تحلیل پوششی داده ها

Insurance companies, like any other company, must have a strong and successful performance in order to achieve their predetermined goals and missions. In this regard, it is effective to know how successful their organization has been in achieving these goals. In Iran, the growth and development of companies operating in the financial sector has always faced challenges, since one of the most important economic sectors of any country is its financial sector, in this research, first, based on the data Based on the data obtained from the Central Insurance Statistics, insurance companies were prioritized and then the challenges faced by these companies were identified using the content analysis method. We believe that part of these challenges is caused by the traditional view of the currents of this field from the consumers, which needs to modify the way of looking at the audience. The identified challenges were placed in five dimensions of uncertainty in the environment, structural, strategic, internal/external, systemic barriers.

this research, with the aim of evaluating the green innovation ecosystem and the way of green science and technology policy of selected European countries in order to ensure that Europe is moving towards minimizing Carbon, holistic sustainable development, and the green, innovative and competitive economy are on the move. This research is trying to provide a set of useful input, mediator and output indicators to determine the model indicating the stages affecting the performance of the green innovation ecosystem of the selected countries by examining the background of similar research. By collecting the available data through data banks, and preparing the ground for mathematical modeling, the mathematical model was designed by combining methods of network data envelopment analysis and game theory with the help of Lingo software to combine relative efficiency in functional areas and create a Calculate the final weighted score to evaluate the performance of the green innovation ecosystem for EU member states. The results indicate that according to the designed conceptual model including four stages of knowledge creation and development, knowledge implementation, financial and economic transformations and environmental protection, with the change in the performance of countries in the stage of financial and economic transformations, efficiency The total number of countries increases significantly;

When two or more organizations seek to enhance their collaboration, they may opt to form strategic alliances. These alliances aim to progress cooperatively toward shared goals through resource sharing, while maintaining their independence. Maturity models are essential tools for aiding manufacturing organizations in developing their partnerships. However, there is a lack of empirical research on creating a strategic alliance maturity model with clear guidelines. Consequently, no existing model effectively measures the maturity of a strategic alliance, particularly one that can address inaccuracies due to human judgment and inherent evaluation uncertainties. This research aims to design a method to assess the maturity level of strategic alliances, providing a better understanding of the current state of cooperation based on strategic alliance maturity criteria.

This research developed a maturity model using fuzzy logic to evaluate the status of a collaboration at a specific point in time. The strategic alliance maturity model, based on fuzzy logic, was created through a clear and precise procedure and a multi-method approach, including literature reviews, interviews, focus groups, and case studies. A weighted fuzzy inference system combined with the fuzzy data envelopment analysis technique was employed to measure maturity levels using specific indicators. Additionally, a genetic algorithm was applied to generate a set of fuzzy rules. Like all maturity models, the one developed in this research consists of two main components: the maturity levels of the strategic alliance and its maturity dimensions.

The research model defines five levels of maturity: ad-hoc, initial, managed, planned, and optimized strategic alliance. A 44-item list of indicators for measuring strategic alliance maturity was compiled from articles, expert interviews, and analysis of successful and unsuccessful alliances. This list was then categorized into 17 criteria across six dimensions. Essential indicators were identified using the content validity ratio technique, and their relative importance was determined through data envelopment analysis. Expert surveys were used to create fuzzy sets for the variables of the fuzzy inference system. Additionally, a set of fuzzy rules was developed by examining examples of strategic alliances both domestically and internationally, and refining them through expert surveys.

The proposed model has been evaluated and validated through a real case study involving collaboration between a manufacturing organization and its business partner. The research results demonstrate that this approach offers a robust and practical diagnostic tool based on a set of strategic alliance maturity indicators. By analyzing the gaps identified by this model, an action plan can be devised to enhance the maturity level of the strategic alliance.

The petrochemical industry in Iran, as a flagship sector, plays a pivotal role in the national economy, supplying a substantial share of its output to downstream industries. In recent decades, advancements in technology and research within the petrochemical sector have led to substantial improvements, reducing costs and enhancing efficiency. Therefore, considering the importance of the petrochemical industry and its role in economic growth, this article aims to evaluate the efficiency of petrochemical companies using the bootstrap-DEA approach. This method provides statistical inference regarding technical efficiency criteria in non-parametric frontier models.

