African Journal of Business Management Vol. 6(24), pp. 7230-7241, 20 June, 2012 Available online at http://www.academicjournals.org/AJBM DOI: 10.5897/AJBM11.1067 ISSN 1993-8233 ©2012 Academic Journals

Full Length Research Paper

A new two-stage data envelopment analysis (DEA) model for evaluating the branch performance of banks

F. Hosseinzadeh Lotfi1, A. Toloie Eshlaghy2, M. shafiee2*, H. Saleh1, H. Nikoomaram2 and S. M. Seyedhoseini2

1Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.

2Department of Industrial Management, Science and Research Branch, Islamic Azad University, Tehran, Iran.

Accepted 1 November, 2011

The purpose of this paper is to provide a framework for evaluating the overall performance of bank branches in terms of profitability efficiency and effectiveness by means of a two stage data envelopment analysis (DEA) model. DEA is a linear programming problem approach for evaluating efficiency of decision making units (DMU) that have multiple inputs and outputs. In this paper, we use a two stage DEA model for efficiency evaluation of DMUs. In the two stage model all the outputs from the first stage are the only inputs to the second stage, in addition to the inputs to the first stage and the outputs from the second stage. The outputs from the first stage to the second stage are called intermediate measures. Many papers have regressed non parametric estimate of efficiency in the two stage DEA procedure. All of these studies have several problems in the benchmark or projection unit and present the DMU with relative efficiency. Most of these papers do not present an efficient benchmark unit and cannot evaluate the relative efficiency unit. In this paper we review these studies and then create a two stage model that does not have these problems. Our model presents the efficient benchmark unit and also presents DMU with relative efficiency. In the next step we apply our two stage model in bank branches of a large commercial bank in Iran. This study aggregates profitability efficiency and effectiveness into the overall performance. Some relations between profitability efficiency and effectiveness are very important. Without these relations we cannot obtain superior insight about overall performance. So we assume that profitability efficiency and effectiveness are dependent, and with this assumption we design a two stage DEA model. This study shows the importance of profitability efficiency and effectiveness in the overall performance in bank branches in Iran. Key words: Banking, process efficiency, organizational effectiveness, data envelopment analysis (DEA), banks, banks performance.

INTRODUCTION Nowadays, due to the continuous change in economic conditions, evaluating the performance of industrial and economical units has become one of the most important factors in their improvement. The banking sector has experienced profound changes over the past two decades or so. Globalization, deregulation, financial innovation, automation and speed of exchanges have been significant, leaving their impact on the performance of the banking sector (Akhtar, 2010). So to maintain *Corresponding author. E-mail: m_shafiee277@yahoo.com. Tel: +989179248672. Fax: +987116470060.

viability and continuous improvement, bank branches must evaluate their performance, efficiency and productivity. The banks are forced to evaluate their branch networks efficiency and effectiveness in order to improve the overall performance of their branches. Effectiveness and efficiency are the central terms used in the overall performance of the organizations (Kumer and Gulati, 2010). Performance can be defined as an appropriate combination of efficiency and effectiveness (Kumer and Gulati, 2010). Drucker (1977) distinguished efficiency and effectiveness. He defined efficiency as “doing things right” and effectiveness as “doing the right things”. So we can say that efficiency and effectiveness are two components of overall performance.

Industrial and economical units should be evaluated by utilizing scientific methods in order to evaluate and improve the performance and structuring a good position in comparison to other units.

Performance and measurement are two familiar words in the literature of evaluation. Performance is predeter-mined parameters and measurement sounds like the ability to monitor events and activities in a meaningful way, so performance measurement can be defined as the process of quantifying the effectiveness and efficiency of action (Neely et al., 1995). Several approaches are used in order to measure the performance, some of them include: balanced scorecard (Kaplan and Norton, 1992), the performance measurement matrix (Keagan et al., 1989), performance measurement questionnaire (Dixon et al., 1990), criteria for measurement system design (Globerson, 1985) and computer aided manufacturing approaches. Although, effective, we can pointout some shortages such as: lack of strategic focus, forcing managers to encourage local optimization rather than seeking continuous improvement, and they are also unable to provide adequate information about competitors.

