Journal of Optimization

Volume 2016 (2016), Article ID 5259817, 7 pages

http://dx.doi.org/10.1155/2016/5259817

## Prioritization of the Factors Affecting Bank Efficiency Using Combined Data Envelopment Analysis and Analytical Hierarchy Process Methods

Department of Mathematics, Islamic Azad University, Ayatollah Amoli Branch, Amol, Iran

Received 10 December 2015; Revised 3 April 2016; Accepted 14 April 2016

Academic Editor: Adil M. Bagirov

Copyright © 2016 Mehdi Fallah Jelodar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Bank branches have a vital role in the economy of all countries. They collect assets from various sources and put them in the hand of those sectors that need liquidity. Due to the limited financial and human resources and capitals and also because of the unlimited and new customers’ needs and strong competition between banks and financial and credit institutions, the purpose of this study is to provide an answer to the question of which of the factors affecting performance, creating value, and increasing shareholder dividends are superior to others and consequently managers should pay more attention to them. Therefore, in this study, the factors affecting performance (efficiency) in the areas of management, personnel, finance, and customers were segmented and obtained results were ranked using both methods of Data Envelopment Analysis and hierarchical analysis. In both of these methods, the leadership style in the area of management; the recruitment and resource allocation in the area of financing; the employees’ satisfaction, dignity, and self-actualization in the area of employees; and meeting the new needs of customers got more weights.

#### 1. Introduction

Basically, managers of the banks are forced to select and improve methods of providing banking services, investments, marketing, human resource management, customer management, and competition with other banks and ultimately increasing the productivity and efficiency among their branches due to the economic conditions and lack of inputs, production factors, and technology. Obviously, when inefficient units become efficient, at the same time the goals are achieved, the cost of services are reduced, and wasting economic limited resources is avoided and losses due to the inefficiencies in the banks may be reduced to a minimum amount and the banking system as a whole is more efficient and, therefore, the national interests are more provided. Thus, given the role of banks in the development of country and also due to the existence of numerous branches, paying attention to the efficiency of banks has a special importance, so that a variety of studies have been conducted in recent years to identify the factors affecting performance (efficiency) in various areas, some of which are mentioned bellow.

In evaluating the strategic performance of the banks using fuzzy AHP method, Motameni et al. (2010) reached the conclusion that nonfinancial performance is more important than financial performance and, in the evaluation of financial performance, the criterion of resources share earned first place in terms of importance and the criteria of profitability and return on assets were placed in the next position. In nonfinancial performance measurement, the criterion of pricing was ranked first in importance and criteria of e-banking and service quality were next in the rank [1]. Mirjalili (2006) conducted a study to identify and improve employees’ productivity using fuzzy DEA method. According to the results of this study, bank staff motivation in immaterial dimensions (unification of job and occupations and job security and equality in the organization and education) is more important compared to the material dimensions (salary, bonus, welfare, work physical environment, and safety) [2]. Mansoori (2009) compared the DEA and AHP methods using the technique of prioritizing key performance indicators (KPIs) for stock companies. The results showed no significant difference in the prioritization done by these two methods and DEA has a higher ability to prioritize the key performance indicators compared to the Analytical Hierarchy Process (AHP) [3]. Chang and Chiu (2006) studied the long-term profitability of banks in Taiwan and reached this conclusion that the banking services are the most important factors for the increased profitability of banks’ branches. Also, the bank employees were considered as the most important and basic factor to achieve increased profitability [4]. Timothy (2010) examined the tangible and intangible factors and the relative importance of each of these sources in Tanzania. Risk management, management return, services, innovation capability, and the ability to measure the market performance are five important sources affecting the performance of commercial banks in Tanzania. In addition, quantitative analysis shows that the productivity of human capital, physical capital productivity, mobilization of the funds, size of the bank, interest income, and the management return have positive influence on managerial efficiency of banks [5].

#### 2. Literature of the Study

In this section we are going to summarize Analytical Hierarchy Process (AHP), Data Envelopment Analysis (DEA), and combined DEA/AHP methods. We will apply the last method to rank the factors affecting bank efficiency.