To achieve this objective, a comprehensive two-stage approach was adopted. First, input-oriented efficiency scores were estimated under the assumptions of constant, variable, and non-increasing returns to scale for all companies, using radial (Debro-Farrell efficiency) and non-radial (Russell efficiency) methodologies to provide a robust evaluation. Then, a non-parametric independence test was conducted to identify the appropriate bootstrap implementation approach. Finally, considering the test results, the efficiency scores of petrochemical companies were estimated using the bootstrap-DEA approach. The bootstrap process allows for bias estimation and the calculation of confidence intervals for initial estimates.

The results indicate that Tondgoyan Company achieved Debro-Farrell efficiency under all three scenarios: constant, variable, and non-increasing returns to scale. Additionally, Zagros and Fanavaran companies exhibited Debro-Farrell efficiency under variable returns to scale. However, 18 other companies were inefficient, with Ghadir Petrochemical Company displaying the worst performance, achieving an efficiency score of 0.68 under constant returns to scale. Bias-corrected radial technical efficiency scores across homogeneous, heterogeneous, and subsampling bootstrap methods revealed that none of the 21 petrochemical companies exhibited full technical efficiency. Among them, Fanavaran and Tondgoyan showed better performance, while Aria, Pardis, Shiraz, and Isfahan Oil companies demonstrated the lowest input-oriented technical efficiency. Output-oriented technical efficiency findings indicated that Tondgoyan and Zagros were efficient, while Ghadir had the worst performance, with an efficiency score of 1.37, signifying 37% excess input consumption. The results further demonstrate that radial efficiency estimates are prone to overestimation, as confirmed by heterogeneous smooth bootstrap and subsampling techniques.

One of the primary objectives of Iran's 7th Development Plan is achieving 8% economic growth, with 2.8% attributed to productivity and efficiency improvements in production factors, including capital, human resources, technology, and management. Emphasis has been placed on bolstering the value-added chain within the petrochemical industry. Therefore, attention to the development of midstream and downstream petrochemical industries through reinvesting revenues from the export of upstream products is crucial for completing the value chain of the petrochemical sector.

In this paper, a mathematical modeling is presented to determine efficient locations for deployment of support forces using data envelopment analysis.

The proposed model has the possibility to first change the manageable inputs in order to improve the outputs according to the principle of managerial accessibility and also if it is not possible to reduce the unmanageable inputs according to the principle of natural accessibility, it keeps them at least at the existing level. Therefore, the most important innovation and contribution of the present research is the modeling of the positioning of the support forces to support the ground forces in future battles, which is created by using data envelopment analysis and the simultaneous use of natural and managerial accessibility principles.

The intended model has been used to evaluate 25 potential locations that are ready to provide ground support services to help local forces in the disputed area so that the fire of war ends in favor of local forces. Finally, by providing a sensitivity analysis on the manageable input values, the maximum possible changes on the value of this type of input for each of the locations are specified.

Originality:

 The results of this research are of great importance considering the conditions raised in making and the effectiveness of commanders' decisions in order to locate support forces in future battles.

Undesirable outputs are an integral part of production in various decision-making units, and to bring analyses closer to the real world, it is necessary to consider, undesirable outputs in performance evaluation research. In this paper, a new hybrid model for evaluating the efficiency of decision-making units in the oil industry is presented, which uses slack-based data envelopment analysis techniques and advanced machine learning algorithms. The proposed model specifically focuses on improving efficiency considering undesirable outputs and conditions of uncertainty. Three machine learning algorithms including artificial neural networks, support vector machines, and XGBoost are used to predict and improve the results of slack-based models. This study involves the evaluation of 37 decision-making units within the National Petroleum Products Distribution Company, and the results show a significant improvement in efficiency using predicted data compared to actual data. This research not only contributes to new perspectives in efficiency evaluation and improvement but also offers innovative hybrid methods to address challenges in operational management.

The main purpose of this article is to measure the efficiency of the multi-level sustainable supply network in Iran's transportation industry using a radial model in the envelopment analysis of network data with a double border and combining it with Malmquist index

The research method is based on operational research and presenting a new model based on the overlay analysis technique of network-oriented data. The desired model is built considering the unfavorable output indicators and the double border.