The main aim of this paper is to study bank profitability efficiency, effectiveness and overall performance by utilizing two stage DEA model. Charnes et al. (1978) proposed the DEA model to produce the efficiency frontier based on the concept of Pareto optimum. DEA is a nonparametric powerful tool in analyzing efficiency with multiple inputs and outputs which can consider both qualitative and quantitative measures.

The two stage concept in DEA dates back to the work by Schinnar et al. (1990) to evaluate the performance of mental health care programs (Kao and Hwang, 2008) for a recent survey). Kao and Hwang (2008) modify the standard DEA model by determining the relationship of the two stages within the whole process. Under their framework, the whole efficiency can be decomposed into the product of the efficiencies of the two sub-processes. Note that such efficiency decomposition is not available in the standard DEA approach of Seiford and Zhu (1999) and the two stage approach of Chen and Zhu (2004) and Chen et al. (2009).

The two stage DEA model keeping each stage independent from one another was applied by Wang et al. (1997), Rho and An (2007), and Tsolas (2010). Other works appearing in the banking literature are those by Seiford and Zhu (1999) to divide the production process of a commercial bank into marketability and profitability, analyze the banking operation by Chen (2002), evaluate the profitability and marketability efficiencies of large banks by Luo (2003), and measure the performance of Taiwan`s commercial banks by Ho and Zhu (2004). Related studies analyze the financial efficiency of firms by Zhu (2000), measure the efficiency of the American Major Baseball League by Sexton and Lewis (2003), measure information technology`s indirect impact on firm

Lotfi et al. 7231 performance by Chen and Zhu (2004), decompose the efficiency of non-life insurance companies in Taiwan into the product of the efficiencies of the two sub-processes by Kao and Hwang (2008), and examine relations and the equivalence between the approach of Chen and Zhu (2004) and Kao and Hwang (2008) by Chen et al. (2009).

These studies have several problems, so we have reviewed some of them. Kao and Hwang (2008) proposed the two stage model based on DEA for evaluating the efficiencies of non-life insurance companies in Taiwan. Their models and approach do not present overall information about DMUs. For example, in their model, none of the DMUs are relatively efficient, and there is no efficient unit. Their model doesn't determine the projection unit. On the other hand, the produced projection is not efficient either, and the model in variable return to scale (VRS) mood is nonlinear.

Chen et al. (2009) modified the Kao and Hwang (2008) model, but their modal has the same problem. The model proposed by Chen et al. (2009) does not determine the efficient projection unit, and the produced projection is not efficient. Also, in this model results, none of the DMUs are relatively efficient.

Chen et al. (2009) in an article entitled "additive efficiency decomposition in two-stage DEA" proposed the additive model to evaluate efficiency. They developed their model in constant and variable return to scale (CVR and VRS) mood. Their model is linear in both mood, but none of the DMUs are relative efficient, and the model does not present information about the projection unit. This model was modified by Cook et al. (2010), who proposed a multi stage model by modifying the Chen et al. (2009) model. But this model cannot calculate the relative efficiency.

The model proposed by Tone and Tsutsui (2009), determine the efficient projection units, but none of the DMUs are relative efficient. So the main aim of this article is to build the models that do not have these problems. These problems are solved in our model; the efficient projection presented, the relative efficiency presented for one of the DMUs, the model can be developed into the CRS and VRS mood, and the model is linear.

Different sections of this paper can be structured as: a brief description on efficiency, effectiveness and overall performance, followed by a DEA review and related applications and concepts with performance evaluation. The next section contains an explanation of methodology and two stage DEA models to overall performance and demonstrates their applications in bank branches in Iran. Finally, some conclusions are provided about the research. EFFICIENCY, EFFECTIVENESS AND PERFORMANCE EVALUATION Drucker (1977) distinguished efficiency and effectiveness.

