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学者姓名：陈磊
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Abstract ：
The efficiency decomposition and frontier projection of traditional two-stage network data envelopment analysis (DEA) model under variable returns to scale (VRS) are often not equivalent; which not only contradicts DEA theory, but also reduces the scientificity of the model. The main reason for this inequivalence is that there is a synergistic effect of variable scale return in two different stages. Therefore, this paper describes the production frontier of two-stage DEA under VRS for analyzing this synergistic effect, and then the efficiency evaluation pitfalls of two-stage DEA under VRS are identified. From the input orientation, output orientation, non- orientation perspectives, different two-stage network DEA models under VRS are respectively constructed to solve these evaluation pitfalls, and the equivalence relationships of their multiplier model and envelopment model are proved; and then the efficiency decomposition and frontier projection with equivalence relationship can be obtained to meet the different needs of decision-makers. Furthermore, variable intermediate element is discussed in the non-orientation model for achieving the Pareto optimality of two stages during the process of efficiency decomposition and frontier projection. By these models, the theoretical foundation of two-stage network DEA under VRS has been further improved. Finally, two examples are provided to illustrate the effectiveness of the new models.
Keyword ：
Data envelopment analysis Data envelopment analysis Efficiency decomposition Efficiency decomposition Equivalence relationship Equivalence relationship Frontier projection Frontier projection Two-stage network Two-stage network Variable returns to scale Variable returns to scale
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| GB/T 7714 | Chen, Lei , Wang, Ying-Ming . Efficiency decomposition and frontier projection of two-stage network DEA under variable returns to scale [J]. | EUROPEAN JOURNAL OF OPERATIONAL RESEARCH , 2025 , 322 (1) : 157-170 . |
| MLA | Chen, Lei 等. "Efficiency decomposition and frontier projection of two-stage network DEA under variable returns to scale" . | EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 322 . 1 (2025) : 157-170 . |
| APA | Chen, Lei , Wang, Ying-Ming . Efficiency decomposition and frontier projection of two-stage network DEA under variable returns to scale . | EUROPEAN JOURNAL OF OPERATIONAL RESEARCH , 2025 , 322 (1) , 157-170 . |
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Abstract ：
Inverse data envelopment analysis (DEA), which is an effective tool for determining inputs and outputs, is commonly applied in areas such as output prediction, resource allocation, and target setting. However, existing inverse DEA methods typically assume precise and deterministic data, which limits applicability in uncertain production environments, particularly when both random and fuzzy environments are present. This study introduces a novel inverse DEA approach for optimizing inputs and outputs in mixed uncertainty environments. The proposed model allows decision-makers to achieve target efficiency and meet various input/output targets under different production scale assumptions. First, a new optimality principle for multi-objective fuzzy random problems is presented and the necessary theoretical conditions for input/output calculations are derived. Second, an equivalent linear model is introduced to solve the inverse DEA problem with fuzzy random variables, thereby overcoming the challenges associated with nonlinear programming. Notably, the proposed model offers enhanced flexibility as it does not rely on specific fuzzy numbers or predefined assumptions regarding random distributions. Finally, the effectiveness of the model is validated through numerical examples and a case study, demonstrating its practical application in complex decision-making scenarios.
