Generalized Data Envelopment Analysis Model Research Articles

Examining the efficiency of regional university technology transfer in China: A mixed-integer generalized data envelopment analysis framework

In university technology transfer performance assessment, some variables, such as labor and contracts, must be treated as integer-valued variables. Usually, the reference points obtained by the conventional data envelopment analysis (DEA) method are unrealistic when one of the input/output measures is an integer value. As a result, several integer DEA models have been proposed over the last decade. However, these models are based only on self-evaluation. In some cases, when a large gap exists between the best- and worst-performing units, the improvement path based on self-evaluation can be inappropriate. To overcome this issue, we propose a mixed-integer generalized DEA model based on peer evaluation to evaluate the efficiency level of regional university technology transfer in China. A sample of 27 provinces in China from 2008 to 2015 is used in the study. The results reveal that the eastern region, on average, obtained the highest level of efficiency among the three regions in China, whereas the western region presented a poor efficiency level. This is consistent with the current stage of development. Several recommendations are suggested for promoting technology transfer in the western region.

NETWORK DATA ENVELOPMENT ANALYSIS WITH COMMON WEIGHTS: AN APPLICATION TO THE SUSTAINABILITY MEASUREMENT OF OECD COUNTRIES

This work considers a general common-weights network data envelopment analysis (DEA) model which is applicable to most network systems, except those with feedbacks and cycles. The principle of compromise, of the technique for order preference by similarity ideal solution (TOPSIS), is employed to find the common set of weights in the general network DEA model. The proposed method is applied to assess the environmental sustainability performance of the Organization for Economic Co-operation and Development (OECD) countries. Our results show that most countries have a large difference in the rank of efficiencies between the eco-efficiency and production efficiency stages, which reveals the source that causes the low environmental sustainability scores of the whole process.

Analysis of China’s Regional Economic Environmental Performance: A Non-radial Multi-objective DEA Approach

One of the hot topics is how to achieve more accurate results of economic and environmental efficiency evaluation in China. Previous data envelopment analysis (DEA) literature on environmental performance measurement often follow the concept of non-radial efficiency measure for calculating the performance on resources and economic-environmental factors respectively. This paper proposes a non-radial and multi-objective generalized DEA model for economic-environmental efficiency evaluation. The results illustrate that this model can not only analyze the relationship between DEA efficiency and Pareto optimality of the multi-objective programming problem defined on the production possibility set, but also obtain the performance improvement direction by using the projection of decision making units. Finally, a case on measuring the economic-environmental performance of Chinese provincial regions is employed to indicate that the proposed model can be helpful to promote the accuracy of economic-environmental efficiency evaluation.

Towards a new model to benchmark firms’ operating efficiency: A data envelopment analysis approach

The purpose of the study was to construct two similar data envelopment analysis (DEA) models. The first contains only published accounting-based data and the second added weighted average cost of capital (WACC), a primary market-based determinant, as an input variable. The efficiency scores of firms according to the two models are compared to determine whether there is a significant difference between the two models’ results. In total, 206 company years were analysed. This includes all the manufacturing firms which published financial statements on the Johannesburg Security Exchange (JSE) from 2011 to 2013. The study found that there is a good chance that the efficiency score of a firm will be significantly lower when WACC is added as a variable. Therefore, ignoring WACC in a general benchmarking DEA model may provide a misleading, too optimistic, sugar-coated answer to firms’ managers with regard to their firms’ relative operating efficiency. The study contributes to the existing body of literature by revealing evidence that WACC is an important component in a DEA model that aims to benchmark firms’ operating efficiency. Therefore, accounting-based data should be used in conjunction with WACC, a primary market-based determinant, which adds a further dimension to the benchmarking model.

A fuzzy expected value approach under generalized data envelopment analysis

Fuzzy data envelopment analysis (DEA) models emerge as another class of DEA models to account for imprecise inputs and outputs for decision making units (DMUs). Although several approaches for solving fuzzy DEA models have been developed, there are some drawbacks, ranging from the inability to provide satisfactory discrimination power to simplistic numerical examples that handles only triangular fuzzy numbers or symmetrical fuzzy numbers. To address these drawbacks, this paper proposes using the concept of expected value in generalized DEA (GDEA) model. This allows the unification of three models – fuzzy expected CCR, fuzzy expected BCC, and fuzzy expected FDH models – and the ability of these models to handle both symmetrical and asymmetrical fuzzy numbers. We also explored the role of fuzzy GDEA model as a ranking method and compared it to existing super-efficiency evaluation models. Our proposed model is always feasible, while infeasibility problems remain in certain cases under existing super-efficiency models. In order to illustrate the performance of the proposed method, it is first tested using two established numerical examples and compared with the results obtained from alternative methods. A third example on energy dependency among 23 European Union (EU) member countries is further used to validate and describe the efficacy of our approach under asymmetric fuzzy numbers.

