Machine Learning-driven Group Ranking in Data Envelopment Analysis: Applications in the Banking Sector
الموضوعات :
Mohammad Sajjad Shahbazifar
1
,
Reza Kazemi Matin
2
,
Mohsen Khounsiavash
3
,
Fereshteh Koushki
4
1 - Department of Mathematics, Qazvin Branch, Islamic Azad University, Qazvin,
2 - Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
3 - Department of Mathematics, Qazvin Branch, Islamic Azad University, Qazvin, Iran.
4 - Department of Mathematics, Qazvin Branch, Islamic Azad University, Qazvin, Iran.
الکلمات المفتاحية: Group Efficiency, Banking Groups, Machine Learning, Neural Network, Data Envelopment Analysis, Ranking,
ملخص المقالة :
This paper explores the intersection of Group Ranking in Data Envelopment Analysis (DEA) and the potent capabilities of Machine Learning (ML) within the insurance sector, aiming to redefine group efficiency assessment. While DEA has been a cornerstone for evaluating Decision-Making Units (DMUs), the traditional models fall short in the nuanced insurance sector. To address these limitations, ML is integrated into DEA, enabling more effective DMU ranking. The study includes an empirical application within the banking industry, emphasizing the methodology's relevance and potential to transform the insurance landscape.
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3. Zhu, N., C. Zhu, and A. Emrouznejad, A combined machine learning algorithms and DEA method for measuring and predicting the efficiency of Chinese manufacturing listed companies. Journal of Management Science and Engineering, 2021. 6(4): p. 435-448.
4. Adler, N., L. Friedman, and Z. Sinuany-Stern, Review of ranking methods in the data envelopment analysis context. European journal of operational research, 2002. 140(2): p. 249-265.
5. Chen, Y., Ranking efficient units in DEA. Omega, 2004. 32(3): p. 213-219.
6. Sexton, T.R., R.H. Silkman, and A.J. Hogan, Data envelopment analysis: Critique and extensions. New directions for program evaluation, 1986. 1986(32): p. 73-105.
7. Liu, H.-h., Y.-y. Song, and G.-l. Yang, Cross-efficiency evaluation in data envelopment analysis based on prospect theory. European Journal of Operational Research, 2019. 273(1): p. 364-375.
8. Doyle, J. and R. Green, Efficiency and cross-efficiency in DEA: Derivations, meanings and uses. Journal of the operational research society, 1994. 45: p. 567-578.
9. Andersen, P. and N.C. Petersen, A procedure for ranking efficient units in data envelopment analysis. Management science, 1993. 39(10): p. 1261-1264.
10. Mehrabian, S., M.R. Alirezaee, and G.R. Jahanshahloo, A complete efficiency ranking of decision making units in data envelopment analysis. Computational optimization and applications, 1999. 14(2): p. 261-266.
11. Memariani, A. and G. Jahanshahloo, A model for ranking decision making units in data envelopment analysis. Ricerca Operativa, 2001(2001/97).
12. Ang, S., M. Chen, and F. Yang, Group cross-efficiency evaluation in data envelopment analysis: An application to Taiwan hotels. Computers & Industrial Engineering, 2018. 125: p. 190-199.
13. Shahbazifar, M.S., et al., Group ranking of two-stage production units in network data envelopment analysis. RAIRO-Operations Research, 2021. 55(3): p. 1825-1840.
14. Brunetti, A., et al., Computer vision and deep learning techniques for pedestrian detection and tracking: A survey. Neurocomputing, 2018. 300: p. 17-33.
15. Emrouznejad, A. and E. Shale, A combined neural network and DEA for measuring efficiency of large scale datasets. Computers & Industrial Engineering, 2009. 56(1): p. 249-254.
16. Misiunas, N., et al., DEANN: A healthcare analytic methodology of data envelopment analysis and artificial neural networks for the prediction of organ recipient functional status. Omega, 2016. 58: p. 46-54.
17. Thaker, K., et al., A DEA and random forest regression approach to studying bank efficiency and corporate governance. Journal of the Operational Research Society, 2022. 73(6): p. 1258-1277.