The findings showed that the presented model is able to evaluate the sustainable supply chain in the presence of favorable and unfavorable data. This model measures and evaluates three indicators of the sustainable supply chain of the industry including input, intermediate and final output sectors and by creating a double border. In addition, it evaluates this chain in the passenger sector of Iran's transportation industry and compared to similar models, it has an advantage in calculating the efficiency of the multi-level chain and combining it with Malmquist's efficiency index in optimistic and pessimistic states.

According to the obtained results, the efficiency of the transportation network of each province has been calculated according to the efficiency score in the desired years and the average period. Then, by combining the Malmquist index, the progress or regression of the transportation network's productivity has been investigated during a consecutive period of time. The results of this research can be used in the strategic planning of the transportation industry.

Organisational Citizenship Behaviour (OCB) is one of the important concepts that has been used as an effective factor in the success of organisations in recent years. Despite the proven effect of OCB on the effectiveness and efficiency of the organisation, the appropriate method to determine the extent of its effect is less known. OCB is a qualitative indicator as an output in performance evaluation. In this article, we measure the effect of the OCB quality index on the efficiency of institutions using the envelopment analysis method of ordinal data without compensatory properties.

Data coverage analysis is a powerful tool for assessing the performance of decision-making institutions based on a large number of input and output indicators, which can be quantitative or qualitative. Data coverage analysis models have compensatory properties, i.e. the weakness of one index is covered by the strength of another, and efficient institutions do not necessarily have a favourable quality level. This article presents a new method for performance evaluation that includes the quality index of OCB and a modification of the data envelopment analysis model without compensability. Another feature of the proposed model is the ability to separate qualitative and quantitative indicators in the evaluation. In the presented method for ranking institutions, the improvement of quality is considered simultaneously with the reduction of costs without compensability.

In this study, ten public and applied scientific institutions in three cities of the country were evaluated with the proposed model. Four quantitative indicators and one qualitative index of OCB were used in the evaluation.

Originality/Value: 

The OCB index was measured using 1024 questionnaires and the results show the efficiency of 7 institutions. Then, by using the proposed new method, the ranking of institutions with logical results in performance evaluation was achieved. To validate the method, the results of the proposed method were compared with the ranking results of the hierarchical process method.

Data Envelopment Analysis (DEA) is an approach based on mathematical programming for the relative evaluation of decision-making units treated as similar yet distinct production systems. In this approach, the performance of each unit is characterized by describing the transformation of specific inputs into specific outputs. Traditional DEA models assume that the role of each performance factor is clearly defined. However, in some real-world problems, certain factors might be identified as dual-role factors depending on the evaluation nature or the decision-makers' perspective. These factors can play the role of both input and output, or even be considered neutral in assessing the units' performance. In the current paper, to determine the status of dual-role factors and calculate the efficiency of DMUs, two new linear programming models, based on the concept of deviation in the efficiency constraint and a common set of weights, are suggested. The main advantages of the proposed models are significantly reducing the computations and iterations required to solve the model, and involving all DMUs to determine the role of factors. To assess the performance of the proposed models, a data set for the evaluation of eighteen suppliers in the presence of two inputs, three outputs, and two dual-role factors has been employed. The obtained results showed that, compared to other models, the proposed models are computationally more efficient, and the role determination and evaluation of the units, based on the obtained weights from these models, are better aligned with the expectations of decision-makers

In health care provider organizations (HCPOs), there are several sub-units, simultaneously providing health and preventive services to the population covered, in which measuring productivity is one of the most important challenges for the managers of these organizations. Hence, the purpose of this study is to provide an integrative approach of data envelopment analysis (DEA) and Malmquist productivity index (MPI) to monitor the productivity in Iranian Petroleum Industry Health Organization (PIHO) as an HCPO. In this study, using the indicators related to efficiency and defining the specialized indicators affecting the performance of the sub-units of this organization, the growth rate of the performance of the sub-units was determined through calculating four distance functions and Malmquist productivity Index. According to the results of this study, 27 specialized indicators in the fields of direct and indirect health and preventive services for monitoring the effectiveness of proposed HCPO have been presented. Also, the growth rate of productivity of the fifteen areas of the organization under study has been evaluated from 2019 to 2021. The innovative aspect of this article lies in the definition of effectiveness measurement indicators and presentation of a theoretical framework for monitoring the rate of productivity in HCPOs. The findings of this applied research in health service organizations can be used to enhance capacity in different areas of health care and save resources.