Maintaining the Regular Ultra Passum Law in data envelopment analysis

The variable returns to scale data envelopment analysis (DEA) model is developed with a maintained hypothesis of convexity in input–output space. This hypothesis is not consistent with standard microeconomic production theory that posits an S-shape for the production frontier, i.e. for production technologies that obey the Regular Ultra Passum Law. Consequently, measures of technical efficiency assuming convexity are biased downward. In this paper, we provide a more general DEA model that allows the S-shape.

유입량의 변동성을 고려한 Fuzzy DEA 기반의 댐 군 연계운영 가중치 대안 평가

The multi-reservoir operation problem for efficient utilization of water resources involves conflicting objec-tives, and the problem can be solved by varying weight coefficient on objective functions. Accordingly, decision makers need to choose appropriate weight coefficients balancing the trade-offs among multiple objectives. Although the appropriateness of the weight coefficients may depend on the total amount of water inflow, reservoir operating policy may not be changed to a certain degree for different hydrological conditions on inflow. Therefore, we propose to use fuzzy Data Envelopment Analysis (DEA) to rank the weight coefficients in consideration of the inflow variation. In this approach, we generate a set of Pareto- optimal solutions by applying different weight coefficients on Coordinated Multi-reservoir Operating Model. Then, we rank the Pareto-optimal solutions or the corresponding weight coefficients by using Fuzzy DEA model. With the proposed approach, we can suggest the best weight coefficients that can produce the appropriate Pareto-optimal solution considering the uncertainty of inflow, whereas the general DEA model cannot pinpoint the best weight coefficients.

A bi-objective generalized data envelopment analysis model and point-to-set mapping projection

This work introduces a bi-objective generalized data envelopment analysis (Bi-GDEA) model and defines its efficiency. We show the equivalence between the Bi-GDEA efficiency and the non-dominated solutions of the multi-objective programming problem defined on the production possibility set (PPS) and discuss the returns to scale under the Bi-GDEA model. The most essential contribution is that we further define a point-to-set mapping and the mapping projection of a decision making unit (DMU) on the frontier of the PPS under the Bi-GDEA model. We give an effective approach for the construction of the point-to-set-mapping projection which distinguishes our model from other non-radial models for simultaneously considering input and output. The Bi-GDEA model represents decision makers’ specific preference on input and output and the point-to-set mapping projection provides decision makers with more possibility to determine different input and output alternatives when considering efficiency improvement. Numerical examples are employed for the illustration of the procedure of point-to-set mapping.

Generalized DEA model of fundamental analysis and its application to portfolio optimization

Fundamental analysis is used in asset selection for equity portfolio management. In this paper, a generalized data envelopment analysis (DEA) model is developed to analyze a firm’s financial statements over time in order to determine a relative financial strength indicator (RFSI) that is predictive of firm’s stock price returns. RFSI is based on maximizing the correlation between the DEA-based score of financial strength and the stock market performance. This maximization involves a difficult binary nonlinear program that requires iterative re-configuration of parameters of financial statements as inputs and outputs. We utilize a two-step heuristic algorithm that combines random sampling and local search optimization. The proposed approach is tested with 230 firms from various US technology-industries to determine optimized RFSI indicators for stock selection. Then, those selected stocks are used within portfolio optimization models to demonstrate the usefulness of the scheme for portfolio risk management.

A generalized model for data envelopment analysis

Data envelopment analysis (DEA) is a method to estimate a relative efficiency of decision making units (DMUs) performing similar tasks in a production system that consumes multiple inputs to produce multiple outputs. So far, a number of DEA models have been developed: The CCR model, the BCC model and the FDH model are well known as basic DEA models. These models based on the domination structure in primal form are characterized by how to determine the production possibility set from a viewpoint of dual form; the convex cone, the convex hull and the free disposable hull for the observed data, respectively. In this study, we suggest a model called generalized DEA (GDEA) model, which can treat the above stated basic DEA models in a unified way. In addition, by establishing the theoretical properties on relationships among the GDEA model and those DEA models, we prove that the GDEA model makes it possible to calculate the efficiency of DMU incorporating various preference structures of decision makers. Furthermore, we propose a dual approach to GDEA, GDEA D and also show that GDEA D can reveal domination relations among all DMUs.

A general model framework for DEA

Analyzing the efficiency of actions, productions, or organizational units is a fundamental problem of economic research. Data Envelopment Analysis (DEA) is designed to measure the efficiency of decision making units. The set of reference units in DEA is generated on the assumption of a specific production technology. From a decision theoretical view, DEA models are based on scalarizing functions known from Multi-Criteria Decision Making. On these grounds it is possible to formulate a general DEA model. This formulation is a basis for well-known and new DEA approaches, as a classification scheme for DEA models shows.