Keyword ：
Fuzzy random variable Fuzzy random variable Inverse data envelopment analysis Inverse data envelopment analysis Mixed uncertainty Mixed uncertainty Multi-objective programming Multi-objective programming
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| GB/T 7714 | Huang, Lizhen , Chen, Lei . Fuzzy random multi-objective optimization using a novel mixed fuzzy random inverse DEA model in input-output production [J]. | JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS , 2025 , 470 . |
| MLA | Huang, Lizhen 等. "Fuzzy random multi-objective optimization using a novel mixed fuzzy random inverse DEA model in input-output production" . | JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 470 (2025) . |
| APA | Huang, Lizhen , Chen, Lei . Fuzzy random multi-objective optimization using a novel mixed fuzzy random inverse DEA model in input-output production . | JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS , 2025 , 470 . |
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As a direction selection in the direction distance function (DDF), endogenous DDF can accurately reflect the numerical characteristics of inputs/outputs, but it is difficult to effectively popularize. And it is also difficult to effectively combine with reality. To solve those problems, this paper introduces slack variables to construct a new endogenous direction-setting mechanism, which makes the endogenous model have the conditions to be popularized. Based on the original endogenous DDF, we consider environmental concern, economic concern, coordinated development, and priority development, and then construct six new extended DDF models with slack variables. Based on priority development, we further propose six new extended DDF models. These new extended models can not only realize the complete internalization of direction determination but also overcome the limitations of traditional endogenous models. Combined with the actual case, the emission reduction potential of different areas is revealed, and the improved path is proposed. The results show that the new extended DDF models effectively reflect the different development modes of carbon emissions, and different development modes have a significant impact on emission reduction potential. In addition, compared with economic concern and priority development, coordinated development and environmental concern are most beneficial to carbon emission reduction, but the development mode of environmental concern can better reveal the improved path of environmental development.
Keyword ：
emission reduction potential emission reduction potential endogenous DDF endogenous DDF extended DDF models extended DDF models improved path improved path slack variables slack variables
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| GB/T 7714 | Wang, Junchao , Ye, Jun-Hong , Chen, Lei . A New Endogenous Direction Selection Mechanism for the Direction Distance Function Method Applied to Different Economic-Environmental Development Modes [J]. | SUSTAINABILITY , 2025 , 17 (7) . |
| MLA | Wang, Junchao 等. "A New Endogenous Direction Selection Mechanism for the Direction Distance Function Method Applied to Different Economic-Environmental Development Modes" . | SUSTAINABILITY 17 . 7 (2025) . |
| APA | Wang, Junchao , Ye, Jun-Hong , Chen, Lei . A New Endogenous Direction Selection Mechanism for the Direction Distance Function Method Applied to Different Economic-Environmental Development Modes . | SUSTAINABILITY , 2025 , 17 (7) . |
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The resource allocation of commercial banks is a multiple-criteria decision-making issue with complex internal structure, and traditional inverse data envelopment analysis cannot meet its decision-making needs. A two-stage structure with undesirable outputs is constructed to describe the operations of a Chinese commercial bank, and then a new two-stage inverse data envelopment analysis with undesirable outputs is proposed to address its resource allocation multiple criteria decision-making issue. The new method can be used to calculate the minimum input increment required to achieve the goals of desirable and undesirable output under a certain efficiency, and then a specific resource allocation plan can be obtained to promote the sustainable development of commercial banks. Finally, the new method is applied to the resource allocation of 16 Chinese listed commercial banks in 2013, and the application results fully demonstrate the effectiveness of the new method.
Keyword ：
commercial bank commercial bank inverse data envelopment analysis inverse data envelopment analysis resource allocation resource allocation two-stage two-stage undesirable outputs undesirable outputs
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| GB/T 7714 | Liao, Li-Huan , Chen, Lei , Wang, Junchao . A New Resource Allocation Multiple Criteria Decision-Making Method in a Two-Stage Inverse Data Envelopment Analysis Framework for the Sustainable Development of Chinese Commercial Banks [J]. | SUSTAINABILITY , 2024 , 16 (4) . |
| MLA | Liao, Li-Huan 等. "A New Resource Allocation Multiple Criteria Decision-Making Method in a Two-Stage Inverse Data Envelopment Analysis Framework for the Sustainable Development of Chinese Commercial Banks" . | SUSTAINABILITY 16 . 4 (2024) . |
| APA | Liao, Li-Huan , Chen, Lei , Wang, Junchao . A New Resource Allocation Multiple Criteria Decision-Making Method in a Two-Stage Inverse Data Envelopment Analysis Framework for the Sustainable Development of Chinese Commercial Banks . | SUSTAINABILITY , 2024 , 16 (4) . |
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Compared with two-level meta-frontier, three-level meta-frontier can have more projection direction to select. However, at present, three-level meta-frontier framework mainly adopts the traditional exogenous projection, which makes it continue the defects of two-level meta-frontier, that is, in the non-radial data envelopment analysis (DEA) model, there may be an unreasonable technology gap ratio (TGR), which is not conducive to effectively evaluating the efficiency of decision-making units (DMUs). By decomposing the projection process, the combined projection method is proposed to solve the above problems. In the selection of projection direction, the selection methods of layer-by-layer accumulation projection (LA) and accumulation consistency projection (AC) are proposed, and thus some new combined projection methods are established. In addition, the improvement of projection methods in two-level meta-frontier are introduced into three-level meta-frontier, and then different combined projection methods are compared. A numerical example and an empirical application are given to compare different combined projection methods, and the results support the use of our proposed combined projection methods.
