^{1}

^{2}

^{1}

^{2}

Nowadays, vicissitude in administrative systems through Performance Measurement (PM) is one of the necessary and inevitable subjects, on which the improvement of efficiency and effectiveness in banking systems depend greatly. In this paper, we focused on efficiency analysis of Tejarat bank branches in order to propose the corrective actions on utilizing resources. Hence, we compute the efficiencies of units based on input-oriented CCR model with three approaches which differ on combination method of inputs and outputs and then rank them by Anderson & Peterson (AP) model. The results represent that the CCR model based on confined fuzzy weights presents the high level of accuracy in identifying efficient units as well as giving useful information on improving the inefficient branches.

Performance measurement is the process that allows organizations to prevent principal problems before occurrence. So, PM can predicate as a major control mechanism for organization strategies by providing information on coordination of units with plans. The present PM methods of banks consist of financial ratios, which lead to various results because of the heterogeneity of standards. Hence, recently the new techniques have recommended for PM of banks that one of the most frequently used methods is Data Envelopment Analysis (DEA). DEA is a nonparametric mathematical programming technique that was introduced based on Farrell’s pioneering work, aiming at the measurement of Decision Making Units’ (DMUs) relative efficiencies [

In this paper, we utilize the input-oriented CCR model in order to evaluate the efficiency of Tejarat bank branches by three approaches, which differ on combination type of inputs and outputs according to expert opinions. So, we use the mixed fuzzy approach of Analytic Hierarchy Process (AHP) and CCR model consisting two stages; first, the paired comparisons matrix begets from performing the CCR multiplier model for each unit and then, the final ranking will be done by solving an AHP model. In other words, in this model the paired comparisons have been done by DEA and the final ranking by AHP model.

This paper is organized as follows: next section, Section

The first utilization of nonparametric methods for PM was presented in 1957 with the publication of an article by Farrell [

In initial DEA model, according the optimum condition model can allot zero weight to some inputs or outputs. It means the useless of related parameter in evaluation and thus meaningful skew exists in results. This problem is highlighted specially by assigning zero weight to more important factors in model. Avoiding this defect, Charnes et al. assigned the positive lower bound like

As DEA is a boundary method which is sensitive to outliers, it is very difficult to evaluate the efficiency of DMUs with varied input and output by conventional DEA models. Most of previous researches utilized simulation techniques faced with imprecise data [

In this paper, fuzzy variables are explicitly defined and interpreted as a result of expert opinion in which no variable is completely ignored, as mentioned before in Section

For two symmetric triangular fuzzy variables of

It is clear that the fuzzy unequal

In first constraint of (

The optimal value of the model above is

This model use symmetric triangular fuzzy inputs and outputs as

In order to rank the efficient units, Sexton and Colleagues presented firstly cross-evaluation matrix for full ranking of DMUs [

This method is a kind of compensation models for decision-making problems which was firstly proposed by Saaty based on analysis of human brain for complex fuzzy problems [

First, all of paired comparisons should be converted to trapezoidal fuzzy number. So, triangular fuzzy number of (

Compute the geometric mean of

According Step

Synthetic AHP/DEA model combines the two separate models of AHP and DEA, which consist of two stages: first, DEA model runs for both DMUs separately and then, considering the result of first stage, the paired comparisons matrix has existed for alternatives and then the ranking caused by solving AHP model. In other words, in this model the paired comparisons have been obtained through DEA model and the final ranking results by AHP model.

Considering applied aspect of research, the objectives can be summarized to as follows: (1) model design, (2) efficiency measurement of bank with fuzzy approach and (3) determining the efficiency by deleting each input or output. In this research, the method of collecting information is based on study of bank documents. Also, we used the literature and expert opinion regarding the importance of inputs and outputs variables jointly, which was done through paired comparisons questionnaires. So, we have selected the inputs and outputs by two stages: first, the components have been gathered through library studies and expert opinions and then, the number of components has been modified by experts in order to prevent the skew in efficiency. The inputs and outputs are considered as shown in Table

List of model inputs and outputs.