7232 Afr. J. Bus. Manage. He defined efficiency as “doing things right” and effectiveness as “doing the right things”. In this terminology, efficiency is defined as the ability of an organization to attain the outputs with the minimum level of inputs, and effectiveness is defined as the ability of an organization to reach its goals and objectives. So we can say that efficiency and effectiveness are two components of overall performance. Ho and Zhu (2004) introduced overall performance as a product of efficiency and effectiveness. He defined Return on assets (ROA) as performance (Ho and Zhu, 2004), and obtained performance from the product of Profit margin ratio as effectiveness and Total assets turnover ratio as efficiency. Ho and Zho (2004) introduced a model with two stages to obtain overall performance. Other researchers have combined this model with the DEA model such as Tsolas (2010), Kumar and Gulati (2010), Keh et al. (2006), and Garcia-Sanchez (2007). In these studies researchers designed a model with two stages, one stage from efficiency and another from effectiveness. Efficiency and effectiveness score were then obtained with a DEA model separately. Finally, they determined the overall performance by product the efficiency and effectiveness score.

We can categorize measurement tools into 2 types which are used to evaluate different tools. Gap based techniques like Spider and Radar diagram and Z chart are used in parametric analysis. These tools are very graphical in nature, which makes them more understandable; however, when an analyst needs to integrate different elements into one complete picture they are not be useful.

Ratio is another parametric method which has been used in different areas and can compute and calculate the relative efficiency of output versus input easily. But different ratios provide different interpretations and integrating the entire set of ratios into a single one would be difficult.

Another robust tool in performance measurement to analyze data is analytical hierarchy process. In order to convert various weighted scores into a single score, AHP utilizes the personal views of experts. Although it provides managerial insights in quantifying measures, it is subjugated to a high degree of subjectivity.

Regression is a statistical method which provides meaningful relationships for decision makers, but its main limitation is analyzing one single output at a time, which means by adding another criterion the approach has to be repeated. Also, it considers average values instead of real ones that may not occur in the real world. This means regression considers one method in combining different factors in all firms.

The other non parametric tool in evaluation is data envelopment analysis (DEA). DEA considers both qualitative and quantitative measures. This is why managers would be able to provide reasonable judgments based on resource usage. DEA works based

on the concept of efficient frontier suggested by Farrell (1957) and can consider multiple inputs and outputs by dividing the weighted sum of outputs by a weighted sum of inputs. Efficiency numbers are between 0 and 1. In ranking, DMU with an efficiency number of 1 is the most efficient, and the DMU with an efficiency number of 0 is the least efficient. Although it has a wide range of covering shortages of other tools, utilizing DEA reveals some limitations as well:

1. Meaningful results in DEA require the availability of data about different inputs and outputs. But sometimes some of these data are unreachable or sometimes firms are not interested in sharing data. 2. Number of DMUs being compared cannot be less than a certain limit. By decreasing the number of DMUs, we would have an increase in the number of efficient DMUs too. 3. Since DEA considers the same strategic goals and objectives for all of the DMUs in the firm, we cannot compare DMUs which are different in these aspects. 4. It is so critical to interpret the results of DEA precisely. Although it provides reasonable rankings for efficient DMUs, DEA is unable to address the reasons for inefficiencies or provide suitable solutions.

As mentioned before, each tool has its own profits and shortages together, so it is difficult to choose the best one, however, the distinguished advantages of DEA can convince us to utilize this tool. First of all, it is important to choose a simple tool that is easy to work with (Maskell, 1991; Sheridan, 1993; Detoro, 1995; Blossom and Bradley, 1998). Also, its reliability in supporting the process of decision making is so important. DEA is a robust, standardized and transparent methodology that can fulfill all the requirements above. It also provides some other features which make it an appropriate tool in order to measure performance. Some of them are listed as follows:

1. DEA can process multiple elements (Charnes et al., 1978). 2. DEA does not need to specify the relationships among the performance measures. 3. It utilizes the concept of efficient frontier, which is an empirical standard of excellence. 4. This toll can analyze both the qualitative and quantitative measures simultaneously. 5. There is no need to assume priority estimates, so the reliability of the results increases. 6. It can provide valuable information about inefficient DMUs as well as efficient ones. 7. Its flexibility enables the researcher to mold it to other analytical methods such as statistical analysis and other multi criteria decision making techniques (Zhu et al., 2004; Golany, 1988; Spronk and Post, 1999).