18. Barros, C.P. and P. Wanke, Insurance companies in Mozambique: A two-stage DEA and neural networks on efficiency and capacity slacks. Applied Economics, 2014. 46(29): p. 3591-3600.
19. Kwon, H.-B. and J. Lee, Two-stage production modeling of large US banks: A DEA-neural network approach. Expert Systems with Applications, 2015. 42(19): p. 6758-6766.
20. Hebb, D.O., The organization of behavior: A neuropsychological theory. 2005: Psychology press.
21. Stuart, R. and N. Peter, Artificial intelligence: a modern approach. 1995, Prentice-Hall.
22. Mehryar, M., R. Afshin, and T. Ameet, Foundations of Machine Learning. Adaptive computation and machine learning. 2012, MIT Press.
23. McCulloch, W.S. and W. Pitts, A logical calculus of the ideas immanent in nervous activity. The bulletin of mathematical biophysics, 1943. 5: p. 115-133.
24. Cheng, C.-S., A multi-layer neural network model for detecting changes in the process mean. Computers & Industrial Engineering, 1995. 28(1): p. 51-61.
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Islamic Azad University Rasht Branch ISSN: 2588-5723 E-ISSN:2008-5427
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Optimization Iranian Journal of Optimization Volume 15, Issue 3, 2023, 171-182 Research Paper |
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Online version is available on: https://sanad.iau.ir/journal/ijo
Machine Learning-driven Group Ranking in Data Envelopment Analysis: Applications in the Banking Sector
Mohammad Sajjad Shahbazifar 1, Reza Kazemi Matin 2, Mohsen Khounsiavash 1* and Fereshteh Koushki 1
1 Department of Mathematics, Qazvin Branch, Islamic Azad University, Qazvin, Iran
2* Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
Revise Date: 26 May 2024 Abstract
Keywords: Group Efficiency Banking Groups Machine Learning Neural Network Data Envelopment Analysis Ranking |
*Correspondence E‐mail: mfsiavash@gmail.com |
INTRODUCTION
Efficiency measurement of Decision-Making Units (DMUs) has been a focal point in organizational performance assessment since the pioneering work of Farrell (1957), who laid the groundwork for Data Envelopment Analysis (DEA). DEA, introduced by Charnes et al. (1979), employs linear programming techniques to evaluate the efficiency of DMUs with multiple inputs and outputs, thus offering a comprehensive framework for performance evaluation. Over the years, DEA has evolved, with new methodologies and applications emerging to address the complexities of diverse organizational settings across sectors such as government, healthcare, finance, and manufacturing. Despite its widespread adoption, traditional DEA approaches encounter challenges, particularly when assessing the efficiency of new DMUs. The proliferation of DMU datasets, fueled by the advent of big data, compounds this challenge. For instance, mainland China has witnessed a rapid increase in the number of small and micro-sized companies, surpassing 73 million (Emrouznejad et al., 2024).
Various methods have been developed to enhance the discrimination power of basic Data Envelopment Analysis (DEA) models and address challenges in evaluating organizational performance. Over the past three decades, numerous ranking methods have emerged within the DEA context. Adler et al. (2002) and Chen (2004) have extensively reviewed these ranking methods. Among them, the cross-efficiency evaluation, initially proposed by Sexton et al. (1986), stands out as the most popular. This method utilizes peer evaluation instead of self-evaluation information, overcoming some limitations of basic DEA models like CCR and BCC. However, its utility may diminish due to the non-uniqueness of optimal weights (Liu et al., 2019). To mitigate this issue, Doyle and Green (1994) introduced aggressive and benevolent formulations as secondary goals to select a solution from multiple optimal weights.
Another method proposed for ranking efficient units is super-efficiency, introduced by Andersen and Petersen (1993). This method involves eliminating the DMU under assessment from the DMU set and computing its distance from the new efficient border. However, this elimination can render associated DEA models infeasible (Mehrabian et al., 1999). To address this challenge, Memariani et al. (2001) modified the non-radial model presented by Mehrabian et al. (1999), ensuring the feasibility of the linear programming model.
