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A Study of the Relative Efficiency of Bank Branches: An Application of Data Envelopment Analysis Author(s): M Vassiloglou and D Giokas Source: The Journal of the Operational Research Society, Vol 41, No (Jul., 1990), pp 591597 Published by: Palgrave Macmillan Journals on behalf of the Operational Research Society Stable URL: http://www.jstor.org/stable/2583436 Accessed: 07/09/2013 23:17 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive We use information technology and tools to increase productivity and facilitate new forms of scholarship For more information about JSTOR, please contact support@jstor.org Palgrave Macmillan Journals and Operational Research Society are collaborating with JSTOR to digitize, preserve and extend access to The Journal of the Operational Research Society http://www.jstor.org This content downloaded from 194.214.27.178 on Sat, Sep 2013 23:17:48 PM All use subject to JSTOR Terms and Conditions J Opt Res Soc Vol 41, No 7, pp 591-597, 1990 Printed in Great Britain All rights reserved 0160-5682/90 $3.50 + 0.00 Copyright ) 1990 Operational Research Society Ltd A Study of the Relative Efficiency of Bank Branches: An Application of Data Envelopment Analysis M VASSILOGLOU and D GIOKAS Operational Research Sector, Economics Division, Commercial Bank of Greece Data envelopment analysis (DEA) has become an accepted approach for identifying inefficient decisionmaking units in an organization This paper presents a systematic application of DEA carried out at the Commercial Bank of Greece in assessing the relative efficiency of bank branches After a description of the model and the data, the results of the analysis are discussed, and a note is made of certain aspects of the follow-up analysis Key words: banking, data envelopment analysis, linear programming INTRODUCTION The emerging financial integration of EEC countries is bringing about fundamental changes in the operation of European institutions In the banks, strategic planning is gradually gaining greater emphasis, leading to a new drive towards the rationalization of bank decision-making This is being supported in many cases through the use of operational research techniques Over the past few years, this trend has started becoming evident in Greece Although operational research applications are by no means widespread in Greek banks, recently a number have been reported at conferences and in the literature.1-4 This reflects the gradual emergence of specialist teams in the banks and the consequent trend towards the introduction of more sophisticated quantitative techniques The Operational Research Sector of the Commercial Bank of Greece is the first such specialist team to be set up in a Greek bank At this relatively early stage of its development, one of its main objectives is, by necessity, the illustration and overall promotion of decision support ideas at the managerial levels of the Bank Thus, the benefits of projects undertaken by the Sector tend to be evaluated in terms of both the value of immediate results and the dissemination of relevant ideas achieved through the follow-up process This paper discusses a recent project of the OR Sector, which dealt with the evaluation of the relative efficiency of a number of the Bank's branches using data envelopment analysis The first part focuses on the technical aspects of the project This is followed by a discussion of the results and certain aspects of the follow-up process DATA ENVELOPMENT ANALYSIS: THE MODEL APPLIED AT THE COMMERCIAL BANK OF GREECE Data envelopment analysis (DEA) is a non-parametric methodology developed by Charnes et al.5 to handle the assessment of non-profit-making organizations where accounting profit measures are of little value In general, DEA measures efficiency by estimating an empirical production function which represents the highest values of outputs/benefits that could be generated by inputs/resources as given by a range of observed input/output measures As Golany points out, 'DEA is quickly emerging as a leading method for efficiency evaluation in terms of both the number of research papers published and the number of applications to real-world problems.' The technique was first applied to the banking context by Sherman and Gold,8 who used it to explore some operating aspects of bank branches By explicitly considering the mix of resources used and services provided by individual branches, they succeeded not only in identifying inefficient branches, but also in locating specific areas of inefficiency at each branch DEA measures the efficiency of each branch in comparison to the set of branches under investigation Its objective is to specify the subset of relatively inefficient branches and the scale of their 591 This content downloaded from 194.214.27.178 on Sat, Sep 2013 23:17:48 PM All