##### 2.1. Analytical Hierarchy Process (AHP)

Classic Analytical Hierarchy Process method, proposed by T. L. Saati, is the most popular and practical methods of MADM. This method is used when there is a need for simultaneous consideration of qualitative and quantitative aspects of a decision. AHP technique, using pairwise comparisons (one by one) and combined results, reduces the complexity of decisions; thus, not only could it help decision-makers to obtain the best decision, but also it provides a clear justification for showing that the obtained decision is the best one [6]. AHP method is the organization of decision-making at different hierarchical levels where a set of options are in lower levels, a set of decision criteria and standards are at the average level, and the static goals are at the top levels of decision-making hierarchy. Elements of decision-making usually represent a finite set of alternatives and decision-making regulations represent a set of properties that are effective in decision-making [7]. In order to control the outcome of this procedure, the consistency ratio is calculated for each paired comparison and it shows how judgments are consistent and can be relied on [8].

Some key and basic steps involved in this methodology are as follows.

*Step 1 (structuring of the decision problem into a hierarchical model). *It includes decomposition of the decision problem into elements according to their common characteristics and the formation of a hierarchical model having different levels. A simple AHP model has three levels (goal, criteria, and alternatives); more complex models containing more than three levels are also used in the literature. For example, criteria can be divided further into subcriteria and sub-subcriteria. Additional levels containing different actors relevant to the problem under consideration may also be included in AHP studies.

*Step 2 (making pairwise comparisons and obtaining the judgment matrix). *In this step, the elements of a particular level are compared with respect to a specific element in the immediate upper level. The resulting weights of the elements may be called the local weights. The opinion of a decision-maker (DM) is elicited for comparing the elements. Elements are compared pairwise and judgments on comparative attractiveness of elements are captured using a rating scale (1-to-9 scale in traditional AHP). Usually, an element receiving higher rating is viewed as superior (or more attractive) compared to another one that receives a lower rating. The comparisons are used to form a matrix of pairwise comparisons called the judgment matrix . Each entry of the judgment matrix is governed by the three rules: ; ; and for all . If the transitivity property holds, that is, , for all the entries of the matrix, then the matrix is said to be consistent. If the property does not hold for all the entries, the level of inconsistency can be captured by a measure called consistency ratio (see next step).

*Step 3 (local weights and consistency of comparisons). *In this step, local weights of the elements are calculated from the judgment matrices using the eigenvector method (EVM). The normalized eigenvector corresponding to the principal eigenvalue of the judgment matrix provides the weights of the corresponding elements. Though EVM is followed widely in traditional AHP computations, other methods are also suggested for calculating weights, including the logarithmic least-square technique (LLST) and goal programming. When EVM is used, consistency ratio (CR) can be computed. For a consistent matrix value of CR less than 0.1 is considered acceptable because human judgments need not be always consistent, and there may be inconsistencies introduced because of the nature of scale used. If CR for a matrix is more than 0.1, judgments should be elicited once again from the DM till they give more consistent judgments.

*Step 4 (aggregation of weights across various levels to obtain the final weights of alternatives). *Once the local weights of elements of different levels are obtained as outlined in Step 3, they are aggregated to obtain final weights of the decision alternatives (elements at the lowest level).

##### 2.2. Data Envelopment Analysis (DEA)

Data Envelopment Analysis is a mathematical programming method which is used to evaluate the efficiency of DMUs with multiple inputs and outputs. Efficiency measurement has always been considered by researchers because of its importance in assessing the performance of a company or organization. In 1957, Farrell measured efficiency of a manufacturing unit using a method such as efficiency measurement in engineering issues. The case considered by Farrell to measure the efficiency included an output and an input. Charnes, Cooper, and Rhodes developed Farrell’s viewpoint (approach) and provided a model that was able to measure the efficiency with multiple inputs and outputs. This pattern was named Data Envelopment Analysis and was used for the first time in 1978 by The University of Texas in the Ph.D. thesis (dissertation) of Edward Rhodes (supervised by Cooper), entitled “An assessment of educational progress of students in the national American schools” [9]. DEA focuses on the analysis of different concepts of relative efficiency such as cost, revenue and profit efficiency, productivity of the whole components, and factors of organizational units (the so-called decision-making units (DMUs)) in the use of inputs to produce output. Decomposition to the elements of efficiency is an opportunity to analyze the performance and to avoid the risk of nonprofitability of banks. Cost efficiency reflects the company’s ability to minimize costs given a particular level of output and income return shows whether the bank has reached the maximum level of income and productivity using a part of input and ultimately the profit efficiency seeks to minimize costs and maximize income [10]. This method is not sensitive to the measurement unit and inputs can have different units and also it does not need any specific functional form of data in order to determine the efficiency of banks. In fact it is an empirical function of the observations. DEA standard does not control optimization of multiple periods and may be at the risk of managerial decision-making. Therefore, after identification of an efficient unit, one must again control data and outputs and ensure their accuracy [11]. The use of Data Envelopment Analysis model to relatively evaluate the units requires the two basic characteristics: the nature of the model (input-oriented nature and the output-oriented nature) and returns to scale (CCR fixed and BCC variable).