There are numerous studies on bank efficiency evaluation

with the DEA model such as Aly et al. (1990), Elyasiani and Mehdian (1990), Yue (1992), Grabowski et al. (1994), Fukuyama (1993), Berg et al. (1993), Avkiran (1999), Cook and Hababou (2001), Vivas et al. (2002), Luo (2003), Drake and Hall (2003), Kao and Liu (2004), Oliveira and Tabak (2005), Kirkwood and Nahm (2006), Havrylchyk (2006), Drake et al. (2006), Hahn (2007), Sharkas et al. (2008), Sherman and Gold (1985), Tulkens (1993), Drake and Howcroft (1994), Haag and Jaska (1995), Sherman and Ladino (1995), Athanassopoulos (1998), Berger et al. (1997), Lovell and Pastor (1997), Camanho and Dyson (1999, 2005), Zenios et al. (1999), Schaffnit et al. (1997), Golany and Storbeck (1999), Avkiran (1999), Kantor and Maital (1999), Soteriou et al. (1999), Cook et al. (2000), Cook and Hababou (2001), Dekker and Post (2001), Hartman et al. (2001), Bala and Cook (2003), Portela et al. (2003, 2004), Paradi and Schaffnit (2004), and Portela and Thanassoulis (2005, 2007).

Several researchers have worked on profitability efficiency such as Athanassopoulos (1997), Oral et al. (1992), Oral and Yolalan (1990), Soteriou and Zenios (1999), and Manandhar and Tang (2002). Profitability efficiency evaluates the ability of branches to minimize inputs for the level of outputs generated. Profitability efficiency is obtained from the ratio of the weighted sum of revenue to the weighted sum of expenses (Giokas, 2008a, 2008b).

In recent years, few studies have been completed which explicitly recognize the efficiency and effectiveness as two mutually exclusive components of the overall performance of an organization. For example, Schinnar et al. (1990), Karlaftis (2004), Ho and Zhu (2004, 2007), Mouzas (2006), Keh et al. (2006), Garcia-Sanchez (2007), Yu and Lin (2007), Rho and An (2007), and Kao and Hwang (2008).

Data envelopment analysis DEA is a linear programming based methodology which can calculate multiple inputs and outputs and can also evaluate DMUs both qualitatively and quantitatively. DMU, which can be related to different firms or the condition of the same firm over time, stands for decision making unit.

DEA was first proposed by Charnes, Cooper and Rhodes (CCR) in 1978. The evolutionary form of CCR model was suggested by Banker et al. (1984). In subsequent years, several models were developed by a large number of researchers. Orientation, disposability, diversification, and return to scale are different aspects that can be seen in these models.

DEA utilizes frontier function in measuring efficiency. It then introduces a set of efficient and inefficient units. The analysis of inefficient units has two aspects. First, it can show the maximum input level in order to attain a given

Lotfi et al. 7233 amount of outputs. Secondly, it can also show the highest output level attained for a given amount of inputs. These approaches are called "minimal principle of efficiency" and "maximum principle of efficiency" respectively.

CCR and BCC models

Efficiency is derived from physical and engineering science and demonstrates the relationships between inputs and outputs. Ratio definition of efficiency was introduced by Charnes et al. (1978), and is also known as the CCR ratio definition. CCR is the classical science of applying single-input to single-output ratio definition to multiple outputs and inputs without requiring pre-assigned weights.

We have been dealing with the pairs of positive input

and output vectors of n DMUs. We

will call a pair of such semi positive input and

output an activity and express them by

notation . The set of feasible activities is called the production possibility set and is denoted by P. We postulate the following properties of P: The observed

activities belong to P.

If activities belong to P, then the activities

belong to P for any positive scalar t. we call this property the constant return to scale assumption. For

activities in P, any semi positive activity

with and is included in P. That is, any activity with input of no less than x in any component and with output no greater than y in any component is feasible.

Any semi positive linear combination of activities in P belongs to P.

