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

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

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 new slacks-based measure of Malmquist-Luenberger index in the presence of undesirable outputs

In the majority of production processes, noticeable amounts of bad byproducts or bad outputs are produced. The negative effects of the bad outputs on efficiency cannot be handled by the standard Malmquist index to measure productivity change over time. Toward this end, the Malmquist-Luenberger index (MLI) has been introduced, when undesirable outputs are present. In this paper, we introduce a Data Envelopment Analysis (DEA) model as well as an algorithm, which can successfully eliminate a common infeasibility problem encountered in MLI mixed period problems. This model incorporates the best endogenous direction amongst all other possible directions to increase desirable output and decrease the undesirable outputs at the same time. A simple example used to illustrate the new algorithm and a real application of steam power plants is used to show the applicability of the proposed model

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

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

Banks’ efficiency and credit risk analysis using by-production approach: the case of Iranian banks

This article uses a by-production approach that integrates credit risk to monitor bank efficiency. The method overcomes the possible misspecification issues of the commonly assumed weak disposability (WDA) of undesirable outputs. In addition, our measure extends the classic by-production approach by including statistical aspects through subsampling techniques. We have also provided an algorithm to correct related infeasibilities. Using this approach, we investigate the performance of Iranian banks and credit risk management in the sector for the period 1998–2012. Non-performing loans (NPLs) have been used as an undesirable output and proxy for credit risk in our models. Based on our empirical results, although the banks generally exhibited efficiency improvements over time, their credit risk performance deteriorated considerably after the regulatory changes introduced in 2005. These findings confirm that credit quality can be monitored more actively across Iranian banks

Farm efficiency related to animal welfare performance and management of sheep farms in marginal areas of Central Italy: a two-stage DEA model

The development of specific actions to increase animal health and welfare is indicated as a strategy to improve the efficiency and sustainability of many livestock systems, including sheep farming. In this paper, efficiency measures are provided to confirm the hypothesis that farms that are higher-performing in terms of animal welfare and management are also more technically efficient. A two-stage Data Envelopment Analysis (DEA) approach was adopted with the following twofold objectives: 1) to evaluate the efficiency and super-efficiency of 76 meat-producing sheep farms situated in marginal lands in central Italy, through DEA and Super-DEA (S-DEA) models; and 2) to assess the influence of animal welfare and management indicators on technical efficiency values through the application of a Tobit regression model. An overall efficiency performance varying within a range of 0.44–1 was estimated, with an average value of 0.80, implying a potential increase of 20% in terms of output production from both management and scale improvements. The ‘pure’ technical inefficiency was found to contribute three times more than scale inefficiency in determining the overall technical inefficiency. Adopting a more extensive farming system and increasing replacement rate were found to affect negatively the efficiency scores. On the other hand, having less than 5% of animals with body condition score beyond acceptable limits, presence of access control structures, well managed lambing pens, and dedicated feed stocking areas resulted in a positive influence on efficiency. Improvements in animal welfare aspects did not appear to be farm-scale-dependent.Highlights DEA and Super-DEA models were applied to assess sheep farm technical efficiency in Central Italy. An overall potential 20% increase in output production was estimated. Animal welfare factors were found to significantly affect efficiency performance

A DEA-based incentives system for centrally managed multi-unit organisations

In multi-unit organisations such as a bank and its branches or a national body delivering publicly funded health or education services through local operating units, the need arises to incentivize the units to operate efficiently. In such instances, it is generally accepted that units found to be inefficient can be encouraged to make efficiency savings. However, units which are found to be efficient need to be incentivized in a different manner. It has been suggested that efficient units could be incentivized by some reward compatible with the level to which their attainment exceeds that of the best of the rest, normally referred to as “super-efficiency”. A recent approach to this issue (Varmaz et. al. 2013) has used Data Envelopment Analysis (DEA) models to measure the super-efficiency of the whole system of operating units with and without the involvement of each unit in turn in order to provide incentives. We identify shortcomings in this approach and use it as a starting point to develop a new DEA-based system for incentivizing operating units to operate efficiently for the benefit of the aggregate system of units. Data from a small German retail bank is used to illustrate our method