Traditional Data Envelopment Analysis Models Research Articles

Integrating spatial relationships in the DEA approach for ecological efficiency evaluation: A case study of the Chaohu watershed

This study introduces an innovative Data Envelopment Analysis (DEA) model that integrates spatial relationships among decision-making units (DMUs) to determine relative prices of all variables for evaluating ecological efficiency more accurately, particularly in the context of water resource management. To better capture ecological performance, we propose a model that includes spatial correlation, addressing interdependencies that traditional DEA models often overlook. By incorporating a spatial weight matrix, the model delineates interactions between DMUs, offering a comprehensive evaluation that considers both technical efficiency and the spatial efficiency impact. We demonstrate the utility of our model through an empirical analysis of 17 national monitoring cross-sections within the Chaohu Watershed, a critical ecological and economic zone within China’s Yangtze River Delta. This research contributes to the fields of environmental economics, resource management, and spatial analysis by providing a robust methodological framework and actionable insights for sustainable environmental stewardship.

Variable RTS in hierarchical network DEA: Enhancing efficiency in higher education systems

This study presents a novel approach to Network Data Envelopment Analysis (DEA) by introducing “Returns to Scale (RTS) separation” within a hierarchical network DEA framework. Traditional DEA models, which often assume constant RTS, face limitations when analysing complex multi-functional structures. The proposed method, Variable RTS in Hierarchical Network DEA (VRS-HNDEA), addresses these limitations by integrating variable RTS, enabling a detailed efficiency analysis across hierarchical systems with heterogeneous sub-units. By utilising free variables, this model establishes distinct efficiency planes for simultaneous benchmarking of diverse subsystems, yielding a global efficiency frontier through the Minkowski addition of sub-system sets and analysed using an input-oriented enveloped form. Applied specifically to the higher education sector, the VRS-HNDEA model provides insights into the operational efficiency of various academic functions, including teaching, research, and administration. Key findings from this application demonstrate the model's ability to capture efficiency variations across hierarchical levels, supporting nuanced decisions on resource allocation and scale optimization. This framework, with its capability to recognise scale diversity across sub-systems, offers a significant tool for enhancing efficiency assessment in multi-layered public sector contexts, such as higher education, where comprehensive resource management is crucial.

Enhancing group efficiency through two-stage data envelopment analysis with a modified common set of weights approach: an application in banking

This paper empirically evaluates group efficiency in the banking sector by applying an extended Common Set of Weights (CSWs) approach within a two-stage Data Envelopment Analysis (DEA) framework. Our study assesses efficiency across multiple production stages and adapts CSWs to capture the intermediate processes inherent in banking operations. We provide a comprehensive ranking of bank branches within seven prominent banking groups in Guilan province, Iran. By applying our modified methodology to real-world data, we demonstrate its practical utility in delivering precise efficiency assessments and actionable insights for enhancing operational performance. Our findings highlight the superiority of the extended CSWs methodology over traditional DEA models, offering a more accurate and fair evaluation of group efficiency in the complex and interdependent context of banking processes.

Efficiency assessment and scenario simulation of the water-energy-food system in the Yellow river basin, China

Comprehending the efficiency of the Water-Energy-Food system within basins is crucial to enhance their resource utilization and facilitate high-quality development. This research evaluates the efficiency of the Water-Energy-Food (WEF) system in the Yellow River Basin between 2005 and 2021 using the super efficiency network Data Envelopment Analysis (DEA) model, addressing the limitation of traditional DEA models by considering both input and output within system. A multi-scenario combination is established under different development modalities, and an innovative attempt is made to introduce machine learning into efficiency prediction. The GA-LSTM (Genetic Algorithm-Long Short-Term Memory) model is constructed to forecast the efficiency values across multiple scenarios and identify the optimal scenario namely the scenario with the highest efficiency value, to carry out the spatial-temporal analysis. The results indicate that: (1) The WEF system efficiency in the Yellow River Basin exhibited a variable rising trajectory from 2005 to 2021, with the economic scale playing a significant role as an influencing element; (2) The trained GA-LSTM model can accurately predict the efficiency value and change trend of WEF system in the Yellow River Basin; (3) Under scenario 4 when water and food subsystems are maintained in the baseline scenario, while the energy subsystem is regulated in the general saving scenario, the overall average efficiency value of WEF system in the Yellow River Basin in 2022–2035 is the highest, reaching 1.28, which is the optimal enhancement path; (4) Under the optimal scenario, the WEF system efficiency in the Yellow River Basin increases by 6.89 % annually, with Shandong having the greatest efficiency level and Qinghai the lowest.