Arranging the data sets in matrices and , we can define the PPS satisfying 1 through 4 by:

(1)

Where is a semi positive vector in . Based on the matrix (X,Y), the CCR model with row vector v for input and row vector u as output was formulated.

Let and be the ith input and rth output, respectively, of the jth DMU, j = 1...n. The DEA model for measuring the relative efficiency of

under an assumption of constant returns to scale is the CCR model (Charnes et al., 1978):

(2)

7234 Afr. J. Bus. Manage.

We can say that the dual model is:

(3)

The following BCC input oriented value-based model (Banker et al., 1984) can be used to assess efficiencies.

(4)

The dual model is:

(5)

Benchmarking is particularly practical when there is no objective standard available for defining effective performance. So it is used in managing services because it is difficult to define the service standard in comparison with the manufacturing standard.

One of the ways a benchmark is presented is by applying a DEA model. Consider the set of DMUs including DMUj j=1,…,n with m inputs and s outputs such

that =( ,…, ), =( ,…, ) are inputs and

outputs, respectively. Let be optimal solution of the

CCR model and is under evaluation, and

and be optimal solution of model (6).

(6)

Then the reference set is defined as:

Reference set={ j : >o} and and

are benchmarks or improved activities gained from DEA.

PROPOSAL MODEL

Consider a two stage model that is shown in Figure 1. Suppose, we have n DMUs. Each DMU has m inputs to

the first stage, , and D outputs to the

first stage, . These outputs then

Lotfi et al. 7235

Stage 1 Stage 2

Stage 1

Stage 2

Figure 1. A two stage model.

become the inputs to the second stage. DMU has S

outputs to the second stage, . We use the notation in Chen and Zhu (2004), Chen, Liang and Zhu (2009) and Kao and Hwang (2008). Based upon the properties of PPS and arranging the data sets in matrices

, and , we can define the production possibility set of a two stage model that satisfies 1 through 4 is expressed as:

Property 1. The observed activities

belong to P. According to this property, we have:

(7)

Property 2. Any semi positive linear combination of activities in P belongs to P. According to the convexity axiom, we have:

(8)

Property 3. For activities in P, any semi positive

activity with and is included in P and

for an activities in P, any semi positive activity

with and is included in P. With this property we have:

(9)

Property 4) If activities belong to P, then the activities belong to P for any positive scalar t. We call this property the constant return to scale assumption. With accept this assumption the PPS to become changed into:

(10)

Now, to build the model with the use of PPS definition, we have:

(11)

With these properties and the definition of PPS, the two stage DEA model is:

7236 Afr. J. Bus. Manage.

(12)

The dual of this model is:

(13)

Definition: Projections of a network are defined as follows:

Theorem 1. If is under evaluation, then at least one of the constraints in model 13 in optimality is binding.

Proof: Let be an optimal solution for model 13. It is evident that if an optimal solution exists, then an

optimal extreme point exists. Let be an optimal extreme solution for model 13, so it lies on (D+m+s) linearly independent hyper plans.

is binding at every feasible solution, so this constraint is tight at optimal solution. Therefore, we are searching for D+m+s-1 binding hyper plan.

Every cannot be equal to zero, because in this case

So at most, the (m+s-1) of variables in optimality are

binding; consequently the d-1 of constraints

in optimality should be binding.

Theorem 2: If in evaluation the constraint related

to is binding, then is efficient.

Proof: let be an optimal solution for model 13

in evaluating and .

The efficiency of is gained by solving the following model:

(14)

If , then is a feasible solution for model 13 and the proof is completed. Otherwise

So we have:

These relations imply that is a feasible solution for model 13 and the objective value is equal to

1. So is efficient.

Theorem 3: The improved activating is efficient.

Proof: The efficiency of is evaluated by solving the following model:

(15)

Let the optimal objective value be , so we solve model 16 to gain the max-slack solution for improved activating.

(16)

Suppose that an optimal solution for is

. By using the definition of improved activities, we have:

Now we rewrite the above formula:

Where , and

.

If then so so, this is a

contradiction. Therefore .