use subject to JSTOR Terms and Conditions Journal of the Operational Research Society Vol 41, No inefficiency in comparison to other similar branches which have been characterized as relatively efficient The efficiency of each branch is assessed ex post, without explicit knowledge of the input/ output relationships used (see the Appendix for the model formulation) The technique assigns to all the branches being evaluated efficiency ratings (E < 1) conditional on the data set under study That is, the assessment of a branch as relatively inefficient implies the existence in the data set of branches (or combinations of branches) displaying greater efficiency Similarly, the assessment of a branch as relatively efficient implies that the data set does not contain any branches (or combinations of branches) performing more efficiently Consequently, in the case of relative inefficiency it can be shown that the performance of the branch in question can be improved, whereas relative efficiency does not preclude the existence of more efficient branches outside the selected data set For each inefficient branch, DEA identifies an efficiency reference set This is the set of relatively efficient branches to which the inefficient branch has been most directly compared in calculating its efficiency rating This facilitates the exploration of the nature of inefficiencies at a branch, by indicating those relatively efficient ones against which performance comparisons can be drawn PROBLEM SPECIFICATION Input and output specification in the Commercial Bank application was necessarily the result of compromise between desirable model formulation and available data The Bank's information system has been computerized fairly recently and, as would be expected, priority has been given to data for banking operations Consequently, the selection of input/output variables had to take account of the availability of data in the Bank's information system Clearly, in banking operations labour is the major input in terms of its effect on both the level of production and costs The contribution of labour to branch production was measured in personhours at each branch A variety of supplies (e.g stationery) used at the branches is also related to the level of production and, for simplicity of aggregation, was measured in terms of monetary value at standard costs Production levels are also related to the branch installation itself and measured in square metres of branch floor-space, to avoid rent values which would be affected by price variability Of course, branch space itself has certain weaknesses, since it does not reflect aspects such as floor plan, quality of installation, etc., but among available data, this measurement was considered to be the most appropriate Finally, the number of computer terminals at each branch was introduced as a fourth input in order to explore possible variations in output volumes due to automation In the literature, a distinction is made between controllable and non-controllable input variables (e.g Banker and Morey,9 Smullen'0) Non-controllable inputs are those which, although important for branch performance, cannot be affected by branch management Often, an attempt is made to adjust for the impact of factors over which management does not have immediate control A typical example is the factors characterizing the markets in which different branches operate (e.g urban/rural, business/residential, etc.) However, since all the branches in the current data set are located in Athens and operate in reasonably similar markets, it was decided not to complicate the model by introducing non-controllable input variables Branch output was measured in terms of the number of transactions processed at each branch In contrast to the Sherman and Gold application,8 which used the 17 services most commonly offered by the branches, the Commercial Bank model took into consideration the complete range of 72 transactions However, DEA operates more powerfully when the number of branches exceeds the number of inputs and outputs at least twice Consequently, these transactions had to be reduced to a small number of classes This was performed, following Sherman and Gold, on the basis of transaction complexity Four classes of transactions were defined, with type A transactions being the 'easiest' and type D the 'most difficult' The classification of transactions was performed on the basis of responses from a sample of branch managers to a relevant questionnaire aimed at identifying transaction complexity It was evident that most answers were in broad agreement regarding the assessment of transaction complexity on a scale of 1-4 In cases where assessments varied among the respondents, the transactions were classified according to the 'average' classification 592 This content downloaded from 194.214.27.178 on Sat, Sep 2013 23:17:48 