Healthcare performance analytics based on the novel PDA methodology for assessment of efficiency and perceived quality outcomes: A machine learning approach

Efficient resource allocation in healthcare organizations remains a complex challenge, exacerbated by the intricate data structure and myriad variables involved. While traditional methods like Data Envelopment Analysis have been employed, these often lack the requisite discriminatory power for accurate evaluation. This study introduces the PDA methodology, a fusion of Principal Component Analysis, Data Envelopment Analysis, and Analysis of Variance algorithms, developed in a machine learning environment. To further optimize discriminative power, the Particle Swarm Optimization Algorithm was included. By applying the PDA methodology to hospitals in the Apulia region of Italy, we found that facilities with better perceived quality tend to be more efficient. Furthermore, we identified significant variations in efficiency based on network affiliation and hospital level. Machine learning algorithms, including linear regressions and neural networks, confirmed that our methodology outperforms traditional Data Envelopment Analysis models in precisely distinguishing between varying levels of hospital efficiency. In conclusion, this work provides a fresh perspective for future research and policy decisions in the healthcare domain, demonstrating how the use of advanced and machine learning algorithms can result in more accurate evaluations and targeted interventions.

Estimating the eco‐efficiency of urban waste services towards sustainable waste management

AbstractAssessing the eco‐efficiency of municipalities regarding the provision of solid waste services is a useful tool for improving its sustainability. However, robust, and reliable methods are needed to benchmark the performance of municipalities. Data envelopment analysis (DEA) methods typically used to assess the eco‐efficiency of municipal solid waste (MSW) service providers. However, the variables used in the eco‐efficiency assessment bear distinct weights for each individual unit, limiting thus interpretation. Therefore, benchmarking the performance of MSW service providers becomes challenging because different conditions are applied. Thus, this study uses a common set weights DEA (DEA‐CSW) model assess the eco‐efficiency of different municipalities in providing MSW services. Eco‐efficiency scores were estimated by integrating total costs, recycled waste and unsorted waste as input, desirable outputs and undesirable outputs, respectively. The empirical application of the model demonstrated that when using DEA‐CSW, only one municipality (out of 36) was eco‐efficient in managing MSW. The weightings for inputs and outputs were allocated based on the degree of satisfaction estimated for each municipality. Satisfaction ranged from 0.829 to 1.000 indicating that none of the municipalities were heavily penalized based on the eco‐efficiency scores estimation when allocating common weights. In conclusion, this study demonstrates that compared to traditional DEA models, the DEA‐CSW approach is more adequate at benchmarking the performance of municipalities regarding the provision of MSW services.

An Exploration of Prediction Performance Based on Projection Pursuit Regression in Conjunction with Data Envelopment Analysis: A Comparison with Artificial Neural Networks and Support Vector Regression