Keyword ：
Combined projection Combined projection Data envelopment analysis Data envelopment analysis Technology gap ratio Technology gap ratio Three-level meta-frontier Three-level meta-frontier
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| GB/T 7714 | Guo, Xu , Chen, Lei . Extension and improvement of three-level meta-frontier framework based on multiple combined projection methods [J]. | COMPUTATIONAL & APPLIED MATHEMATICS , 2024 , 43 (5) . |
| MLA | Guo, Xu 等. "Extension and improvement of three-level meta-frontier framework based on multiple combined projection methods" . | COMPUTATIONAL & APPLIED MATHEMATICS 43 . 5 (2024) . |
| APA | Guo, Xu , Chen, Lei . Extension and improvement of three-level meta-frontier framework based on multiple combined projection methods . | COMPUTATIONAL & APPLIED MATHEMATICS , 2024 , 43 (5) . |
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Standardized evaluation has been applied in the research and development (R&D) activities of Chinese universities for a long time, which ignores the technological heterogeneity between these activities. Standardized evaluation has thus been difficult to meet the evaluation needs of the Chinese government, and classified evaluation is imperative for the diversified development of R&D activities in Chinese universities. Therefore, this paper introduces directional distance function (DDF) model with endogenous technique into meta-frontier data envelopment analysis framework to construct a new theoretical tool of classified evaluation, and this new method is applied to evaluate the efficiency of R&D activities of 939 Chinese universities. The theoretical contribution is to unify the endogenous directions relative to different frontiers, and then a new meta-frontier DDF framework is constructed; while the practical contribution is to provide the following conclusions and implications: (1) classified evaluation and standardized evaluation have different applicability to different categories of Chinese universities; (2) the homogeneity of the improvement direction is serious in Chinese universities; (3) different categories of Chinese universities have different improvement needs in different inputs and outputs, and the distances between most universities and their two frontiers are not far; (4) the selections of both improvement direction and indicator are important factors affecting the evaluation results. Finally, some useful suggestions are provided to improve the efficiency of R&D activities in Chinese universities.
Keyword ：
Chinese universities Chinese universities Classified evaluation Classified evaluation Directional distance function Directional distance function Efficiency Efficiency Technological heterogeneity Technological heterogeneity
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| GB/T 7714 | Chen, Lei , Luo, Cuiyun , Liao, Li-Huan et al. Classified evaluation of R&D activities in Chinese universities: An application of new meta-frontier directional distance function framework [J]. | TECHNOLOGY IN SOCIETY , 2024 , 78 . |
| MLA | Chen, Lei et al. "Classified evaluation of R&D activities in Chinese universities: An application of new meta-frontier directional distance function framework" . | TECHNOLOGY IN SOCIETY 78 (2024) . |
| APA | Chen, Lei , Luo, Cuiyun , Liao, Li-Huan , Wang, Suhui . Classified evaluation of R&D activities in Chinese universities: An application of new meta-frontier directional distance function framework . | TECHNOLOGY IN SOCIETY , 2024 , 78 . |
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Unlike most existing clustering methods, data envelopment analysis (DEA) clusters decisionmaking units (DMUs) based on production characteristics rather than distance. The clustering results obtained using the DEA clustering approach reflect the production relationship between the inputs and outputs of the DMUs to better identify the inherent production correlation between them. However, existing DEA-based clustering approaches struggle to rationally assign unique clusters to DMUs that exhibit multiple production characteristics and lack the further processing of clustering results. Therefore, this study proposes a new DEA clustering approach based on the individual perspective of DMUs that incorporates prospect theory to reflect the individual preferences of DMUs to assign each DMU to a relatively unique cluster. Furthermore, a clustering adjustment method and a clustering reduction method are proposed to further improve the clustering quality. The former can handle some special clusters according to the decision-maker ' s preference, and the latter permits the realization of an arbitrary number of clusters. The new DEA clustering approach is more reliable and flexible, and more valuable information can be provided for decision-makers. Finally, the validity of the new approach is verified through a comparison with existing approaches in two numerical cases, and an empirical example is used to illustrate its practicability.