PM All use subject to JSTOR Terms and Conditions M Vassiloglou and D Giokas-Bank Branch Efficiency via DEA The study was performed using standard linear programming software (ESP's LP88'1) for a set of 20 branches from the Athens area The application was based on the Bank's 1987 budget RESULTS DEA was applied to each of the 20 branches producing the concise results presented in Table Each row of Table represents the solution to an LP which maximizes the efficiency rating of the corresponding branch under the constraints dictated by the output/input relationships operating in the complete data set TABLE Branch efficiency ratings Branch Efficiency rating Bi B2 B3 B4 B5 B6 B7 B8 B9 B10 Bit B12 B13 B14 B15 B16 B17 B18 B19 B20 1 0.92 0.94 0.74 1 0.87 0.67 0.65 0.89 1 0.77 0.91 0.84 0.92 1 Reference subset B1, B2, B7, B13, B20 B1, B6, B7, B20 B1, B2, B6, B7, B20 B1, B2, B6 B2, B7, B13, B14, B19 B2, B6, B7, B20 B2, B7, B14, B20 B2 B2, B7, B20 B1, B2, B14 B1, B2, B6, B7 Of the 20 branches in the sample, nine have a maximum efficiency rating of Next to each of the 11 relatively inefficient branches (E < 1) appears the corresponding efficiency reference subset This is the subset of relatively efficient branches to which the branch in question has been most directly compared in deriving its efficiency rating Efficiency ratings not rank the branches in order of efficiency, since they have been estimated using different reference sets Rather, they indicate the extent to which their efficiency is lacking in comparison to their corresponding reference sets So, for-example, branch B12 is about 90% as efficient as its reference set (B2, B7, B14, B20), while B8 is about 90% as efficient as its own reference set (B1, B2, B6) This broadly implies that B12 and B8 could reduce the inputs they utilize by approximately 10% without experiencing any negative effects on their output volume For a useful interpretation of DEA results it is necessary to combine the information contained in Table with whatever other information is available about the branches It is, therefore, important to discuss the results of a DEA application with management in the light of their knowledge of special characteristics of the branch network in general and specific branches in particular Such discussions are likely to provide useful insights into the reasons for the variability of efficiency ratings among branches In many cases, management may be able to supply a straightforward explanation to a low efficiency rating For example, a branch may be relatively inefficient due to its proximity to a larger branch, but management may be willing to ignore this if its location has much latent potential (e.g a shopping centre currently under construction nearby) A valuable contribution of DEA occurs when its results contradict management's accepted knowledge about the branches, thus prompting an in-depth investigation Such an investigation may bring into light information about the operation of the branches which up to that moment had been ignored So, DEA can be seen as part of a continuous process of information generation and understanding As a first step towards interpreting the results of DEA, it is worth exploring some explanations of the variation among efficiency ratings One such explanation may be the distinction between 593 This content downloaded from 194.214.27.178 on Sat, Sep 2013 23:17:48 PM All use subject to JSTOR Terms and Conditions Journal of the Operational Research Society Vol 41, No branches which are centres and those which are satellites As their name implies, centres are major branches empowered to perform the complete range of transactions Satellites are branches which, although autonomous, can provide only a restricted range of services It might, therefore, be suggested that different handling of centres and satellites on the part of management has resulted in either of the two becoming more efficient than the other However, this explanation does not stand up to inspection: the proportion of efficient to inefficient branches among centres (i.e branches B12, B13, B17 and B20) does not differ significantly from that among satellites (all remaining branches) Another possible explanation, following a similar rationale, would be the operation of economies of scale in some form By construction, DEA assumes that the branches not benefit from economies of scale However, if such economies did exist, branches processing a larger number of transactions would be more efficient than branches processing fewer transactions This putative explanation was rejected after examination of the distribution of inefficient branches among branches with varying volumes of production DEA can also provide more detailed information about inefficient branches Table sets out TABLE Inefficient branch Excess inputs according to DEA Efficiency rating B3 0.92 B4 