Data envelopment analysis (DEA) is a leading approach in performance analysis and discovering newer benchmarks, and the traditional DEA models cannot forecast the future efficiency of decision-making units (DMUs). Machine learning, such as the artificial neural networks (ANNs), support vector machine/regression (SVM/SVR), projection pursuit regression (PPR), etc., have been viewed as beneficial for managers in predicting system behaviors. PPR is especially suitable for small and non-normal distribution samples, the usual cases in DEA analysis. This paper integrates DEA and PPR to cover the shortcomings we faced while using DEA and DEA-BPNN, DEA-SVR, etc. This study explores the advantages of combining these complementary methods into an integrated performance measurement and prediction model. Firstly, the DEA approach is used to evaluate and rank the efficiency of DMUs. Secondly, we establish two DEA-PPR combined models to describe the DEA efficiency scores (also called the production function) and the DEA-efficient frontier function. The first combined model’s input variables are input–output indicators in the DEA model, and the output variable is the DEA efficiency. In the second model, its input variables are input or output indicators in the DEA model, and the output variable is the optimal input indicator for input-oriented DEA or the output indicator for output-oriented DEA. We conducted positive research on two examples with actual data and virtual small, medium-sized, and large samples. Compared with the DEA-BPNN and DEA-SVR models, the results show that the DEA-PPR combined model has more vital global optimization ability, better convergence, higher accuracy, and a simple topology. The DEA-PPR model can obtain robust results for both small and large cases. The DEA-BPNN and DEA-SVR models cannot obtain robust results for small and medium-sized samples due to overfitting. For large samples, the DEA-PPR model outperforms DEA-BPNN, DEA-SVR, etc. The DEA-PPR combined model possesses better suitability, applicability, and reliability than the DEA-BPNN model, the DEA-SVR model, etc.

Evaluating the efficiency of primary health care institutions in China: an improved three-stage data envelopment analysis approach

BackgroundPrimary health care (PHC) institutions are key to realizing the main functions of the health care system. Since the new health care reform in 2009, the Chinese government has invested heavily in PHC institutions and launched favorable initiatives to improve the efficiency of such institutions. This study is designed to gauge the efficiency of PHC institutions by using 2012–2020 panel data covering 31 provinces in China.MethodsThis study applied an improved three-stage data envelopment analysis (DEA) model to evaluate the efficiency of PHC institutions in China. Unlike the traditional three-stage DEA model, the input-oriented global super-efficiency slack-based measurement (SBM) DEA model is used to calculate the efficiency in the first and third stages of the improved three-stage DEA model, which not only allows the effects of environmental factors and random noise to be taken into account but also deal with the problem of slack, super-efficiency and the comparability of interperiod efficiency values throughout the efficiency measurement.ResultsThe results show that the efficiency of PHC institutions has been overestimated due to the impact of external environmental factors and random noise. From 2012 to 2020, the efficiency of PHC institutions displayed a downward trend. Moreover, there are significant differences in the efficiency of PHC institutions between regions, with the lowest efficiency being found in the northeast region. The efficiency of PHC institutions is significantly affected by residents’ annual average income, per capita GDP, population density, the percentage of the population aged 0–14, the percentage of the population aged 65 and older, the number of people with a college education and above per 100,000 residents, and the proportion of the urban population.ConclusionsSubstantial investment in PHC institutions has not led to the expected efficiency gains. Therefore, more effective measures should be taken to improve the efficiency of PHC institutions in China based on local conditions. This study provides a new analytical approach to calculating the efficiency of PHC institutions, and this approach can be applied to efficiency evaluation either in other fields or in other countries.

GGDP Research Based on Structural Equations And DEA Model

With the advancement of globalization, the climate problem has gradually spread to the world, causing serious effects such as shrinking glaciers. So, we introduced GGDP to calculate economic health to improve the environment. After that, we use fuzzy mathematics to deal with the potential variables affecting climate to obtain a linear relationship between carbon emissions and green resource loss based on a structural equation model. Then we collected data from the World Bank and related data from some countries, and built a Network DEA model based on the traditional data envelopment analysis model. By analyzing data from China, Germany, and Australia, we conclude that using GGDP as a measure does not significantly affect economic strength in the long run, while also protecting the environment. Therefore, expanding GGDP accounting to the whole world has its advantages.

Inverse data envelopment analysis optimization approaches with flexible measures

PurposeThe purpose of this study is to estimate inputs (outputs) and flexible measures when outputs (inputs) are changed provided that the relative efficiency values remain without change.Design/methodology/approachA novel inverse data envelopment analysis (DEA) approach with flexible measures is proposed in this research to assess inputs (outputs) and flexible measures when outputs (inputs) are perturbed on condition that the relative efficiency scores remain unchanged. Furthermore, flexible inverse DEA approaches proposed in this study are used for a numerical example from the literature and an application of Iranian banking industry to clarify and validate them.FindingsThe findings show that including flexible measures into the investigation effects on the changes of performance measures estimated and leads to more reasonable achievements.Originality/valueThe traditional inverse DEA models usually investigate the changes of some determinate input-output factors for the changes of other given input-output indicators assuming that the efficiency values are preserved. However, there are situations that the changes of performance measures should be tackled while some measures, called flexible measures, can play either input or output roles. Accordingly, inverse DEA optimization models with flexible measures are rendered in this paper to address these issues.

