Overcoming the infeasibility of super-efficiency DEA model: a model with generalized orientation

The super-efficiency (SE) model is identical to the standard model, except that the unit under evaluation is excluded from the reference set. This model has been used in ranking efficient units, identifying outliers, sensitivity and stability analysis, measuring productivity changes, and solving two-player games. Under the assumption of variable, non-increasing and non-decreasing returns to scale (VRS, NIRS, NDRS), the SE model may be infeasible for some efficient DMUs. Based on the necessary and sufficient conditions for the infeasibility of SE, in the current paper, we have developed a DEA model with generalized orientation to overcome infeasibility issues. The DEA model with generalized orientation extends the orientation of the DEA model from the traditional input-orientation and output-orientation to the modified input-orientation, input-prioritized non-orientation, modified output-orientation, and output-prioritized non-orientation. All of the extended orientations are always feasible in the associated super-efficiency models. In addition, the modified input-oriented and the modified output-oriented approaches are developed to deal with the problem of infeasibility in super-efficiency models while keeping the concordance with the traditional oriented models. The newly developed model is illustrated with a real world dataset

Overcoming the infeasibility of super-efficiency DEA model: a model with generalized orientation

The super-efficiency (SE) model is identical to the standard model, except that the unit under evaluation is excluded from the reference set. This model has been used in ranking efficient units, identifying outliers, sensitivity and stability analysis, measuring productivity changes, and solving two-player games. Under the assumption of variable, non-increasing and non-decreasing returns to scale (VRS, NIRS, NDRS), the SE model may be infeasible for some efficient DMUs. Based on the necessary and sufficient conditions for the infeasibility of SE, in the current paper, we have developed a DEA model with generalized orientation to overcome infeasibility issues. The DEA model with generalized orientation extends the orientation of the DEA model from the traditional input-orientation and output-orientation to the modified input-orientation, input-prioritized non-orientation, modified output-orientation, and output-prioritized non-orientation. All of the extended orientations are always feasible in the associated super-efficiency models. In addition, the modified input-oriented and the modified output-oriented approaches are developed to deal with the problem of infeasibility in super-efficiency models while keeping the concordance with the traditional oriented models. The newly developed model is illustrated with a real world dataset

A Modified Super-Efficiency in the Range Directional Model

The range directional model (RDM) relaxes the assumption of non-negativity of inputs and outputs in the conventional data envelopment analysis (DEA) with the aim of evaluating the efficiency of a decision-making unit (DMU) when some data are negative. Although the concept of super-efficiency in the RDM contributes to enhancing discriminatory power, the formulated model may lead to the infeasibility problem for some efficient DMUs. In this paper, we modify the super-efficiency RDM (SRDM) model to overcome the infeasibility problem occurring in such cases. Our method leads to a complete ranking of the DMUs with negative data for yielding valuable insights that aid decision makers to better understand the findings from a performance evaluation process. The contribution of this paper is fivefold: (1) we detect the source of infeasibility problems of SRDM in the presence of negative data, (2) the proposed model in this study yields the SRDM measures regardless of feasibility or infeasibility of the model, (3) when feasibility occurs, the modified SRDM model results in the scores that are the same as the original model, (4) we differentiate the efficient units to improve discriminatory power in SRDM, and (5) we provide two numerical examples to elucidate the details of the proposed method

Equivalent standard DEA models to provide super-efficiency scores

DEA super-efficiency models were introduced originally with the objective of providing a tie-breaking procedure for ranking units rated as efficient in conventional DEA models. This objective has been expanded to include sensitivity analysis, outlier identification and inter-temporal analysis. However, not all units rated as efficient in conventional DEA models have feasible solutions in DEA super-efficiency models. We propose a new super-efficiency model that (a) generates the same super-efficiency scores as conventional super-efficiency models for all units having a feasible solution under the latter, and (b) generates a feasible solution for all units not having a feasible solution under the latter. Empirical examples are provided to compare the two super-efficiency models

The Wallis Report and Implications of Bank Mergers for Efficiencies

This paper examines the competitive consequences of bank mergers and acquisitions with particular reference to the Wallis Inquiry into the Australian Financial System in 1996. The Government responded by adopting a four pillars policy preventing mergers among the four major banks. Using the super-efficiency data envelopment analysis model, the technical efficiencies of banks operating in Australia over the period from 1983 to 2001 are estimated. Two separate methods are employed to evaluate the characteristics and determinants of merger and acquisition activities in the sector. The first method examines economic performance of banks involved in merger activities. A second method is also used to determine program efficiency differences between banks of different entry types after adjusting for differences in intra-group managerial inefficiency. The empirical results demonstrate the role of takeover in improving efficiency performance of individual banks, banks of different types and the entire Australian banking sector. Conclusions and policy implications are drawn.bank mergers, data envelopment analysis, technical efficiency, super efficiency

Calculating Super Efficiency of DMUs for Ranking Units in Data Envelopment Analysis Based on SBM Model

There are a number of methods for ranking decision making units (DMUs), among which calculating super efficiency and then ranking the units based on the obtained amount of super efficiency are both valid and efficient. Since most of the proposed models do not provide the projection of Pareto efficiency, a model is developed and presented through this paper based on which in the projection of Pareto-efficient is obtained, in addition to calculating the amount of super efficiency. Moreover, the model is unit invariant, and is always feasible and makes the amount of inefficiency effective in ranking

Super-efficiency and stability intervals in additive DEA

This is a PDF file of an unedited manuscript that has been accepted for publication in Journal of the Operational Research Society. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. The final version will be available at: http://dx.doi.org/10.1057/jors.2012.1

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