Inputs | |||

Costs ( | Personnel ( | Capital ( | Equipment ( |

Doubtful accounts ( | No. of personnel ( | Branch account change ( | No. of computers ( |

Interest charges ( | No. of ATMs ( | ||

Non-interest charges ( | |||

Outputs | |||

Incomes ( | Deposits ( | Facilities ( | Bank services ( |

Revenue of loan ( | Investment deposit ( | Current a note facility ( | No. of payment bote ( |

Penalties of delay ( | Saving deposit ( | Current a note facility ( | No. of guarantees ( |

Bank charges ( | Current deposit ( | Current non-note facility ( | No. of payment loans ( |

Current non-note facility ( |

In order to utilize data as inputs or outputs, the following should be considered: each of inputs and outputs is consists of several separate subfactors. In this research, we considered the number of personnel and equipments to find these input weights in usual CCR model, but in fuzzy CCR model we dedicated different weights to different equipments and sum of them are introduced as input weight. Also, bank personnel are scored by education level and also their experience year in order to get the total score of personnel by summation of two factors.

Statistical population of research includes 25 branches of Tejarat Bank in Rey city. Due to the single level of Fuzzy-AHP table in this study, each table was computed until stage two and then, the weights were calculated by paired comparisons matrix. However the obtained weights are all trapezoidal fuzzy numbers, we can use Minkowsky method in order to convert the fuzzy numbers to definite number and then, change it to numerical scale of 10. We can summarize the process of research implementation as below.

Determine the efficient parameters on performance measurement of bank branches.

Determine the final parameters.

Implement DEA model with different approaches.

Analyze obtained information.

In this paper, we utilize DEA-solver software to solve the DEA model, SPSS software for statistical analysis, and Expert Choice software to compute the inconsistency of components weights.

As mentioned before, efficiency measurement of bank branches has computed through input-oriented CCR model with three different approaches, which differ on combination type of input and output parameters. If we use the similar value criteria for combining the homogenous data, then the problem can be solved by usual CCR model, elsewhere we have to modify the fuzzy weights obtained from expert opinion. These approaches are considered, respectively, as below

usual CCR model with data combination based on similar value criteria (type

usual CCR model with data combination based on group fuzzy weights (type

unusual CCR model with data combinations based on confined fuzzy weights (type

In order to combine the homogenous data based on similar value criteria, we sum the data together and then enter final data as input or output. So, the inputs and outputs of this model have been computed as below

Efficiency value of DMUs based on CCR model with similar value criteria.

Branch no. | Efficiency value | Efficiency value by AP model | Efficiency value of branch by deleting a factor of input or output | |||||||