Network DEA and Its Applications (2017–2022): A Systematic Literature Review

Data Envelopment Analysis (DEA) is one of the fastest growing approaches to solving management problems for the multi-criteria evaluation of the efficiency of homogeneous production systems. The general trend in recent years has been the development of network DEA (NDEA) models, which can consider the complicated structure of Decision Making Units (DMUs) and, therefore, can be more informative from the point of view of management science than traditional DEA models. The aim of this study is the systematization and clarification of general trends in the development of NDEA applications over the past 6 years (2017–2022). This study uses the methodology of a systematic literature review, which includes the analysis of the dynamics of the development of the topic, the selection of the main clusters of publications according to formal (citation, branches of knowledge, individual researchers) and informal (topics) criteria, and the analysis of their content. This review reveals that, most frequently, network structures are used for bank models, supply chain models, models of eco-efficiency of complex production systems, models of innovation processes, and models of universities or their departments and healthcare systems. Two-stage models, where the outputs of the first stage are the inputs of the second (intermediate outputs), are the most commonly used. However, in recent years, there has been a noticeable tendency to complicate DEA models and introduce hierarchical structures into them.

Data Envelopment Analysis for the Efficiency of Higher Education Departments at Sepuluh Nopember Institute of Technology, Indonesia

<p style="text-align: justify;">The quality of higher education is vital for a country’s future, not only in terms of transferring knowledge to younger generation but also for supporting economic development. This paper applies data envelopment analysis (DEA) to evaluate the relative efficiency of 38 academic departments at Sepuluh Nopember Institute of Technology, Surabaya, Indonesia. The input factors are the number of lecturers, the number of staff and budget allocations, whereas the output is the performance achievement level. The empirical analysis incorporates two traditional DEA models: the Charnes, Cooper and Rhodes (CCR) and the Banker, Charnes and Cooper (BCC) models with input orientation. The results indicate that the CCR model considers five departments efficient while the BCC model considers ten departments efficient, five of which are those considered efficient by the CCR model. It may seem counterintuitive that a department with an output performance achievement below 100% is deemed efficient, and vice versa. However, the underlying principle of efficiency under input-oriented DEA model is resource utilization. Finally, we provide recommendations for the departments with low efficiency scores to improve their performance.</p>

Assessing the marine ecological welfare performance of coastal regions in China and analysing its determining factors

This study used three-stage data envelopment analysis (DEA) and Tobit regression models to comprehensively evaluate the performance levels, trends, and differences of marine ecological welfare (MEW) in China, and explore its influencing factors to derive relevant policy suggestions. The evaluation results indicate that the three-stage DEA model performed better on MEW than the traditional DEA model by effectively eliminating the influence of random errors and external environmental factors. However, it underestimated the coastal MEW performance of the country. The southern marine economic circle showed an overall improvement, whereas the overall northern marine economic circle did not improve much; the eastern marine economic circle was stable. Moreover, the external environmental factors significantly impacted the performance of MEW, and the value of average MEW performance of each province changed to some extent under the influence of the slack variables of resource consumption and environmental consumption input. Other factors that significantly influenced China’s coastal MEW performance were the level of economic developments on land and government environmental regulations, which correlated positively. Meanwhile, inadequate development momentum in marine research and technology or poor achievement transformation rate negatively influenced it. Finally, countermeasures and suggestions were proposed based on the results of empirical analysis.