0.94 B5 0.74 B8 0.87 B9 0.67 B11 0.65 B12 0.89 B15 0.77 B16 0.91 B17 0.84 B18 0.92 sq m PH SE T sq m PH SE T sq m PH SE T sq m PH SE T sq m PH SE T sq m PH SE T sq m PH SE T sq m PH SE T sq m PH SE T sq m PH SE T sq m PH SE T Actual input usage Reduction in input usage % decrease 706 5284 727 805.7 55.35 675 889.5 6884 821 725 8133 983 710 4345 619 1114 7831 886 1677 10349 1047 576.2 5348 1147 942 4153 347 2207 19150 1937 364 2378 471 56.5 422.9 58.2 1.6 49.3 338.5 41.3 0.5 232.3 1797.7 214.4 1.4 96.6 1521.9 131 2.1 235.5 1594.4 205.3 0.7 385.5 2709.7 306.6 2.4 375.4 1189.1 120.4 0.6 247.2 1217 644.9 0.7 555 899.4 31.9 0.5 343.4 8238.9 301.4 0.8 28.3 184.8 201.4 0.9 8 40 6.12 6.12 6.12 16.67 26.12 26.11 26.11 35 13.32 18.71 13.33 42 33.17 36.17 33.17 35 34.6 34.6 34.6 48 22.39 11.5 11.5 12 42.9 22.76 56.23 23.33 58.92 21.66 9.19 25 15.56 43.02 15.56 16 7.78 7.77 42.76 45 sq in.: square metres of branch space; PH: person-hours; SE: supplies expenses; T: number of terminals 594 This content downloaded from 194.214.27.178 on Sat, Sep 2013 23:17:48 PM All use subject to JSTOR Terms and Conditions M Vassiloglou and D Giokas-Bank Branch Efficiency via DEA the shortcomings of the relatively inefficient branches of the data set from an input-minimizing viewpoint This presentation illustrates the meaning of the efficiency rating of the branches The rating of branch B3 (E = 0.92) indicates that B3 is 92% as efficient as its reference set and, consequently, it could reduce the resources it utilizes by approximately 8% without reducing its outputs The rightmost column of this table confirms that the branch space, person-hours and supplies of B3 could be reduced by 8%, while the number of its terminals could be reduced by 40% In other words, the efficiency rating indicates, in proportional terms, the maximum reduction that can be effected uniformly across all inputs without causing a reduction in the output volume of the branch (It should be noted that the branches in the data set have no more than five computer terminals and, consequently, large reductions in proportional terms correspond to small ones in absolute terms.) Thus, although, for example, B16 and B18 have approximately the same efficiency rating (0.91 and 0.92 respectively), a detailed analysis of the results reveals that the profile of their potential input reductions differs considerably: B16 is making roughly 60% excess use of space, while B18 is problematic in its use of supplies and computer terminals Their respective efficiency ratings, however, cannot reflect this, as they are determined by the inputs each of them utilizes most efficiently FOLLOW-UP OF THE STUDY AT THE COMMERCIAL BANK Once the first conclusions had been formulated at the OR Sector, the study was forwarded to top management for examination and comments It was also discussed extensively at Head Office with managerial staff responsible for branch operations The discussion took place mainly on the following three themes: (a) acceptability of the evaluation of specific branches; (b) possibility for improvement of the formulation of the model, in view of the experience gained (e.g regarding input/output specification, product classification, etc.); (c) overall benefits of the application for the Bank As far as the acceptability of results is concerned, branch evaluations were examined by Head Office personnel in view of their knowledge of the branch network In general, the assessments seemed to correspond with the evaluations they had arrived at on the basis of information already available to them When unexpected negative branch evaluations were encountered, they were further explored in search of justification In some cases this brought to light weaknesses of the application, which were located mostly in two areas: data collection and input/output specification The existence of weaknesses in the Bank's data collection system was already recognized The recent computerization of several Bank operations has undoubtedly brought a major improvement of the information system, but deficiencies still exist, some of which were encountered during the application of DEA A particularly serious problem, as far as DEA is concerned, relates to ambiguities in bank product specification This directly affects the distinction of products into types, since unclear definitions of products/services complicate the assessment of their 'difficulty'.The identification of this problem led to discussions on the possibility of improvements to model formulation It was found in practice that distinguishing the products in terms of their complexity created problems both at the classification phase and later on during the interpretation of results Thus, it was decided that a more functional criterion for product classification'might be the branch department the products belong to This way, the products can be