Keyword ：
Clustering Clustering Data envelopment analysis Data envelopment analysis Individual perspective Individual perspective Production relationship Production relationship Prospect theory Prospect theory
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| GB/T 7714 | Chen, Lei , Fan, Minghuan , Wang, Junchao . A controlled data envelopment analysis clustering approach based on individual perspective [J]. | INFORMATION SCIENCES , 2024 , 677 . |
| MLA | Chen, Lei et al. "A controlled data envelopment analysis clustering approach based on individual perspective" . | INFORMATION SCIENCES 677 (2024) . |
| APA | Chen, Lei , Fan, Minghuan , Wang, Junchao . A controlled data envelopment analysis clustering approach based on individual perspective . | INFORMATION SCIENCES , 2024 , 677 . |
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Due to a large number of studies on cross-evaluation strategies, the theoretical problem of DEA cross-efficiency approach has been transformed from the non-uniqueness of the optimal solution to the relative uniqueness, because the existing cross-evaluation strategies can only reduce the possibility of non-unique solutions, but cannot prove the existence of a unique optimal solution. This paper illustrates the relative uniqueness of optimal solution of the cross-efficiency approach with traditional cross-evaluation strategies, and the graphic method and theoretical analysis are used to explain the reasons of relative uniqueness. Based on the data characteristic of inputs and outputs, the weight priority rule is made for constructing the new cross-evaluation strategy, and its optimal solution is proved to be unique. In addition, the weight priority strategy can also be introduced into traditional strategies as a supplementary strategy, and then the unique optimal solution can be obtained on the premise of preserving the characteristics of traditional strategies. In general, this paper solves the non-uniqueness and relative uniqueness problem of optimal solution in the DEA cross-efficiency approach, and then the reliability and robustness of the approach are thus improved.
Keyword ：
Cross-efficiency Cross-efficiency Data envelopment analysis Data envelopment analysis Uniqueness Uniqueness Weight priority Weight priority
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| GB/T 7714 | Chen, Lei , Wang, Ying-Ming , Wang, Junchao . Relative uniqueness or uniqueness? A new cross-efficiency evaluation approach with weight priority strategy [J]. | EXPERT SYSTEMS WITH APPLICATIONS , 2024 , 252 . |
| MLA | Chen, Lei et al. "Relative uniqueness or uniqueness? A new cross-efficiency evaluation approach with weight priority strategy" . | EXPERT SYSTEMS WITH APPLICATIONS 252 (2024) . |
| APA | Chen, Lei , Wang, Ying-Ming , Wang, Junchao . Relative uniqueness or uniqueness? A new cross-efficiency evaluation approach with weight priority strategy . | EXPERT SYSTEMS WITH APPLICATIONS , 2024 , 252 . |
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Under the goal of achieving zero carbon or carbon neutrality in the world, three industrial transformation and upgrading is a feasible scheme to achieve low carbon. However, the three industries in different countries are heterogeneous in technology and management. If the efficiency of three industries is evaluated in a unified technical environment, the evaluation results may be limited, so that the industries upgrading cannot be effectively realized. Therefore, this paper considers the technical and management heterogeneity of three industries, constructs new meta-frontier data envelopment analysis framework. Under this framework, the degree of industrial agglomeration is divided, and by considering competitive effect, benchmarking effect and spillover effect in industrial agglomeration, three new meta-frontier non-radial distance function models are proposed, and then the total-factor unified efficiency is obtained. By further extending the framework, the reasons for the inefficiency of three industries under competitive effect, benchmarking effect and spillover effect are analyzed. The results show that industrial development of all countries has great room for improvement, and the three agglomeration effects have different influences on countries with different agglomeration levels, in which the medium agglomeration is most conducive to green development of three industries. Surprisingly, the development of the secondary industry is most vulnerable to spillover effects. Moreover, countries with similar agglomeration levels have the strongest effect, and countries with the same agglomeration level have the same source of inefficiency in three industries.