Evaluation of the integration of industrialization and information-based entropy AHP–cross-efficiency DEA model

PurposeThe purpose of this paper is to provide scientific guidance for the integration of industrialization and information (TIOII). In recent years, TIOII has promoted the development of intelligent manufacturing in China. However, many enterprises blindly invest in TIOII, which affects their normal production and operation.Design/methodology/approachThis study establishes an efficiency evaluation model for TIOII. In this paper, entropy analytic hierarchy process (AHP) constraint cone and cross-efficiency are added based on traditional data envelopment analysis (DEA) model, and entropy AHP–cross-efficiency DEA model is proposed. Then, statistical analysis is carried out on the integration efficiency of enterprises in Guangzhou using cross-sectional data, and the traditional DEA model and entropy AHP–cross-efficiency DEA model are used to analyze the integration efficiency of enterprises.FindingsThe data show that the efficiency of enterprise integration is at a medium level in Guangzhou. The efficiency of enterprise integration has no significant relationship with enterprise size and production type but has a low negative correlation with the development level of enterprise integration. In addition, the improved DEA model can better reflect the real integration efficiency of enterprises and obtain complete ranking results.Originality/valueBy adding the entropy AHP constraint cone and cross-efficiency, the traditional DEA model is improved. The improved DEA model can better reflect the real efficiency of TIOII and obtain complete ranking results.

Benchmarking the performance of water companies for regulatory purposes to improve its sustainability

The regulation of water companies (WCs) is essential to protect the interests of citizens, as companies are natural monopolies. Consequently, several methodological approaches are applied by water regulators to benchmark the performance of WCs, with data envelopment analysis (DEA) being one of the most widely applied. However, traditional DEA models allocate different weights to variables considered in efficiency assessments of each WC. By contrast, this study proposes and applies a common set weights (CSW) DEA model to a sample of Chilean WCs. The results showed that the DEA-CSW approach had greater discriminatory capacity compared to traditional DEA techniques. Moreover, weights allocated to input and output variables involved in efficiency assessment diverged among WCs when the traditional DEA model was employed. By contrast, the DEA-CSW approach generated reliable ranking of WCs based on their efficiency scores, thus facilitating the regulatory decision-making process.

Operational performance model for banks: a dynamic data envelopment approach

PurposeOperational performance is critical for the banking sector for both managers and other stakeholders as it strongly affects the overall performance of the banking system. Traditional performance measures such as ratio analysis encountered certain shortcomings. At this juncture, data envelopment analysis (DEA) approaches are increasingly applied in bank efficiency studies. However, basic DEA models ignored the interactions between consecutive terms and focused primarily on measuring performance independently for each study period. All this is required to develop an operational performance model that can enable the long-term decision model.Design/methodology/approachAn attempt has been made to develop a dynamic DEA within a non-radial category to measure interconnection activities considering non-performing loans as an undesirable link. This study uses the Indian banking dataset from 2015 to 2019. The study's research design directs three directions: ‘comparison of the dynamic DEA with the traditional static DEA model, areas of inefficiencies that are investigated for each factor using the factor efficiency index and the robustness results highlighting the performance difference between bank categories.'FindingsComparing with static DEA results, the study confirms that the dynamic model best measures long-term operational performance due to the linkage between consecutive terms. The efficiency analysis concludes that the input factor that requires the most improvement is ‘fixed assets' and ‘deposits'. The output factor that needs the most progress is ‘non-interest income'. The robustness of the developed model is proven by ownership categories present within the Indian banking system. At a significance level of 10%, the result of both the separate and dynamic model for privately owned banks is significantly better than that of publicly owned banks.Originality/valueThis paper proposes an operational efficiency model for Indian banks in line with undesirable output. The mean factor efficiency analysis related to non-radial DEA modelling enhances managerial flexibilities in determining improvement initiatives.