1 | 0.728 | * | 0.569 | * | 0.674 | 0.643 | 0.720 | * | * | * |

2 | 0.958 | * | 0.780 | 0.785 | 0.924 | 0.958 | 0.764 | 0.915 | 0.837 | 0.924 |

3 | 0.458 | * | 0.456 | 0.434 | 0.436 | 0.437 | * | 0.341 | 0.454 | 0.405 |

4 | 1 | 1.319 | * | 0.878 | * | * | * | * | * | 0.864 |

5 | 1 | 5.376 | * | * | * | * | * | * | * | * |

6 | 0.608 | * | 0.586 | 0.574 | 0.593 | * | 0.584 | * | 0.603 | 0.565 |

7 | 0.961 | * | 0.604 | * | 0.854 | * | 0.620 | 0.816 | 0.821 | 0.861 |

8 | 1 | 2.047 | * | * | * | * | * | * | * | * |

9 | 1 | 1.929 | * | * | * | * | * | * | * | * |

10 | 0.502 | * | 0.375 | 0.677 | 0.505 | 0.497 | 0.345 | * | 0.672 | 0.477 |

11 | 0.709 | * | 0.590 | * | 0.599 | 0.669 | * | 0.655 | * | 0.676 |

12 | 0.794 | * | 0.783 | 0.771 | 0.781 | * | 0.684 | * | * | * |

13 | 0.735 | * | 0.678 | * | 0.671 | * | * | 0.390 | * | * |

14 | 1 | 2.024 | * | * | * | * | * | * | 0.939 | * |

15 | 1 | 1.137 | * | * | * | * | * | * | * | * |

16 | 1 | 1.393 | * | * | * | * | * | * | * | * |

17 | 0.939 | * | 1 | 0.836 | 0.798 | * | 0.559 | 1 | 1 | 0.970 |

18 | 0.633 | * | * | 0.586 | 0.622 | * | 0.621 | * | * | * |

19 | 1 | 1.622 | * | * | * | 0.875 | * | * | * | * |

20 | 1 | 1.354 | * | * | * | * | * | * | * | * |

21 | 0.915 | * | 0.718 | * | 0.799 | 0.762 | 0.468 | 0.762 | * | 0.761 |

22 | 1 | 3.587 | * | * | * | * | * | * | * | * |

23 | 1 | 1.278 | * | * | 0.785 | * | * | 0.820 | * | * |

24 | 0.674 | * | 0.566 | * | 0.672 | 0.669 | 0.560 | 0.671 | 0.648 | * |

25 | 0.678 | * | 0.575 | 1 | 0.937 | * | 0.608 | 0.668 | 0.543 | * |

By using AP model for ranking the efficient units, the result indicates that 44% of bank branches identify as efficient units, which represents the unsuitable segregation of branches.

As Table

As a result, by deleting the inputs, cost, personnel, capital, and equipment, the efficiency value of, respectively, 13, 9, 15 and 8 branches has been changed. So, two factors of cost and capital have more importance between inputs, and among outputs by deleting; income, deposit, facility, and services, the efficiency value of, respectively, 11, 10, 9, and 9 branches has been changed which justify the importance of income between outputs. Also, the equipment of banks has the least effect on efficiency of branches.

This model utilizes the usual input-oriented CCR model and unlike type

The fuzzy weights of inputs and outputs have been obtained through paired comparison tables of which a sample exists in the appendix. So, these tables have been distributed among 10 experts in order to get the final fuzzy weight of each factor. Thus, the similar process should be done that income fuzzy weights are described for instance as below.

Convert the linguistic variables such as old equipment into trapezoid fuzzy numbers.

Determine the incompatible matrix before analysis of data on paired comparisons matrix. So, first, all of matrix data should be defuzzificated and entered in matrix as definite data. Then, by computing the incompatibility of each matrix it is observed that only four matrixes had information incompatibility. After sending the incompatible questionaries and remustering of them it has found that finally 50% of paired comparisons matrixes have information compatible and so rest of them are deleted.

Determine the weight of each component by fuzzy AHP method. This process has been done for five decision maker units as below.

All components of comparisons matrix should be written as trapezoid fuzzy number, nee (

Constitute a new matrix with components based on trapezoid fuzzy number as (

Solve the matrix above by fuzzy AHP method. Considering the single level of matrix, it can run until stage two in fuzzy AHP method.

After running the mentioned process, fuzzy weights of income components are obtained as

If we implement the process above for all inputs and outputs according to expert opinions, then the final fuzzy weights of factors can be obtained as shown in Table

Final fuzzy weights of inputs and outputs.

Inputs weights | ||

Costs ( | Personnel ( | Equipment ( |

Outputs weights | ||

Incomes ( | Deposits ( | Facilities ( |

Due to the constant weights of capital and bank services among major factors, these components will be computed based on countable units and entered rightly for measuring the efficiency. Meanwhile, as mentioned before, in fuzzy CCR model the bank’s personnel are scored by education level and also their experience year in order to get the total score of personnel by summation of two factors. Table

Final fuzzy weights of personnel.

Final personal weights ( | |||||
---|---|---|---|---|---|

Personal level | Secondary sch. | Diploma | college cr. | bachelor | Ms.c |

Education level weight | 2.436 | 4.518 | 5.805 | 7.845 | 10 |

Experience year score | 0.223 | 0.457 | 0.549 | 0.815 | 1 |

In order to compute the quantity of inputs and outputs, we have combined the components of factors by multiplying of each component to its related fuzzy weight. These accounts have been obtained as below

The final quantity of inputs and outputs have entered the usual CCR model based on group fuzzy weights and so we can obtain the efficiency of bank branches and classify them through AP model. The results have been indicated in Table

Efficiency value of DMUs based on group fuzzy weights.