Since the healthcare system is one of the most important pillars of community health, and considering that providing healthcare services to the people is one of the elements of individual development in any country, attention and supervision of this sector can lead to development and social welfare. To ensure better and higher quality healthcare services, performance evaluation in the health sector plays a crucial role. In order to achieve this, proper and proportional use of existing facilities and assets is inevitable. In this study, by introducing an application in the field of healthcare systems, the educational hospitals of the country have been measured in terms of performance and their managerial ability has been calculated. Additionally, by identifying and introducing the impact of contextual variables on the performance of decision-making units, their efficiency has been assessed. For this purpose, data related to educational hospitals in 31 provinces of the country was collected, and then by identifying contextual variables and with the presence of undesirable factors, the efficiency was evaluated and the managerial ability of each was calculated. To reach this goal, in the first step, technical efficiency with the presence of undesirable factors was calculated using data envelopment analysis technique, and then the logarithm of technical efficiency obtained from the first stage was regressed on a set of contextual variables that affect hospital performance. In the next stage, managerial ability was extracted from the residual of the regression obtained from the previous stage. Finally, a unique ranking based on the managerial ability of each unit was provided. Ultimately, the results obtained were analyzed and examined in order to provide valuable suggestions for managers and more efficient management of the country's hospitals to maintain public health. According to the study, without considering contextual variables, 25 effective units were evaluated, but by applying the effect of contextual variables on the efficiency index, no unit becomes effective, proving the high impact of such indices on the performance of units. Additionally, in the ranking of units based on managerial ability, Lorestan province ranked first and Golestan province ranked last.

One of the important issues that has attracted the attention of economists over the past decades is the role of financial systems in the economic growth of countries. Insurance industry is one significant component of financial markets. Therefore, the stability and efficiency of insurance industry as a financial market sector is important for a country's economy. One of the most crucial changes in Iran's insurance industry is the regulations having been made in recent years. One main goal of regulation is to eliminate problems of market failure and improve efficiency. This research investigates the effect of these regulations on the efficiency of insurance companies in Iran.

The studied community is 27 insurance companies in the country and the relevant statistics were collected for the years 1385-1400 Persian Year (2005-2020). This study was conducted in two stages. In the first stage, the efficiency of insurance companies has been measured, using the method of data envelopment analysis (DEA) with the bootstrap approach. The implicit assumption of the traditional data envelopment analysis method is that the inputs and outputs are definite. But the output of an insurer is not necessarily certain. To solve this problem, we can use the bootstrap approach to obtain statistical characteristics for this technique. In the second stage, in order to investigate the effect of regulation on efficiency, according to the reviewed studies, the purpose of the present study, and the conditions of Iran's insurance industry, the effective factors on efficiency are determined and the regression model is defined. Then, the dynamic regression model was estimated using the generalized method of moments (GMM) and the related tests confirmed the validity of the results of the model. To calculate the efficiency and estimation of the model, MATLAB and Eviews software were used.

The most important finding of the research is the significant effect of regulation on efficiency. Also the coefficient of regulation, market share, and privateness of insurance companies are estimated as -0.066, 0.041 and 0.306 respectively.

The results of the research show that regulation had a negative effect on the efficiency of insurers and led to a decrease in their efficiency, but the market share and the privateness of insurance companies had a positive effect on the efficiency. In the end, suggestions for improving the efficiency of insurers have been presented.

The purpose of this study is to provide operational strategies during the Khoy earthquake in the humanitarian supply chain in order to maintain relief and help the victims and meet their needs quickly.The above research method is qualitative.The present research is applied research in terms of purpose and survey-descriptive in terms of nature.The statistical population of this research is the victims and crisis management experts. In this research, firstly, the needs of victims and the strategies to meet these needs were identified by reviewing the literature and conducting semi-structured interviews.Then, the needs of the victims through BMW and humanitarian supply chain strategies through combined approach of QFD and DEA according to Limitations of cost, time, urgency, effectiveness and ease of implementation were prioritized by distributing questionnaires among them.The final findings of the study showed that the strategy of “creating an accident command and crisis management system to plan, coordinate and assign tasks between organizations and institutions involved in the earthquake crisis in order to enable and expedite rescue operations”and“continuous evaluation for continuous improvement in rescue operations and various measures” were the most important strategy, and the need for "relief for the injured" was the most important need for the injured.Therefore, it is recommended to the authorities in the field of crisis management, by setting up the incident command post and the crisis management system, timely response, speeding up rescue operations, preventing parallel actions, creating unity of action and also regular evaluations cause continuous improvement in the process of rescue operations.