While the mentioned methods primarily focus on individual evaluation of DMUs, many real-world scenarios involve DMUs as members of distinct groups. For instance, sales units of a brand operate independently but under a single management for achieving common targets. In such cases, group efficiency evaluation becomes crucial. Ang et al. (2018) examined this evaluation from two perspectives: group efficiency evaluation based on average performance and weakest performance.
To develop this method, Shahbazifar et al. (2021) proposed a novel two-stage network group efficiency evaluation method. This method, based on network DEA, offers a broader insight and yields more accurate results compared to conventional approaches. Their goal is to determine the true ranking of two-stage network production groups, presenting new network DEA models for efficiency evaluation based on both average and weakest performance criteria.
Evaluating the efficiency of each new DMU using conventional DEA methods necessitates substantial computational resources in terms of memory and CPU time. In response, there is a growing interest in leveraging Machine Learning (ML) algorithms to predict efficiency scores without the need for extensive re-analysis. ML algorithms, which learn from data to make predictions or decisions, present a promising approach to enhance efficiency assessment. Previous studies have explored various ML-DEA methodologies, including neural network back-propagation DEA algorithms (NNDEA), genetic algorithms, support vector machines (SVM), and integrated support vector machines (ISVM) (Emrouznejad et al., 2024). While existing literature highlights the potential of hybrid ML-DEA methodologies, several limitations persist. Many studies predominantly focus on neural networks or back-propagation neural networks for prediction tasks, with limited exploration of other ML algorithms. Moreover, there is a scarcity of research comparing the performance of integrated ML-DEA models with individual ML models (Emrouznejad et al., 2024). To address these gaps, Emrouznejad et al. (2024) aim to bridge traditional DEA methods with ML algorithms by proposing a comprehensive ML-DEA framework. Specifically, they introduce the ML-DEA algorithm: DEA-CCR model combined with back-propagation neural network (BPNN-DEA).
Subsequent to the seminal work by Charnes et al. (1979), numerous sophisticated applications have emerged, incorporating additional variables and complex models to assess the efficiency and productivity changes of Decision-Making Units (DMUs). These endeavors aim to enhance organizational performance across various sectors, both public and private. Additionally, Mahmoudi et al. (2024) proposed an incremental weighted cross-entropy loss function for convolutional neural networks to tackle class imbalance. Their method enhances performance by gradually increasing the weight of minority classes during training, showing superior results compared to other techniques on various datasets. Moreover, due to the intricate nature of DEA calculations, specialized software tools have been developed to facilitate analysis. However, in the process of assessing organizational performance, the addition of a new Decision-Making Unit (DMU) necessitates the rerunning of the DEA model. To circumvent the need for recalculating the efficiency of all DMUs, some studies have proposed predicting the DEA efficiency of new DMUs by integrating the DEA model with various Machine Learning (ML) algorithms. For instance, Liu et al. (2013) utilized DEA, a three-stage DEA, and artificial neural network (ANN) to evaluate the technical efficiency of 29 semiconductor firms in Taiwan. They observed that employing different approaches (DEA vs. NN) within a similar methodological framework yielded divergent results.
In today's era of rapid big data expansion, the growth of datasets has surged exponentially. Consequently, conducting Data Envelopment Analysis (DEA) on large datasets containing numerous inputs and outputs poses significant challenges due to the immense computational resources required, including memory and CPU time. Emrouznejad et al. (2009) introduced a novel solution to this issue with their proposal of a neural network back-propagation DEA algorithm (NNDEA). This innovative algorithm aims to streamline the efficiency assessment process by randomly selecting a subset of Decision-Making Units (DMUs) for neural network training. Subsequently, the trained model can be leveraged to estimate efficiency scores without the need to solve linear programming problems for each individual DMU.
Furthermore, in the realm of financial services, researchers have investigated the integration of DEA with machine learning techniques to enhance efficiency assessment in banking operations. For instance, Thaker et al. (2022) developed a hybrid DEA-Random Forest model to evaluate the operational efficiency of commercial banks. Additionally, in the context of manufacturing industries, Lee et al. (2019) proposed a novel approach that combines DEA with Convolutional Neural Networks (CNN) for assessing the operational efficiency of production processes. Barros et al. (2014) introduced a DEA-BPNN approach for evaluating and forecasting the efficiency ratings of insurance firms in Mozambique, while Kwon et al. (2015) developed a similar method for assessing efficiency in major US banking institutions.