Branch no. | Efficiency value based on group fuzzy weights | Efficiency value based on AP model | Branch ranking based on group fuzzy weights |
---|---|---|---|

1 | 0.850 | * | 16 |

2 | 1 | 1.032 | 12 |

3 | 0.782 | * | 18 |

4 | 1 | 1.790 | 5 |

5 | 1 | 5.170 | 1 |

6 | 0.749 | * | 19 |

7 | 0.893 | * | 15 |

8 | 1 | 2.44 | 3 |

9 | 1 | 1.408 | 9 |

10 | 0.550 | * | 25 |

11 | 0.714 | * | 20 |

12 | 0.909 | * | 14 |

13 | 0.646 | * | 22 |

14 | 1 | 1.889 | 4 |

15 | 1 | 1.157 | 10 |

16 | 1 | 1.476 | 7 |

17 | 0.923 | * | 13 |

18 | 0.627 | * | 23 |

19 | 1 | 1.640 | 6 |

20 | 1 | 1.424 | 8 |

21 | 0.680 | * | 21 |

22 | 1 | 3.240 | 2 |

23 | 1 | 1.090 | 11 |

24 | 0.826 | * | 17 |

25 | 0.596 | * | 24 |

According to the result, the number of efficient units in this usual model is relatively high as well as obtained in type

In usual CCR model based on group fuzzy weights, we used expert opinion for combination of homogenous parameters. One of the major problems of this model is disability of fuzzy model to control the final weights of inputs and outputs after solving the model. So, CCR model based on confined fuzzy weights is extended in order to control the weights of parameters. Meanwhile, we add some constraints to original fuzzy model for weights control by using the below process: first, we determine the final weights of inputs and outputs by paired comparisons matrix which is made of expert opinions. This process is similar to one as presented in Section

The final weights of factors based on confined fuzzy weights.

Inputs weights | |||

Costs ( | Personnel ( | Capital ( | Equipment ( |

Outputs Weights | |||

Incomes ( | Deposits ( | Facilities ( | Bank services ( |

By utilizing the final weights in original fuzzy CCR model, the definite efficiency of each bank branch is obtained, but the solution area of problem may be changed to infeasible area. Therefore, it is necessary to determine the certain area for obtained weights. So, we assume the large domain as certain area and enter a new variable called

This constraint is indicator of triangular fuzzy number as (

According to

Considering these constraints, the fuzzy CCR model converts to unusual model based on confined fuzzy weights which can be solved in order to compute the efficiency of bank branches. Table

Comparative result of efficiency value through three types of CCR model.

Branch no. | Similar value criteria (a) | Group fuzzy weights (b) | Confined fuzzy weights (c) | ||||||

Efficiency value | AP efficiency value | Full ranking | Efficiency value | AP efficiency value | Full ranking | Efficiency value | AP efficiency value | Full ranking | |