The necessary and sufficient conditions for returns to scale properties in generalized data envelopment analysis model

We give definitions on increasing, constant and decreasing returns to scale under the generalized data envelopment analysis (GDEA) model. The GDEA model prossesses cone structures for describing evaluators’ preferences toward different decision making units (DMU) and toward different input / output categories. The GDEA model contains many important DEA models as its subclasses. Based upon the definition, we discuss and rigorously prove the necessary and sufficient conditions for a DMU to have increasing, constant and decreasing returns to scale under a GDEA model, and discuss and clarify the differences and relationships of these conditions under different subclasses of the GDEA model. Furthermore, we describe a method based on a two-stage linear program to test returns to scale properties.

The generalized DEA model and the convex cone constrained game

This study extends the research on relating the data envelopment analysis (DEA) with the game theory context. We propose a generalized model for the two-person zero-sum finite game with closed convex cone constraints. We prove that the strategy of the closed convex cone constrained two-person zero-sum finite game is equivalent to the solution of the corresponding cone constrained programming problem. We show the existence of an optimal strategy of closed convex cone constrained two-person zero-sum finite game. As a special case of this, we give the optimal strategy of a polyhedral constrained game. In this case, the corresponding dual programming problems are a pair of linear dual programming problems. We then build up the connection between the proposed convex cone constrained game model and the generalized DEA model. With this relationship, a more robust correspondence between game family and the DEA family is established.

Analyzing properties of K-cones in the generalized data envelopment analysis model

We study the properties of the K-cone in a generalized Data Envelopment Analysis (DEA) model. This model includes the following four important classes of models: Charnes et al. (1978) model, Banker et al. (1984) and Charnes et al. (1985) model, Färe and Grosskopf (1985) model, and Seiford and Thrall (1990) model as its special cases. The main contribution of this paper is to introduce to the above four models (a) the input-output preference cone W to represent the relative importance of different input/output categories viewed by the evaluator (one who evaluates the decision-making units (DMUs)); and (b) the so-called predilection cone to describe preference of the evaluator to selected DMUs. We discuss the new characterizations of DEA efficient DMUs in the case of K-cone. We also describe the use of elementary predilection operators to achieve special preference for one or more DMUs. This method can be easily applied to find all the DEA efficient DMUs that are on a common efficient face as one or more prespecified DMUs. The method provided in this paper is complete in the sense that only those DMUs that are on a common efficient face with the predileccted ones will be DEA efficient after predilection. We believe that the results of this paper will play in important role in determining the structure of efficient frontiers.

Construction of all DEA efficient surfaces of the production possibility set under the Generalized Data Envelopment Analysis Model

In this paper, we study the structural properties of DEA efficient surfaces of the production possibility set under the Generalized Data Envelopment Analysis (GDEA) model introduced by Yu, Wei and Brockett (1996). The GDEA model contains the following well-known Data Envelopment Analysis (DEA) models as its special cases: the CCR model by Charnes, Cooper, and Rhodes (1978); the BCC model by Banker, Charnes and Cooper (1984); The FG model by Färe and Grosskopf (1985); and the ST model by Seiford and Thrall (1990). The relationships among Decision Making Units (DMUs) can be found by solving the GDEA model with predilection cone description. Using these relations to identify relative positions of the DMUs on the DEA efficient surface, we devise an efficient algorithm for constructing all the DEA efficient surfaces. Through further analysis, we show properties of DEA-efficient surfaces under several important subclasses of DEA models. Analytical expressions for the DEA efficient surfaces are obtained, which are useful in analyzing the structure of DEA efficiencies and in strategic group classifications. Results from this paper suggest important applications in constructing Pareto solutions (or nondominated solutions) and in analyzing structural properties of Pareto solutions in multiobjective programming.

Chapter 2 A generalized data envelopment analysis model: A unification and extension of existing methods for efficiency analysis of decision making units

In this paper, we introduce a generalized Data Envelopment Analysis (DEA) model which unifies and extends most of the well-known DEA models developed over the past fifteen years and points the way to new models. By setting three binary parameters of this model to different values, we obtain subclasses of the DEA models with generalK cone andW cone descriptions to represent the evaluator's preferences for the Decision Making Units (DMU) and the input/output categories. We also show relationships among the various different subclasses of the generalized DEA model and give special attention to efficiency definitions and solutions. Furthermore, we state and rigorously prove the equivalence between DEA efficiency and the nondominated solutions of a corresponding multi-objective program. This latter result is especially important for understanding and interpreting the concept of efficiency. Detailed examples are also presented to demonstrate the functions ofK cone andW cone, as well as their characteristics.