reserve requirements, deposit insurance and interest rate controls but these are the same for all banks participating in the Canadian financial markets. here are other constraints on banking at the branch level which are imposed by their own corporate policies, competitive pressures and traditional business practices to mention only a few. Subject to these constraints, each bank can adopt any strategy it deems appropriate to maximize its profit. But when we want to compare branch efficiencies and set benchmarks by comparing different banks to each other using DEA, we face the problem that the performance of the branch can be materially affected by upper management's strategic decisions that the branch can not control. Moreover, these decisions, as we see later, do not lend themselves to be incorporated into input or output variables even if these are considered exogenous variables. Hence, the treatment offered by Banker and Morey [4] can not be applied. Consequently, we had come up with a handicapping system that should ensure that the branch s ability to produce financial products at the customer level is the same for all branches in the study area, regardless of their individual corporate strategic constraints placed on them. We use the working definition that the handicapping function for each bank is the ratio of tactical and strategic heterogeneity between the banks compared. Our handicapping function is based upon one of the index number approaches reported in the literature, which has been applied to the banking industry by Fixler and Zieschang []. his approach views the technological difference between the different entities as the source of inefficiency and therefore, the relative productivity is the ratio of the technology differences between the banks. We had adopted this approach but used the ratio to develop a value that reflects, in a specific way, the strategic differences between the competing banks. We had to identify such strategic differences (pseudo "products" for our purposes) between these competitors and classify them as "inputs" and "outputs". Hence, the Fixler and Zieschang approach could be adopted as our handicapping factor and was defined as the ratio of the output index over the input index of these management strategies for each bank. We assume that there are N banks to be evaluated and each of them produces m different strategic products. Specifically, bank i offered the value {y k i } of these products (k =, 2, m). i is the index of the banks under comparison. Using Fixler and Zieschang s approach, the output index of bank i (Y i ) is given by the following []: m i i i ln Y = (/ 2) ( π + π )[ln y ln y ] k= k k k k where is the output share, k is the index for the m strategic "products" offered by a bank, and nyk is the logarithm of the geometric mean of the outputs for all the involved banks and N i πk = ( πk)/ N i= 6

7 N i nyk = ( nyk)/ N i= he values of these strategic products are obtained by applying the user cost of money approach [2]. In order to construct the user cost, interest rate paid, capital gains rate, service charge earned per dollar, provision for loan losses, interest rate payable, deposit insurance premium rate, reserve requirement on liability and the amount of financial products secured by each bank are incorporated. he same approach is used to construct the input index []. he difference is that we use input values x instead of y. able 2 shows the results from calculating the handicapping function for each bank. his factor can be used to adjust the bank s ability to produce financial services for its customers and reflects management strategy at the bank level. he higher this factor is, the more advantaged that particular bank's branches are. able 2 Handicapping factor table Bank A Bank B Bank C Output Index Input Index Handicapping Factor From able 2 we can observe that the handicapping factor for Bank A is the highest, which indicates that Bank A branches enjoy more strategic advantages at the institutional level than the branches from the other banks. herefore, when we do crossbank branch comparisons, Bank A branches should be handicapped most heavily. On the other hand, Bank C branches should be compensated most since its handicapping factor is the lowest. 6. Results 6.. Banks' Individual DEA Result he banks' individual results for the CCR and BCC models are summarized in able 3. able 3. DEA results for Bank A, B and C % technically efficient branches Average BCC % technically and scale efficient Average CCR Average scale efficiency returns to scale No. of increasing return to scale No. of constant return to scale No. of decreasing return to scale Bank A Bank Bank C 66% 44% 46% % 5% 25% he DEA model identifies 2.5%, 3% and 6% technical inefficiency for the three banks. Scale efficiency can be calculated as the ratio of the CCR and BCC s. If the frontiers of the CCR and the BCC models are very close, one can conclude that the industry operates at constant returns to scale. Otherwise, there can be significant scale inefficiency. Comparison of the BCC s with CCR s shows that the conclusion can be drawn that most of the bank branches are operating under constant returns to scale since the scale efficiency is very close to. his finding is consistent with the other researchers work [9] [7] [6] [2] [8] [5]. hus, the CCR efficiency will be used in the following analysis unless otherwise stated Combined DEA Results In order to compare the branch performance for Bank A, B and C, all the branch data were aggregated. able 4 shows the results. 7