One of the models that is used to measure the efficiency and decision support is DEA, but considering all the merits, it also has its own limitations, which has led to the idea of combining it with artificial neural networks. ANN is increasingly used in model and data-based approaches to enrich analytical and predictive capabilities and thus improve decision-making. The present research presents a model for evaluating the efficiency of units by integrating neural networks. The studied sector is the active pharmaceutical industry in the Tehran stock market. To create the model, the efficiency of 4 DEA models on a variable scale, including input-oriented and output-oriented BCC model, SBM model and RAM model during the years 2018 to 2022 was calculated in GAMS. The efficiency values of these four models were ANN'S education vector. Also cost, income and profit data from 2018 to 2022 was entered into MATLAB as ANN'S input. To generalize education, the data of 2023 was used. The results showed that the trained efficiency boundary shows a more comprehensive and accurate approximation of efficiency for the ranking of pharmaceutical companies. The results of this research will help pharmaceutical companies in the fields of investment, resource allocation, predicting the results of policies and planning.

Profitability is a crucial indicator of insurance company performance, as it reflects their ability to invest and grow. Supervisors also rely on financial characteristics, including profitability, to determine the viability of insurers. The data envelopment analysis (DEA) method has been widely used to evaluate the performance of insurance companies. However, conventional financial ratios are often lacking in such studies, making DEA an effective alternative for measuring profitability. Given the rapid growth of the insurance industry in Iran, this research aims to examine the profitability of non-life insurance companies in Iran and expand coverage analysis. The study focuses on 18 insurance companies listed on the Tehran Stock Exchange from 2013 to 2014, with complete and available information during the research period. Profitability is measured using DEA, and the Tobit estimator model is used to investigate the impact of company size, company age, and product variety on profitability. The results highlight the importance of properly managing expenses and incomes for insurers. Additionally, the study finds that company size, company age, and product variety do not have a significant relationship with profitability. Insurance companies need to effectively organize their expenses and various types of business to maximize profit ratios. Optimizing cost structures and diversifying business ventures are key strategies for achieving profitability. This research provides insights into insurance company performance, allowing for a better understanding of their relative profitability within the industry and the formulation of targeted strategies. It also aids the government in developing policies that support the industry's growth.

The utilization of data envelopment analysis models for assessing and ranking organizational performance is on the rise. One of the important challenges of this model is the diminishing of the decision-making unit’s precision when dealing with a multitude of inputs and outputs. Hence, the aim of the present research was to develop a comprehensive performance evaluation model while enhancing the resolution of decision-making units. To this end, a balanced scorecard was used to identify comprehensive indicators. At the same time, for the first time, two objective and subjective approaches based on factor analysis and fuzzy inference system were used simultaneously to reduce indicators and improve the resolution of decision-making units. This study used an explanatory-descriptive method and was conducted as an applied-developmental research. The statistical population for identifying performance evaluation indicators and developing fuzzy inference rules included the experts of higher education institutions of Semnan city. Moreover, twenty-four higher education institutions of Semnan city were selected for model testing. The researcher made two questionnaires for the data collection. The validity of the questionnaires was confirmed by content and construct validity, respectively. Also, the reliability of the questionnaires was confirmed by Cronbach's alpha value and composite reliability of more than 0.7 respectively. The main accomplishment of the research can be designing a unified model with objective and subjective approaches to improve the resolution of decision units. In this regard, 26 indicators were identified and reduced to 8 structures by factor analysis. Also, the structures were scored by relying on the designed fuzzy inference system. The results demonstrated a significant improvement in the resolution of decision-making units when utilizing the proposed model, in contrast to conventional models which are mostly based on objective and subjective methods. As a result, the number of effective units in the proposed model effectively reduced to 10. Additionally, the results of the Kruskal-Wallis test and the calculation of the standard deviation of the efficiency scores revealed that the proposed model with an average rating of 48.29 and a dispersion of 0.221 has a lower efficiency rating and a greater dispersion as compered to other models. This finding serves as a confirmation of the enhanced resolution achieved by the proposed model