1 | 0.728 | * | 0.850 | * | 0.613 | * | |||

2 | 0.958 | * | 1 | 1.032 | 0.445 | * | |||

3 | 0.458 | * | 0.782 | * | 0.492 | * | |||

4 | 1 | 1.319 | 1 | 1.79 | 0.529 | * | |||

5 | 1 | 5.376 | 1 | 5.17 | 1 | 2.356 | |||

6 | 0.608 | * | 0.749 | * | 0.552 | * | |||

7 | 0.961 | * | 0.893 | * | 0.628 | * | |||

8 | 1 | 2.047 | 1 | 2.44 | 1 | 1.829 | |||

9 | 1 | 1.929 | 1 | 1.408 | 0.303 | * | |||

10 | 0.502 | * | 0.550 | * | 0.407 | * | |||

11 | 0.710 | * | 0.714 | * | 0.672 | * | |||

12 | 0.794 | * | 0.909 | * | 0.578 | * | |||

13 | 0.735 | * | 0.646 | * | 0.399 | * | |||

14 | 1 | 2.024 | 1 | 1.889 | 1 | 1.033 | |||

15 | 1 | 1.137 | 1 | 1.157 | 0.386 | * | |||

16 | 1 | 1.393 | 1 | 1.476 | 0.627 | * | |||

17 | 0.939 | * | 0.923 | * | 0.695 | * | |||

18 | 0.633 | * | 0.627 | * | 0.504 | * | |||

19 | 1 | 1.622 | 1 | 1.64 | 0.852 | * | |||

20 | 1 | 1.354 | 1 | 1.424 | 0.669 | * | |||

21 | 0.915 | * | 0.680 | * | 0.439 | * | |||

22 | 1 | 3.587 | 1 | 3.24 | 1 | 1.063 | |||

23 | 1 | 1.278 | 1 | 1.09 | 0.589 | * | |||

24 | 0.674 | * | 0.826 | * | 0.552 | * | |||

25 | 0.678 | * | 0.596 | * | 0.454 | * | 19 | ||

Mean of efficiency value | 0.864 | — | — | 0.870 | — | — | 0.615 | — | — |

In order to prevent the infeasible solution for some of branches, we have to utilize property coefficient of

It should be mentioned that in this research we solved totally 375 CCR models, with 9*25 models related to approach

In this section, we survey the correlation of efficiency for branches which has been obtained by three approaches and also their ranking through AP model. Therefore, we utilized the coefficient of the correlation in order to survey the efficiency computed for three approaches as below:

Also, we utilized the Spearman rank correlation coefficient to survey the correlation of ranking of units together which have been obtained through three approaches and can be computed as below, where

The results are shown in Table

Analysis of correlation for efficiency and rank of DMUs.

Correlation of coefficient ( | |
---|---|

Between similar value criteria and group fuzzy weights approaches | |

Between similar value criteria and confined fuzzy weights approaches | |

Between group fuzzy weights and confined fuzzy weights approaches | |

Spearman rank correlation coefficient ( | |

Between similar value criteria and group fuzzy weights approaches | |

Between similar value criteria and confined fuzzy weights approaches | |

Between group fuzzy weights and confined fuzzy weights approaches |

As Table

Considering different CCR models which are solved in this research, it results that the branch number five is the best branch totally with the rank and efficiency number of one in all approaches. After that, respectively, branches numbers 8, 14, and 22 can be predicated as good branches at all with efficiency of one. Also, it has been observed that the efficiency and ranking of branches have been strongly affected by exerting the confined fuzzy weights for inputs and outputs. For instance, branch number 9 with the rank of 5 and 9 in two types of

In order to provide the comparative condition for different types of CCR model, we summarize the results of problems based on different aspect of efficiency as shown in Table

Comparative display of efficiency for bank branches.

Different approaches of CCR model | |||

Similar value criteria | Group fuzzy weights | Confined fuzzy weights | |

Number of efficient units | 11 | 12 | 4 |

Percent of efficient units | 44% | 48% | 16% |

Minimum of efficiency | 0.458 | 0.550 | 0.303 |

Maximum of efficiency | 1 | 1 | 1 |

Mean of efficiency | 0.864 | 0.868 | 0.615 |

This comparative study displays that the fuzzy approach based on confined fuzzy weights have stronger segregation than other approaches by two reasons; first is the minimum number of efficient branches in this approach and second is that there is meaningful difference between efficiency of this approach and the others. Furthermore, in this approach in order to compute the efficiency of DMUs the expert opinions have been considered as much as possible.

In this study, the performance measurement of bank branches has been considered by applying the different approaches of basic input-oriented CCR model, which differ together in combination type of inputs and outputs. Also, we have improved the major problems of DEA models from two aspects of infirmity of segregation and illusive distribution of weights by configuring the fuzzy approach based on confined weights. The results represent the high correlation of efficiency and ranking for two approaches of CCR model based on similar value criteria and group fuzzy weights, whereas it has descended for confined fuzzy weights approach. As a result, the obtained efficiency for branches can indicate the performance power of branches in using inputs and producing outputs. Also, the CCR model based on confined fuzzy weights presented the high level of accuracy in identifying the efficient units in order to offer the corrective actions on applying resources.

See Tables