classified into approximately eight categories corresponding to the departments in a branch, and the results of the analysis can be interpreted in terms of the performance of the branch departments Unfortunately, this approach creates a complication which did not previously exist: the relative complexity of products within each category or department must now be evaluated before branch output can be measured In other words, coefficients of equivalence are required for the products within each department, in order for the volume of production to be reliably measured This modified specification of the problem is currently being tested in a new application of DEA at the Commercial Bank 595 This content downloaded from 194.214.27.178 on Sat, Sep 2013 23:17:48 PM All use subject to JSTOR Terms and Conditions Journal of the Operational Research Society Vol 41, No As far as the overall benefits from the application are concerned, particular emphasis should be placed on the exchange of knowledge that took place during the follow-up process Apart from the immediate results of the application, the project offered an opportunity for the OR Sector to communicate with middle management at a number of the Bank's divisions These discussions were extremely valuable for both sides: OR staff became familiar with a variety of operational issues of the Bank, while personnel from the other divisions had the opportunity to experience certain aspects of the application of a quantitative technique to their area of work APPENDIX DEA is composed of several mathematical models sharing the principle of envelopment The original model proposed by Charnes et al.5'6 and adopted by Sherman and Gold8 is formulated as follows Objectivefunction k E UiCiO max Eo = i- E VjXjo j=z where = the branch being assessed from the set of r = 1, 2, o ., n bank branches; k = the number of outputs at the branches; m = the number of inputs at the branches; Cir = observed output i at branch r; Xjr = observed input j at branch r Constraints k Z Ui (a) ir n m Z VjXjr j=1 (b) ui,vj0i=> , k, j= 1, ,m The above analysis is performed repetitively, with each bank branch in the objective function, producing an efficiency rating for each of the n branches The solution sought is the set of (us, vi) values that maximize the efficiency ratio Eo of the bank branch being rated, without resulting in an output/input ratio exceeding (100% efficiency) when applied to each one of the other branches in the data set Consequently, if a relative efficiency rating of 100% is not attained under this set of weights, it cannot be attained under any other set (for the same sample of branches) This fractional programming problem is replaced with a linear programming equivalent through a series of transformations which are set out in detail in Charnes et al.5 REFERENCES G P PRASTAKOS (1986) Management science and information technology in the banking sector: a review In Proceedings of the 7th Conference of the Greek Operational Research Association (G P PRASTAKOS, Ed.), pp 281-307 Greek Operational Research Society, Athens (publication in Greek) A BRILLIsand G P PRASTAKOS (1988) SMEP: a decision support for asset and liability management Presented at the Euro IX - TIMS XVIII International Conference,Paris, France, July 1988 D GIoKAS(1988) Analysis of portfolio selection an application of the analytic hierarchy process Presented at the First Balkan Conferenceon OperationalResearch, Thessaloniki, Greece, October 1988 S H PAGANOPOULOS (1988) Operational research in banking Presented at the First Balkan Conferenceon Operational Research, Thessaloniki, Greece, October 1988 A CHARNES, W W COOPER and E RHODES (1978) Measuring the efficiency of decision making units Eur J Opl Res 2, 429-444 596 This content downloaded from 194.214.27.178 on Sat, Sep 2013 23:17:48 PM All use subject to JSTOR Terms and Conditions M Vassiloglou and D Giokas-Bank Branch Efficiency via DEA A CHARNES,W W COOPERand E RHODES (1979) Short communication: measuring the efficiency of decision making units Eur J Opl Res 3, 339 B GOLANY (1988) An interactive MOLP procedure for the extension of DEA to effectiveness analysis J Opl Res Soc 39, 725-734 H D SHERMAN and F GOLD(1985) Bank branch operating efficiency-evaluation with data envelopment analysis J Bank Fin 9, 297-315 R D BANKER and R C MOREY (1986) The use of categorical variables in data envelopment analysis Mgmt Sci 32, 1613-1627 10 J SMULLEN (1989) The application of data envelopment analysis to branch planning and management appraisal Presented at the European Working Group of OperationalResearch in Banking (Eurobanking),Heemskerk, The Netherlands, May 1989 11 ESP (1987) LP88 User's Manual Eastern Software Products Inc., Virginia, USA 597 This content downloaded from 194.214.27.178 on Sat, Sep 2013 23:17:48 PM All use subject to JSTOR Terms and Conditions