With we have:

Since is maximal, we must have

so . Hence improved activity is efficient. A TWO STAGE PERFORMANCEEVALUATION MODEL FOR IRANIAN BANK BRANCHES In order to appraise the efficiency, effectiveness, and performance of Iranian banks, we apply a two-stage model as proposed in this paper. So in this section we calculate the overall performance directly. This performance is a combination of profitability efficiency and effectiveness. Based on the above definition of performance, this paper evaluates the performance of 37 Iranian bank branches via a two stage evaluation process that separates profitability and effectiveness. A two stage evaluation process is defined as that level of assets required to generate profitability in the first stage, and generate effectiveness in the second stage.

Determination of inputs and outputs to calculate profitability efficiency and effectiveness are an important step in performance evaluation. Since we want to evaluate profitability efficiency and effectiveness, we must have two sets of inputs and outputs.

Lotfi et al. 7237

In this study we want to obtain the overall performance directly. The overall performance obtains from net income/total cost. The overall performance can be divided into two concepts. The first concept is profitability that obtains from Total income/Total cost, and the second concept is effectiveness that obtains from Net income/Total income (Ho and Zhu, 2004, Ho, 2007; Tsolas, 2010, Kumer and Gulati`s, 2010).

Net income/total income (effectiveness) could be treated as a metric of effectiveness in this study and is defined as the ability to achieve the expected level of income generation (Tsolas, 2010).

Total income/total cost (profitability) assesses the ability of the branch to generate income with the available resources expressed in monetary values and it is an index of profitability (Tsolas, 2010).

The choice of inputs and outputs is influenced by the literature on the DEA application in the banking industry. The inputs and outputs used in earlier DEA applications studies are listed in Table 1. Based on the literature of DEA application in the banking industry, only the inputs and outputs in banking efficiency that there are in the literature of bank efficiency are listed. Then, with expert supervision and the bank`s staff ideal, the most important indexes of profitability and effectiveness in Iranian banks are selected. In fact, we determine two sets of indexes. The first set of indexes is for profitability efficiency evaluation in stage 1 and the second set for effectiveness evaluation in stage 2. The inputs and outputs set for profitability efficiency consisted of personal expenses, equipment expenses and operational expenses as inputs and non-operational income, sum of deposits, and commissions as outputs. These inputs and outputs are shown in the figure below (Figure 2).

The inputs and outputs set for effectiveness evaluation consisted of non-operational income, sum of deposits, and commissions as inputs and net-income as output. These inputs and outputs are shown in the figure below (Figure 3).

As seen, the outputs in profitability efficiency evaluation then become the inputs of effectiveness evaluation in stage 2. So we have a two stage model for overall performance evaluation (Figure 4).

In this study, we used the inputs and outputs data from April 2010. In this step we apply the proposal model for performance evaluation in Iranian bank branches. As previously mentioned, this method calculates the overall performance directly. The results of this model are shown in Table 2.

As seen in Table 2, the DMU 1, 2, 3, 6, 8, 13, 15, 16, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 33 and 34 are efficient, and the other DMUs are non efficient.

Conclusion A general framework to evaluate the overall performance in terms of profitability efficiency and effectiveness

7238 Afr. J. Bus. Manage. Table 1. An overview of inputs and outputs variables used in some of the studies.

S/N Author Year Country of study

Input indexes Output indexes

1 Sherman and Gold 1985 USA Employees, expenses, space No. of transactions

2 Parkan 1987 Canada Employees, expenses, space, rent, terminals No. of transactions, customer response, corrections

3 Oral and Yolalan 1990 Turkey Employee, terminals, no. of accounts, credit applications No. of transactions

4 Giokas 1991 Greece Employee, expenses, rent No. of transactions

5 Bhattacharya et al. 1997 India Interest expenses, operating expenses Advances, deposits, investment

6 Jackson et al. 1998 Turkey Employees, non-labor operating expenses Total loans, total demand deposits, total time deposits

7 Chen and Yeh 1998 Taiwan Assets, branches, operating cost, deposits, interest expenses Interest income, non interest income