8 able 4. DEA results comparison Whole sample % technically efficient branches Average BCC % technically and Scale efficient Average CCR Standard deviation Bank A % technically and scale efficient Average CCR Bank B % technically and scale efficient Average CCR Bank C % technically and scale efficient Average CCR Normal Approach Handicapped Approach 5% 5% % 29% % 4% % 22% % 29% he handicapped DEA results suggest that branch performance from the three banks were very similar. his result agrees with Schaffnit et al s [8] and Paradi and Schaffnit's [6] statement that the large Canadian banks are quite sophisticated and technologically intensive and all branches operate at high efficiencies. Inefficiently operated bank branches cannot survive for long in the Canadian financial markets because of the heavily regulated nature and intensive competition that exists. he handicapping function for Bank B and C compensate their branches as they operate under unfavorable head office imposed strategic environments; therefore, their branches efficiency s increase. As to Bank A, the handicapping function penalizes its branches since they operate under favourable strategic environments, which results in a decrease of its efficiency s. It is prudent, however, to examine these results critically and offer some proof of their robustness and accuracy. he following sections present some approaches to accomplish this goal Validation o validate these results, we generated sets of random numbers to be used as handicapping factors and then examine whether they have the same or different effects than our specific handicapping factors defined in Section 5. Since. represents the average performance and the standard deviation (σ) is.38 in our handicapping system, we generated these random numbers to have the population mean of. and standard deviation of.38. herefore, the randomly generated numbers were kept within the range of.±2σ, hence covering the range of our handicapping factors. he results show that most of the random numbers increased average performance differences and the standard deviation among the three banks, which contradicts the findings by others and ourselves that the large Canadian banks have similar performance levels. Some of these values influenced the average efficiency minimally and the standard deviation of the three banks became more similar among the three banks, but the differences were still much larger than our handicapped results from Section 6.2. Only one set of random numbers produced results closely matching our handicapping system. After looking into it, we found that this set of randomly generated handicapping factors is almost the same as our handicapping factor set in Section 5, hence the very close results. his supports the conclusion that our handicapping system is the correct one. 7. Management Use of the Results DEA is a very useful analytical assessment tool which provides management with the information upon which to base decisions. he innovation presented in this paper increases the usefulness of DEA by incorporating multiple variables of a noncontrollable nature directly into the model formulation by the use of a handicapping function. he approach ensures that the targets for inefficient units are practical since the deviation from the frontier is purely due to management controllable inefficiency. Of course, the handicapped DEA methodology has all the benefits that the normal DEA method has, but it 8

9 provides additional advantages summarized as follows: he handicapped DEA methodology makes it possible to carry out fair and equitable comparisons among DMUs from different backgrounds including across companies or even countries. It provides a managerial strategy neutral framework for evaluating branches relative to the common frontier after incorporating the effects of their head offices strategic differences via a handicapping function. his methodological improvement suggests that all deviations from the frontier are due to inefficiency, rather than a combination of inefficiency and the head office imposed general strategic effects on the branches, thereby allowing for an unbiased comparison of their performance. he handicapping function declares which bank has a more advantaged strategic plan in general. Hence, the other banks might review their operations with the view to changing managerial strategy to redefine their own operational strategies. 