In this paper, we have evaluated 21 banking groups, each consisting of 25 branches, using the Back-Propagation Neural Network (BPNN) method. We predict the group efficiency scores using this approach.
The rest of this paper is organized as follows. Section 2 provides a brief introduction of data envelopment analysis, the group efficiency evaluation method, and the BPNN machine learning algorithm. The research structure is explained in Section 3. In Section 4, some empirical applications are presented, and the efficiency scores obtained from the various methods are reported and analyzed. The last section includes conclusions and possible future research.
METHODOLOGIES
DEA and group efficiency evaluation
Data Envelopment Analysis (DEA) is a method used to evaluate the efficiency of Decision-Making Units (DMUs) by employing linear programming to envelop observed input and output vectors as tightly as possible. The DEA-CCR model, introduced by Charnes et al. (1978), focuses on the ratio of multiple outputs to multiple inputs, providing a measure of how effectively a DMU utilizes its resources to produce valuable outputs. This model imposes a condition whereby these ratios must be less than or equal to one for all other DMUs, eliminating the need for predefined weights on inputs and outputs (Charnes et al., 1978).
Consider a scenario where n Decision Making Units (DMUs) are assessed based on m inputs and s outputs. Let 
and 
represent the input and output values of 
respectively. The efficiency score of 
can be determined using the formula:
In this context, 
and 
represent the weights attributed to the 
-th input and 
-th output of 
respectively. The CCR model used to assess can be articulated as follows:
In this model, 
and 
represent virtual multipliers for the -th input and -th output respectively. The optimal solution to Model 1 for is denoted as 
and 
. is considered efficient if and only if 
, while if the value is below one, the DMU is considered inefficient.
Let's consider a scenario where 
DMUs are organized into 
groups, with each group 
(
) comprising 
members. Each member 
(
) within a group has 
inputs 
and 
outputs 
.. For each group 
(
) under evaluation, the group efficiency score based on average performance is obtained by solving the optimization Model 3.
Model 3 in linear form is as follows:
(4)
Suppose 
are the optimal solutions for Model 4. The optimal solution for model (4) provides the average group efficiency score for group t as follows:
(5)
When the efficiency of the group reaches the optimal level, the efficiency values of each DMU in group can be calculated as follows:
=
(6)
In this paper, we utilize a combination of machine learning and group performance evaluation models to predict group efficiency scores. Prior to that, in the following section, we introduce our selected machine learning algorithm and present its overview.
BPNN ML algorithm
The progression of machine learning (ML) can be delineated into three distinct epochs. Initially, Hebb (2005) laid the foundation for ML by pioneering neuropsychological learning mechanisms, initiating a brief period of development. However, from the mid-1960s to the late 1970s, progress stagnated due to constraints in computer memory and processing speed, impeding the realization of practical AI solutions. Since the late 1970s, ML has experienced a resurgence, expanding beyond single-concept learning to encompass multiple concepts and exploring diverse learning strategies. This revival has attracted considerable scholarly attention, particularly amidst rapid advancements in AI and data mining, resulting in numerous breakthroughs.
ML is inherently multidisciplinary, drawing insights from diverse domains such as probability theory, statistics, approximation theory, convex analysis, and algorithm complexity theory. At its core, ML aims to emulate human learning behaviors, facilitating the acquisition of new knowledge and skills to continually enhance performance. Over decades of evolution, ML has garnered widespread recognition, featuring algorithms that scrutinize data, glean insights, and make informed decisions or predictions regarding unknown phenomena. Its applications span a plethora of domains, including data mining, computer vision, biometric recognition, stock market analysis, and robotics. In essence, ML relies on algorithms to scrutinize data, extract patterns, and derive actionable insights. This paradigm shift obviates the need for explicitly programmed tasks, instead fostering autonomous algorithmic development. ML encompasses a gamut of methodologies, including supervised learning, unsupervised learning, semi-supervised learning, and reinforcement learning, each exhibiting distinct strengths and weaknesses. Supervised learning, for instance, is widely employed for classification and regression tasks, as elucidated in spam filtering and weather forecasting applications, respectively. For further elucidation on ML, one may refer to Stuart and Peter (1995), Mehryar, Afshin, and Ameet (2012), along with a myriad of other pertinent literature.