Regret-based cross efficiency evaluation method in a general two-stage DEA system

Cross efficiency (CE) evaluation in data envelopment analysis (DEA) has significant advantages in ranking decision making units (DMUs). A variety of CE evaluation methods with different secondary goals are proposed in traditional black-box DEA models. At present, some scholars have studied the CE evaluation approaches in two-stage DEA systems. However, these studies commonly think of decision makers (DMs) as perfectly rational and ignore the influence of DMs’ psychological factors on the evaluation results. To conquer these limitations, this study introduces regret theory to portray DMs’ psychological preferences and investigates two-stage CE evaluation models based on regret theory. We bring in the comprehensive perceived utility of DMUs by combining direct utility and indirect utility at first, and then develop the regret-based two-stage cross efficiency (RTCE) models in a centralized and a decentralized decision environments respectively. The efficiency of Chinese “double first-class” universities are evaluated to verify our models and a completely ranking of them can be obtained. Finally, a comparative analysis is conducted to illustrate the effectiveness of our proposed models.

글로벌 금융위기와 유럽 금융위기 기간의 항공사 효율성 분석 연구

The global financial crisis and economic recession lead to a decline in airline returns and deterioration in the business environment. In this regard, we compared and analyzed the efficiency of airlines during the global financial crisis and the European financial crisis by using the two-stage Network Data Envelopment Analysis (DEA) model. Network DEA can complement the shortcomings of the traditional DEA model and explain the transformation process hidden in the intermediate process and compare the relationship between efficiency. For the analysis, 16 airlines in Europe and related countries were selected and the period from 2007 to 2016, when the financial crisis occurred, was used. As variables, ‘operating costs’ and the ‘number of employees’ were used as input, and

Evaluation and Spatial–Temporal Difference Analysis of Urban Water Resource Utilization Efficiency Based on Two-Stage DEA Model

In the present study, a two-stage data envelopment analysis (DEA) model and spatial econometric method were employed to evaluate and analyze the utilization efficiency of urban water resources and spatial–temporal differences in cities of China. The traditional DEA model was enhanced by adopting the Shannon entropy in the first stage. After selecting variables based on the previous step and the Bayes information criterion (BIC), redundant variables were removed. In the meanwhile, a comprehensive efficiency score (CES) was generated to rank the efficiency. Finally, spatial econometric analysis was applied to explore the spatial–temporal differences of urban water resource utilization efficiency. Results demonstrate that: 1) according to the calculations and analysis, communities should concentrate on increasing investment in equipment and technology that can help enhance water consumption efficiency, while overlooking some minor aspects, such as per capita gross domestic product (PCGDP); 2) most cities have poor water resource utilization efficiency (low CES). However, both input and output have much room for the improvement; 3) Lhasa, Beijing, Haikou, and Shanghai have high CES, indicating that the utilization efficiency of water resources is not entirely dependent on economic development; and 4) through performing the Lagrange multiplier (LM) test, the spatial error model (SEM) test is passed at the significant level of 5%. Moreover, the water resource utilization efficiency of a city may be enhanced with the economic development in neighboring cities.

A regret cross-efficiency ranking method considering consensus consistency

Data envelopment analysis (DEA) is a powerful nonparametric approach for assessing the performance of decision making units (DMUs). Traditional DEA models usually utilize a self-evaluation mode to evaluate DMUs, which have the following shortcomings such as efficiency overestimation and incomplete ranking. As the extension of traditional DEA, cross-efficiency (CE) evaluation remedies these limitations. It connects self-evaluation with peer-evaluation to appraise DMUs and rank them. However, most existing studies on CE evaluation utilize the arithmetic average method to aggregate self-evaluation efficiency and peer-evaluation efficiency, while ignoring the significance of self-efficiency and the irrational psychology of decision-makers (DMs). Observed by the aforementioned phenomena, this paper employs regret theory to portray the regret aversion behavior of DMs and further proposes a novel regret cross-efficiency aggregation (RCEA) method. Considering aggressive and benevolent cross-efficiency models, we apply the RCEA method to calculate the regret-based aggressive cross-efficiency and the regret-based benevolent cross-efficiency, and introduce a parameter reflecting the psychological preference of DMs to aggregate them. To attain consensus between DMUs’ expectations for efficiency and the ultimate integration results, we design a regret cross-efficiency adjustment algorithm. This algorithm provides a more acceptable evaluation result and derives a full ranking for all DMUs. Finally, the validity and feasibility of the proposed model are illustrated by evaluating the efficiency of scientific research activities in 13 universities in China.