The electricity industry plays a pivotal role in a country's economic growth and development. Therefore, it is imperative to assess its performance and identify the strengths and weaknesses of its different sectors, such as production, transmission, and distribution, to enhance economic growth in diverse areas. Given the significance of the transmission sector, this research focuses on analyzing and evaluating the performance of 16 regional electricity companies in Iran from 1390 to 1398, with the aim of comprehending the impact of contextual variables on efficiency. To achieve this, the study will utilize two techniques - Data Envelopment Analysis (DEA) and Ordinary Least Squares (OLS) - to determine the efficiency score and estimate the effect of contextual variables on efficiency, respectively. In the first stage, the DEA technique is employed to calculate the technical efficiency of each company, considering their specific inputs and outputs. In the second stage, the logarithm of the efficiency scores obtained is regressed on contextual variables to establish their effect on efficiency. The residual derived from the regression is referred to as managerial ability. Finally, the companies are ranked based on their modified efficiency after removing the impact of contextual variables.

Outsourcing has been the most common method of cooperation. Today, issues such as increased competition, limited resources, technological complications, uncertainty about the future and increased costs have caused organizations to reconsider their management model and turn to new strategies. In such a situation, strategic alliances can replace outsourcing. The purpose of this article is to design a model to evaluate the current state of an outsourcing and to investigate the possibility of developing it into a strategic alliance. For this purpose, in this research, by studying the literature on the subject, examining examples of strategic alliances and also interviewing experts, a list of effective criteria on the formation of a strategic alliance was prepared and categorized into 6 dimensions. Then, using the content validity ratio method, unnecessary criteria were identified in this list. After that, using fuzzy data envelopment analysis without explicit input method, the best combination of weights for essential criteria was obtained. In the next step, by specifying the minimum values for the formation of a strategic alliance for each of the criteria and dimensions of the model, it is possible to compare the current state of the contractor with the minimum value necessary for the formation of a strategic alliance. Results indicates that through this comparison, organizations can identify their weak points in order to become a strategic ally and plan to improve these criteria and, as a result, succeed in developing strategic allies.