Given that the technical efficiency derived from the DEA-CCR model appears as continuous data, this study investigates a machine learning algorithm tailored specifically for regression tasks known as the back-propagation neural network (BPNN).
To introduce BPNN, it is essential to first delve into Artificial Neural Networks (ANNs) (McCulloch & Pitts, 1943). ANNs, prominent in machine learning and cognitive science, are inspired by biological neural networks found in the central nervous systems of animals. They serve to estimate or approximate functions that may depend on numerous inputs, typically of unknown nature. Let's provide a succinct overview of the original concept of ANNs: The foundational neuron model can be depicted as shown in Figure 1, representing the simplest form of a neuron. This model serves as an exemplar to elucidate the fundamental concept of ANNs. Imagine there are Decision-Making Units (DMUs), each possessing features (i.e., n inputs denoted as 
in Figure 1. Additionally, each DMU has a target variable 
, also known as the output variable, unique to each DMU (labeled as 
for 
). Given the varying importance of each feature for , distinct weights are assigned to them (represented as 
in Figure 1). Subsequently, the weighted sum of inputs and establishes a mapping relationship through an activation function.
In Eq. 7, 
represents the weighted sum of inputs, 
denotes the intercept term, and 
symbolizes the activation function. Common activation functions include the sigmoid function, tanh function, rectified linear unit function (ReLU), softmax function, etc. By collecting data from DMUs with known inputs and outputs, the weights 
and can be estimated based on Eq. 7, a process known as model training. Once the trained model is obtained, new DMUs with known inputs but unknown outputs can be evaluated using the model. Any necessary adjustments to the weights and can be made accordingly. The principles of the multilayer neural network model closely resemble this process; for further details, refer to Chen (1995).
Fig. 1. Diagram of single neuron model
Following extensive development, BPNN has emerged as the predominant method for training ANNs (Rumelhart et al., 1986). It boasts two primary features: (a) being a supervised learning method, extending the delta rule, and (b) requiring the use of activation functions that are differentiable everywhere.
The BPNN algorithm evolved from ANN, with its mathematical intricacies extensively discussed in various literature. This paper provides a concise introduction to its core principles: propagation and weight adjustment (namely, the computation of actual output proceeds from input to output, while weight and threshold modifications occur in the opposite direction).
Phase 1: Propagation involves two main steps
a. Forward propagation entails passing a training pattern's input through the neural network to produce output activations.
b. Back-propagation involves propagating the output activations generated in step (a) back through the neural network using the target associated with the training pattern. This step calculates the deltas for all output and hidden neurons.
During this phase, the output value of each node is computed based on various factors, including the output values of nodes in the preceding layer, the weights connecting the current node to all nodes in the previous layer, the current node's threshold, and the activation function. Commonly, the sigmoid function is employed as an activation function in this context.
Phase 2: Weight Update comprises the following steps
a. Compute the gradient of the weight by multiplying its output delta with the input activation.
b. Adjust the weight in the direction opposite to the gradient by subtracting a portion of it from the weight.
This phase constitutes the error back-propagation process. The fundamental concept behind BPNN is to refine network parameters by minimizing the error between the output layer and the expected value, thereby reducing the overall error.
RESEARCH STRUCTURE
The research framework investigates the amalgamation of the DEA method with the BPNN ML algorithm. The DEA-CCR model is initially utilized to evaluate the efficiency of each Decision Making Unit (DMU) within the training datasets. This assessment categorizes DMUs based on their technical efficiency, with the DEA efficiency serving as the target variable and the input/output indicators of the DEA model acting as feature variables. Subsequently, the BPNN algorithm is employed to analyze these categorized DMUs and derive patterns: What input/output combinations correspond to specific DEA efficiencies? Following training with the datasets, the BPNN model is refined until it meets evaluation criteria, and then it's applied to unclassified DMUs with unknown DEA efficiencies. This process facilitates the prediction of efficiency for these DMUs using the trained BPNN model.