Consider , DMUs with inputs and outputs. The input and output vectors of are and in which , , , and .

By using the nonempty, constant return to scale and convexity and possibility postulates, the production possibility set (PPS) is made as follows: Let be evaluated. The multiplier form of CCR model [1], in input-oriented case, is as follows: The above formula is known as envelopment form of CCR model. Its dual problem is known as the multiplier form of CCR model which is as follows:

##### 2.3. DEAHP Method

DEA method is a useful tool for the performance evaluation of decision-making units in the management science which calculates the efficiency of each decision-making unit. The main objective of DEA is to determine the efficiency of a system or a decision-making unit which produces one or more outputs using one or more inputs. On the other hand, AHP is also a useful tool in the Multicriteria Decision-Making (MCDM) to select the best option and to rank different options. Calculation of the relative weights of the elements is the main concept of the AHP method. So far, several approaches have been provided to calculate the weight from the paired comparison matrix. In 2006, Ramanathan [12] provided a method through which the relative weight of the paired comparison matrix is obtained using DEA model. Calculation of the exact weight of each element for the consistent matrices is one of the outstanding points of this method. In this study, the meaning of efficiency in DEA method and the meaning of relative weights in AHP method have become identical. Since the proposed method is a combination of DEA and AHP methods, Ramanathan chose the name of “DEAHP” for this method. In DEAHP method, each row of the paired comparison matrix was considered as a DMU and each of its columns was considered as an output. Therefore, in a paired comparison matrix , there are “” decision-making units (DMUs) and “” outputs corresponding to each DMU. Note that each component of the paired comparison matrix is considered as an output. DEA has logically the characteristics of an output because larger number of is prioritized to a component with the smaller number in AHP. Therefore, the priority in AHP can be considered as identical to the output of the DEA. In DEAHP, Ramanathan used CCR models to calculate the efficiency of each DMU and that is why he considered a fixed input equal to 1 for each DMU and efficiency score of each DMU which is obtained using different models of DEA (CCR envelopment form in the input and output nature, multiplier form of CCR model in the input and output nature) which was considered as the relative weight of each factor. Ramanathan [12] proposed model for the calculation of the relative weights of elements in a paired comparison matrix using multiplier form of CCR is as follows: One may normalize the obtained efficiency scores as follows to be used in AHP content:All the weights are less than or equal to 1 and their summation becomes unity by the above normalization.

This paper is organized as follows: An introduction and literature review are presented in the first two sections. Ranking of the factors affecting bank efficiency is discussed in Section 3. Analysis of the results and conclusion are presented in Sections 4 and 5.

Participants in this study are 80 people, including experts, managing directors engaged in branches management, and managers of Mellat banks in Tehran. Since the current study is related to the collection of standards and options and provides the possibility of deciding on the selection and giving importance to the indicators, therefore, it is an applied research. But, in terms of technique, it is descriptive-survey study because it provides the possibility of analyzing the subject and decision-making through describing the criteria and decision alternatives and also because in this study a questionnaire is designed to complete the calculations. At first, in this study, scientific literature related to the subject and the primary criteria for decision-making were identified using desk method and searching in the valid databases. Then, identified criteria were classified into four categories, management, investors, employees, and customers, and distributed as a questionnaire among experts and professionals and they were asked to provide their comments through pair comparison of the indicators.

#### 3. Prioritization of the Factors Affecting Efficiency

Given the mentioned concepts, factors affecting the efficiency were first prioritized using AHP method. In this method, prioritization of factors affecting performance (efficiency) has been considered at the first level which is the purpose of using this method and the second level is composed of 4 criteria of management, finance, staff, and customers and the third level consisted of 7 items in each field which are summarized in Table 1. Following hierarchical modeling of the decision concept, elements (indicators or options) of any level were compared to the corresponding elements in higher level (2 by 2) and 50 questionnaires were completed. In order to combine tables of the paired comparisons of all respondents, the geometric mean was used and the relative weight was obtained from the arithmetic mean. In all four areas, the consistency ratio was less than 0.1 which represents the good consistency ratio among the comparisons. Then, in the second method, weights of options were calculated based on the model proposed by Ramanathan using GAMS software which is DEA linear programming model. The results of both methods were similar to each other. The first priority is the same in all 4 areas and other indicators were ranked with a slight difference and the obtained percentages had also a small difference. The results are summarized in Tables 2, 3, 4, and 5.