It is inevitable for a manager to consider the performance effects of each component of a multi-stage financial equity capital. These components serve as inputs in the first stage to raise investments. The investments, as outputs of the first stage, become inputs for the second stage and are used in bank services, such as bank facilities, which are outputs of the second stage. Therefore, when evaluating bank performance, the connectivity between the stages must be considered; otherwise, efficiency may not be calculated correctly. Traditional methods often assess multi-stage systems as black boxes, neglecting the potential connectivity that may exist among the stages. We delve into the system and propose models to improve overall efficiency and the efficiency of each stage. Additionally, the continuity and relationships among stages introduce numerous variables and constraints to linear programming for evaluating the entire system. A centralized approach calculates the efficiency score of units simultaneously by solving only one linear programming problem, significantly reducing computational complexity. This approach, especially in large organizations, is commonly employed by central managers. In this paper, we introduce a centralized method for evaluating units with a multi-stage structure. We apply the proposed models to evaluate the efficiencies of bank branches and insurance companies, demonstrating the superiority of the improved network approach and centralized method in enhancing overall system efficiency. Bank branches typically have a two-stage structure, involving labor, physical capital, and other factors.IntroductionBank branches operate under the supervision of a central management team. The central manager, acting as the decision-maker, allocates resources such as labor and financial equity capital as inputs for these branches. The goal is to optimize the overall efficiency of the branches by minimizing the total consumption of resources while maximizing the desired outputs, such as security investments. A common approach to enhancing the performance of banks involves evaluating each branch separately. However, this method does not guarantee the minimization of total resource consumption and can be time-consuming. Since all bank branches are under the control of central management, the decision-maker can optimize the efficiency scores of branches by allocating resources to them simultaneously. This approach, known as centralized Data Envelopment Analysis (DEA), is particularly relevant when certain variables are controlled by a central authority, such as a Head Office, rather than individual unit managers. DEA is a mathematical programming technique used to assess the performance of homogeneous Decision Making Units (DMUs). However, in cases where DMUs have a network structure, such as banks, where the outputs of one division or sub-process serve as inputs for the next sub-process, traditional DEA models treat two-stage DMUs as black boxes and overlook potential connectivity among the stages. In our approach, we consider the internal activities within the system and propose a non-radial model to optimize multi-stage DMUs by taking into account the connectivity among the stages. Furthermore, in previous network DEA models, constraints related to intermediate activities were treated as inequalities, which, as we will demonstrate in this paper, can lead to contradictions in optimality. We address this issue by carefully considering the connectivity among stages. The presence of connectivity among stages introduces numerous variables and constraints to the corresponding model. This model, when used to measure the overall efficiency scores of all DMUs, would traditionally require solving as many problems as there are DMUs, which can be highly time-consuming. In our paper, we introduce a centralized approach that measures the efficiency scores of multi-stage structure DMUs by solving only one linear programming problem. We have applied these proposed models to evaluate bank branches and insurance companies. This approach provides a more comprehensive and efficient way to assess and improve the performance of multi-stage organizations like banks, taking into account the interconnected nature of their operations.MethodologyWe employ the Data Envelopment Analysis approach to evaluate systems with a multi-stage structure, often referred to as a network structure. Traditional DEA models treat two-stage DMUs as black boxes and overlook the potential for connectivity among these stages. In contrast, we delve into the internal activities of the system and propose a model that optimizes multi-stage DMUs by considering the interconnections among the stages. Moreover, in previous models designed to assess network systems, constraints related to intermediate activities were typically treated as inequalities, which could lead to inconsistencies in optimization. In our approach, we enhance these constraints associated with intermediate activities to ensure more robust optimization. Additionally, we apply a centralized approach to allocate resources to DMUs, allowing for the simultaneous optimization of the efficiency scores of all DMUs through the solution of a single linear programming problem. This centralized method streamlines resource allocation and improves the overall efficiency of the DMUs.ResultsWe evaluated 20 bank branches, treating them as 20 DMUs with a two-stage structure. In the first stage, inputs included paid interest, personnel costs, paid interest related to foreign currency transactions, and personnel costs related to foreign currency transactions. The first stage produced intermediate outputs in the form of raised funds and raised funds related to foreign currency transactions. In the second stage, the outputs consisted of loans and common incomes. Notably, some loans in the second stage might become non-performing, where borrowers are unable to make full or even partial repayments. To address this, we considered non-performing loans as undesirable or bad outputs and transformed them into inverse values to treat them as good outputs. To calculate the efficiency scores of the bank branches, we employed both our improved network model and the traditional DEA approach. Our network-based method revealed that many of the bank branches under evaluation were inefficient, in contrast to the traditional method, which inaccurately identified many of the bank branches as efficient. Subsequently, we extended our network method to a centralized case, significantly reducing computation time. The network-based assessment of bank branches took nearly 5 seconds, whereas solving the centralized model required only 0.1 second. In addition to evaluating bank branches, we applied our methods to assess insurance companies. The results demonstrated that our model provided more accurate efficiency scores compared to previous network-based approaches.ConclusionIn multi-stage production systems, the production process comprises several stages. Banks, for example, operate with a network structure in which labor, physical capital, and financial equity capital serve as inputs in the first stage to generate deposits as intermediate outputs. In the second stage, these banks utilize the deposits obtained from the first stage to create loans and security investments. We have introduced models to assess the efficiency of each stage, whether it's the first, intermediate, or final stage, individually. Additionally, we have developed a non-radial SBM model designed for evaluating DMUs with multi-stage structures. The Centralized DEA approach is a valuable method for central managers, particularly in large organizations like bank branches, to allocate resources effectively. We have extended our network-based method to a centralized approach, allowing us to calculate efficiency scores by solving just one linear programming problem. The results obtained from applying our proposed models to evaluate bank branches and insurance companies, both exhibiting network structures as DMUs, demonstrate the superiority of the network centralized approach over previous models.

In this paper, we study a production system that is subject to network failures and produces perishable goods. We assume that the system has preventive and corrective maintenance activities and can return defective items for rework. Our objective is to find the optimal production rate that minimizes the total cost of production, inventory, spoilage, and maintenance over a long planning horizon. We consider the uncertainty of machine failures and use discrete event simulation and ARENA.14 software to estimate the performance measures of the system. We also use data envelopment analysis to evaluate the efficiency of the system and identify the best scenario. The results show the effectiveness of our proposed model.