Fig.2. Research structure exploring the connection between the DEA and ML
The research framework involves two main stages: the DEA stage and the ML stage, illustrated in Figure 4. In the first stage, known as the DEA stage, DMUs with suitable input and output indicators are selected based on real-world considerations. Their DEA efficiencies are then assessed using a DEA model. Moving to the second stage, known as the ML stage, the DEA outcomes are utilized to predict the DEA efficiency of unclassified DMUs through a frontier formed by the BPNN algorithm. Within this ML stage, four steps are undertaken:
Step1: Data Preprocessing. Primarily involves standardizing the data.
Step2: Model Training. Utilizing the training datasets containing DMUs marked by their DEA efficiency to extract rules, specifically determining the input/output combinations corresponding to specific DEA efficiencies.
Step3: Evaluation Criteria. If the model meets predefined standards regarding accuracy and stability, it is considered trained. Otherwise, further training is conducted.
Step4: Model Prediction. Utilizing the trained BPNN model to predict the DEA efficiency of new DMUs. This involves adding the new DMUs to the testing datasets and executing a Python code, which automatically calculates their predicted efficiency.
During the comparison and conclusion phase, the DEA efficiency is meticulously analyzed and juxtaposed with the ML-DEA efficiency (i.e., prediction efficiency). This analysis encompasses assessing the accuracy and stability of the model, conducting statistical tests, and making inferences.
EMPIRICAL ANALYSIS
In this section, we present the empirical application of our research, aimed at evaluating the efficiency of 525 branches of Mellat Bank in Iran. These branches are divided into 21 groups, each comprising 25 members include the following financial information:
Inputs:
: Regulatory Compliance Costs: Expenses related to ensuring compliance with banking regulations and laws, including hiring compliance officers, conducting audits, and implementing compliance software.
: Marketing and Advertising Expenses: Costs related to advertising campaigns, promotional materials, and marketing strategies aimed at attracting customers.
Outputs:
: Investment Gains: Revenue earned from returns on the bank's investments in stocks, bonds, and other financial instruments.
: Loan Interest Income: Revenue generated from interest payments on loans provided to customers, including personal loans, business loans, and mortgages.
These inputs and outputs were selected to comprehensively capture the factors influencing the bank’s operational efficiency and financial outcomes, ensuring that the model provides a meaningful analysis of the bank’s performance. (See Table 1)
Table. 1 Inputs and Outputs with Related Articles in Banking Industry Studies
Inputs/Outputs | Description | References | ||||
| Expenses related to ensuring compliance with banking regulations and laws. | Berger & Humphrey (1997) Hughes & Mester (2008) | ||||
| Costs related to advertising campaigns, promotional materials, and marketing strategies. | Berger & Humphrey (1997) Hughes & Mester (2008) | ||||
| Revenue earned from returns on the bank's investments in stocks, bonds, and other financial instruments | Berger & Humphrey (1997) Hughes & Mester (2008) | ||||
| Revenue generated from interest payments on loans provided to customers | Berger & Humphrey (1997) Hughes & Mester (2008) |
|
|
|
| |||
Count | 525 | 525 | 525 | 525 | ||
Mean | 4.8E+09 | 6.84E+09 | 3.59E+08 | 7.17E+09 | ||
Std | 1.59E+10 | 4.31E+10 | 2.06E+09 | 4.51E+10 | ||
Min | 22595676 | 15879188 | -9.1E+09 | 12697732 | ||
25% | 7.63E+08 | 4.55E+08 | 45309186 | 5.06E+08 | ||
50% | 1.69E+09 | 1.24E+09 | 97692782 | 1.32E+09 | ||
75% | 3.75E+09 | 3.4E+09 | 2.28E+08 | 3.43E+09 | ||
Max | 2.91E+11 | 9.15E+11 | 4.12E+10 | 9.6E+11 |
GRP | DMUs | DEA-CCR | AGE | DEA-BPNN | AGE-BPNN | P-Value |
|---|---|---|---|---|---|---|
Group 21 | 1 | 0.662 |
0.675 | 0.727 |
0.707 | P<=0.001 |
2 | 0.757 | 0.721 | P<=0.001 | |||