8 Seiford and Zhu 1999 USA Employees, assets, capital stock Revenues, profits

9 Athanassopoulos and Giokas 2000 Greece Labor hours, branch size, computer terminals, operating expenditure No. of transactions, easiest, medium-easy, most-difficult, credit transactions, deposit transactions, foreign receipts

10 Ho 2001 Taiwan Assets, interest expenses, employee, fixed assets Interest income, non interest income

11 Mukherjee et al. 2002 India Net worth, borrowings, operating expenses, employee, branches Deposit, net income, advance, non-interest income, interest spread

12 Galagedera and Edirisuriya 2004 India Customer and short term funding and total operating expenses Loans and other earning assets

13 Sturm and Williams 2004 Australia Employee, deposits and equity capital Loans and off-balance sheet items

14 Kumbhakar and Lozano-Vivas 2005 Spain Purchase funds and core deposits, labor, and physical capital Loans and securities

15 Chambers and Cifter 2006 Turkey No. of branches, personal members per branch, share in total assets, share in total loans, share in total deposits

Non-interest income, total assets and net interest income, total operating income

16 Rezitis 2006 Greece Labor, capital expenses, value of deposits Value of loans, advances and value of investment assets

17 Sturm and Williams 2007 Australia Interest expenses, non-interest expenses Net interest income and non-interest income

18 Gikas 2008a Greece Personal costs, running and other operating costs Value of loan portfolio, value of deposits, non interest income, loan transactions, deposit transactions, remaining transactions

19 Gikas 2008b Greece Interest costs, non interest costs, personal costs, running costs, operating expenses

Interest income, non interest income, value of deposits, value of loans, non interest income

20 Kumar and Gulati 2009 India Physical capital, loanable funds, labor Advances investment, net interest income,

21 Tsolas 2010 Greece Rental expenses, personal expenses, other operating expenses, depreciation

Origination income, outcome of a predetermined function mapping loans selling branch performance, commissions, other non interest incme, net income

Lotfi et al. 7239

Figure 2. Inputs and outputs indexes of profitability efficiency in Iranian banks (stage 1).

Figure 3. Inputs and outputs indexes of effectiveness in Iranian banks (stage 2).

Figure 4. Inputs and outputs of profitability efficiency (stage 1) and effectiveness (stage 2) in Iranian banks.

Table 2. Result of performance evaluation.

DMUs Overall

performance DMUs

Overall performance

DMU (1) 1.000 DMU (20) 0.7636

DMU (2) 1.000 DMU(21) 1.000

DMU (3) 1.000 DMU(22) 1.000

DMU (4) 0.4649 DMU(23) 1.000

DMU (5) 0.6481 DMU(24) 1.000

DMU (6) 1.000 DMU(25) 1.000

DMU (7) 0.8241 DMU(26) 1.000

DMU (8) 1.000 DMU(27) 1.000

DMU (9) 0.5159 DMU(28) 1.000

DMU (10) 0.6762 DMU(29) 0.5681

DMU(11) 0.5118 DMU(30) 0.9902

DMU(12) 0.6344 DMU(31) 0.7286

DMU(13) 1.000 DMU(32) 0.7939

DMU(14) 0.7420 DMU(33) 1.000

DMU(15) 1.000 DMU(34) 1.000

DMU(16) 1.000 DMU(35) 0.5930

DMU(17) 0.4745 DMU(36) 0.6841

DMU(18) 1.000 DMU(37) 0.8029

DMU(19) 1.000 - -

by means of two stage DEA model is proposed. There are several studies about two stage DEA model in the literature of DEA. The most of these models have several problems, such as, they cannot determine the relative efficiency of DMUs, nor can they determine an efficient projection unit. In our model, these problems have been solved. The proposed model can determine the relative efficiency and an efficient projection unit.

In the next step we apply the performance for a sample of the Iranian bank. We used our two stage DEA model to evaluate the Iranian bank performance. In this case study, we have 3 inputs for the first stage, 3 outputs in the second stage and 3 immediate measures. The results show that the DMU 1, 2, 3, 6, 8, 13, 15, 16, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 33 and 34 are efficient.

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