Keyword ：
Agglomeration effect Agglomeration effect Industrial green development Industrial green development Technical heterogeneity Technical heterogeneity Total-factor unified efficiency Total-factor unified efficiency
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| GB/T 7714 | Guo, X. , Chen, L. . Impact of agglomeration effect on industrial green development from the perspective of technology gap [J]. | INTERNATIONAL JOURNAL OF ENVIRONMENTAL SCIENCE AND TECHNOLOGY , 2024 , 22 (10) : 9445-9468 . |
| MLA | Guo, X. et al. "Impact of agglomeration effect on industrial green development from the perspective of technology gap" . | INTERNATIONAL JOURNAL OF ENVIRONMENTAL SCIENCE AND TECHNOLOGY 22 . 10 (2024) : 9445-9468 . |
| APA | Guo, X. , Chen, L. . Impact of agglomeration effect on industrial green development from the perspective of technology gap . | INTERNATIONAL JOURNAL OF ENVIRONMENTAL SCIENCE AND TECHNOLOGY , 2024 , 22 (10) , 9445-9468 . |
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Data envelopment analysis (DEA) is a widely used approach for evaluating the relative efficiency of decision-making units (DMUs) in multiple-input and multiple-output situations. Although traditional DEA models use precise input-output data, real-world problems often involve mixed uncertainties, including fuzziness and stochasticity. This paper focuses on dealing with situations where inputs and outputs have both fuzzy and stochastic characteristics, using DEA models for efficiency evaluation. Through the integration of the alpha-level approach and chance-constrained programming, novel DEA models with fuzzy stochastic variables (FSVs) are proposed, and deterministic equivalent interval DEA models with linear constraints are provided to address this problem. The main contributions and advantages of the proposed model over existing DEA models with FSVs are fourfold: (1) linear and always-feasible models are proposed; (2) a fixed and uniform production boundary (i.e., the same set of constraints) is used to measure the efficiency of DMUs with fuzzy stochastic input and output; (3) the obtained results can distinguish between efficient and inefficient DMUs; (4) Equivalent interval DEA models were obtained to provide a more comprehensive assessment of the efficiency of the DMUs. Finally, a numerical example is presented to demonstrate the applicability of the proposed models and the feasibility of the obtained solutions.
Keyword ：
alpha-Level approach alpha-Level approach Chance-constrained programming Chance-constrained programming Data envelopment analysis Data envelopment analysis Fuzzy stochastic variables Fuzzy stochastic variables Interval efficiency Interval efficiency
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| GB/T 7714 | Huang, Lizhen , Chen, Lei . A Novel Approach for Efficiency Evaluation in Data Envelopment Analysis Framework with Fuzzy Stochastic Variables [J]. | INTERNATIONAL JOURNAL OF FUZZY SYSTEMS , 2024 , 27 (3) : 866-881 . |
| MLA | Huang, Lizhen et al. "A Novel Approach for Efficiency Evaluation in Data Envelopment Analysis Framework with Fuzzy Stochastic Variables" . | INTERNATIONAL JOURNAL OF FUZZY SYSTEMS 27 . 3 (2024) : 866-881 . |
| APA | Huang, Lizhen , Chen, Lei . A Novel Approach for Efficiency Evaluation in Data Envelopment Analysis Framework with Fuzzy Stochastic Variables . | INTERNATIONAL JOURNAL OF FUZZY SYSTEMS , 2024 , 27 (3) , 866-881 . |
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