3 | 0.870 | 0.744 | P<=0.001 | |||
4 | 0.542 | 0.706 | P<=0.001 | |||
5 | 0.592 | 0.716 | P<=0.001 | |||
6 | 0.769 | 0.746 | P<=0.001 | |||
7 | 0.791 | 0.755 | P<=0.001 | |||
8 | 0.742 | 0.672 | P<=0.001 | |||
9 | 0.492 | 0.678 | P<=0.001 | |||
10 | 0.564 | 0.627 | P<=0.001 | |||
11 | 0.737 | 0.728 | P<=0.001 | |||
12 | 0.781 | 0.770 | P<=0.001 | |||
13 | 0.426 | 0.697 | P<=0.001 | |||
14 | 0.915 | 0.740 | P<=0.001 | |||
15 | 0.660 | 0.703 | P<=0.001 | |||
16 | 0.847 | 0.794 | P<=0.001 | |||
17 | 0.685 | 0.723 | P<=0.001 | |||
18 | 0.674 | 0.711 | P<=0.001 | |||
19 | 0.680 | 0.601 | P<=0.001 | |||
20 | 0.644 | 0.709 | P<=0.001 | |||
21 | 0.666 | 0.714 | P<=0.001 | |||
22 | 0.740 | 0.720 | P<=0.001 | |||
23 | 0.560 | 0.581 | P<=0.001 | |||
24 | 0.600 | 0.702 | P<=0.001 | |||
25 | 0.548 | 0.685 | P<=0.001 |
As depicted in Table 3, the DEA-CCR scores for individual branches within Group 21 range from 0.492 to 0.915, indicating varying levels of efficiency in resource utilization. Furthermore, the DEA-BPNN scores demonstrate slight variations compared to the DEA-CCR scores, suggesting the effectiveness of neural network-based modeling in capturing nuanced efficiency metrics.
Notably, the p-values associated with the DEA-BPNN scores are all less than or equal to 0.001, indicating statistical significance and reinforcing the reliability of our findings.
The results obtained from our empirical analysis provide valuable insights into the efficiency of Iranian Mellat Bank branches. By identifying and analyzing the efficiency scores of individual branches within Group 21, we gain a deeper understanding of the factors influencing bank performance. Moreover, the application of advanced modeling techniques such as DEA-BPNN enhances the accuracy of our predictions, enabling more robust decision-making processes within the banking sector. In conclusion, our empirical application underscores the efficacy of Data Envelopment Analysis (DEA) methodologies in assessing the efficiency of Mellat Bank branches in Iran. Through meticulous analysis, we have elucidated the nuanced factors influencing bank performance, providing valuable insights for strategic management decisions. By accurately predicting individual and group efficiency scores, our approach equips bank managers with reliable metrics to inform decision-making processes. With a clearer understanding of resource allocation efficiency, managers can make informed strategic choices aimed at optimizing operations and enhancing overall bank performance.
Moreover, our findings offer invaluable implications for risk management within the banking sector. By identifying inefficiencies and areas for improvement, banks can proactively mitigate risks and bolster their resilience in an increasingly competitive market landscape.
In essence, our research not only contributes to enhancing the operational efficiency of Mellat Bank branches but also empowers managers with the tools and insights necessary to navigate challenges and capitalize on opportunities in the dynamic banking industry.
CONCLUSION
In this paper, we have applied Data Envelopment Analysis (DEA) in conjunction with Backpropagation Neural Network (BPNN) modeling to evaluate the efficiency of Mellat Bank branches in Iran. Through rigorous analysis of input-output relationships, we have provided valuable insights into the factors shaping bank performance. By accurately predicting individual and group efficiency scores, our approach equips bank managers with reliable metrics to drive strategic decision-making processes. The findings of this study offer actionable insights for optimizing resource allocation and enhancing overall bank performance. Additionally, they underscore the significance of advanced modeling techniques in capturing nuanced efficiency metrics within the banking sector. By leveraging DEA and BPNN methodologies, we have contributed to the empirical literature on bank efficiency evaluation and provided practical implications for strategic management in the banking industry.
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