8. Concluding Remarks and Future Work he reader should note that the application of the handicapped DEA approach is not a methodology applicable only to the banking industry, indeed, it could be a useful tool in any situation where normal DEA analysis might be used if an outside central factor caused strategic differences did not exist. he three components of normal DEA analyses are: inputs, outputs and similar operating circumstances (culture), the handicapped DEA approach relaxes the last component and allows the comparison of dissimilar units (even across firms in the same business as we did here) if we can use a deterministic or stochastic handicapping function to quantify the differences between the DMUs under study. he entire paper focuses on how to incorporate the complex management strategy imposed impact on the branches that can not control such strategy while comparing different firms using adjusted DEA models. For this purpose, the handicapped DEA models were formulated. Furthermore, the handicapping function was developed for the three large Canadian banks we had studied. he functions were based on their annual reports and information gathered from the Canadian Deposit Insurance Corporation (CDIC, the equivalent of the U.S. FDIC - Federal Deposit Insurance Corporation) reports. Finally, this work opens up many new possibilities for interfirm comparisons, industry wide benchmarks and performance standards. Nevertheless, future research is suggested. For example, stochastic variables might be included in the handicapping function in order to best explain the difference between cultures when the information we need contains some degree of uncertainty. References [] Athanassopoulos A. D. and Giokas D., he Use of Data Envelopment Analysis in Banking Institutions: Evidence from the Commercial Bank of Greece, Interfaces 3, No. 2, pp8-95, 2. [2] Banker, R. D., Charnes, S., Cooper, W.W., Some Models for Estimating echnical and Scale Efficiency in Data Envelopment Analysis, Management Science, Vol.3, No.9, 984, pp [3] Banker, R. D., Morey, R. C., he Use of Categorical Variables in Data Envelopment Analysis, Management Science, 32(2), 986, pp [4] Banker, R. D. and Morey, R. C. "Efficiency Analysis for Exogenously Fixed Inputs and Outputs", Operations Research, vol. 34, no. 4, pp , Jul, 986-Aug 3, 986. [5] Camanho, A. S. and Dyson R. G., Cost Efficiency Measurement with Price Uncertainty: a DEA Application to Bank Branch Assessment, European Journal of Operational Research, 6, pp , 25 [6] Canadian Bank Facts, Canadian Bankers Association, 2 Edition. [7] Charnes, A., Cooper, W. W., Rhodes, E., Measuring the Efficiency of Decision Making Units, European Journal of Operational Research, Vol.2, No.6, pp , 978. [8] Cook, W., D., Hababou, M., and uenter, H., Multicomponent Efficiency Measurement in Bank Branches Journal of Productivity Analysis, pp29-224, 2 [9] Cooper, W. W., Seiford, L. M. and one, K., "Data Envelopment Analysis: A Comprehensive ext with Models, Applications, References and DEA-Solver Software", Kluwer Academic Publishers, 2. [] Fixler, D. J., Zieschang K. D., An Index Number Approach to Measuring Bank Efficiency: an Application to Mergers, Journal of Banking and Finance, Vol. 7, , 993 [] Golany B. and Storbeck J. E., A Data Envelopment Analysis of the Operation Efficiency of Bank Branches, Interfaces 29, No. 3, pp4-26, 999. [2] Hancock, D., he Financial Firm: Production with Monetary and Non-Monetary Goods, Journal of Political Economy 93, pp859-88, 985 [3] Lozano-Vivas, A., Pastor, J. P. and Pastor, J. M., An Efficiency Comparison of European Banking Systems Operating Under Different Environmental Conditions, journal of Productivity analysis, 8, pp59-77, 22. [4] Manandhar, R. and ang, C. S., he Evaluation of Bank Branch Performance Using Data Envelopment Analysis A Framework, he Journal of high echnology Management Research, 3, pp-7, 22. 9

10 [5] Oral, M., and Yolalan, R., An Empirical Study on Measuring Operating Efficiency and Profitability of Bank Branches, European Journal of Operational Research 46, pp , 99 [6] Paradi, J. C. and Schaffnit, C. "Commercial Branch Performance Evaluation and Results Communication in a Canadian Bank - a DEA Application ", European Journal of Operations Research, 56(3) pp , 24. [7] Parkan, C., Measuring the Efficiency of Service Operations: an Application to Bank Branches, Engineering costs and Production Economics 2, pp , 987 [8] Schaffnit, C., Rosen, D., Paradi, J. C., Best Practice Analysis of Bank Branches: An Application of DEA in A Large Canadian Bank, European Journal of Operational Research, Vol. 98, pp , 997 [9] Sherman, H. D. and Gold, F., Bank Branch Operating Efficiency: Evaluation with Data Envelopment Analysis, Journal of Banking and Finance 9, pp297-35, 985 [2] Sherman, H. D. and Ladino, G., Managing Bank Productivity using Data Envelopment Analysis, Interfaces 25(2), 995