DEA Efficiency Region for Variations of Inputs and Outputs

Finding efficiency regions (ERs) for extremely efficient decision-making units (DMUs) is one of the important issues from the managerial and economic viewpoints. An extremely efficient DMU will remain efficient if and only if after changing its inputs and/or its outputs this DMU stays within its ER. Thus, by applying the ER information, decision maker(s) of the evaluated extremely efficient DMU can precisely understand the values of input(s) increment and output(s) decrement of this DMU so that it remains efficient. Hence, in this study, we propose a data envelopment analysis (DEA) approach based on the defining hyperplanes of the production possibility set (PPS), which is capable of finding the ERs of the DMUs when their inputs increase and/or their outputs decrease. To demonstrate the applicability of the proposed approach, in the real world, a numerical example and an empirical application to the banking industry in the Czech Republic are provided.

Novel models for obtaining the closest weak and strong efficient projections in data envelopment analysis

Data Envelopment Analysis (DEA) is a nonparametric method for measuring the relative efficiency and performance of Decision Making Units (DMUs). Traditionally, there are two issues regarding the DEA simultaneously i.e., the identification of a reference point on the efficient boundary of the production possibility set (PPS) and the use of some measures of distance from the unit under assessment to the efficient frontier. Due to its importance, in this paper, two alternative target setting models were developed to allow for lowefficient DMUs find the easiest way to improve its efficiency and reach to the efficient boundary. One seeks the closest weak efficient projection and the other suggests the most appropriate direction towards the strong efficient frontier surface. Both of these models provides the closest projection in one stage. Finally, a proposed problem is empirically checked by using a recent data related to 30 European airports.

Modifying the convexity condition in Data Envelopment Analysis (DEA)

Conventional Data Envelopment Analysis (DEA) models are based on a production possibility set (PPS) that satisfies various postulates. Extension or modification of these axioms leads to different DEA models. In this paper, our focus concentrates on the convexity axiom, leaving the other axioms unmodified. Modifying or extending the convexity condition can lead to a different PPS. This adaptation is followed by a two-step procedure to evaluate the efficiency of a unit based on the resulting PPS. The proposed frontier is located between two standard, well-known DEA frontiers. The model presented can differentiate between units more finely than the standard variable return to scale (VRS) model. In order to illustrate the strengths of the proposed model, a real data set describing Iranian banks was employed. The results show that this alternative model outperforms the standard VRS model and increases the discrimination power of (VRS) models.

A generalized fuzzy cost efficiency model

The concept of cost efficiency has become tremendously popular in data envelopment analysis (DEA) as it serves to assess a decision-making unit (DMU) in terms of producing minimum-cost outputs. A large variety of precise and imprecise models have been put forward to measure cost efficiency for the DMUs which have a role in constructing the production possibility set; yet, there’s not an extensive literature on the cost efficiency (CE) measurement for sample DMUs (SDMUs). In an effort to remedy the shortcomings of current models, herein is introduced a generalized cost efficiency model that is capable of operating in a fuzzy environment-involving different types of fuzzy numbers-while preserving the Farrell’s decomposition of cost efficiency. Moreover, to the best of our knowledge, the present paper is the first to measure cost efficiency by using vectors. Ultimately, a useful example is provided to confirm the applicability of the proposed methods.

An algorithm for the anchor points of the PPS of the FRH models

In this paper we deal with a variant of non-convex data envelopment analysis, called free replication hull model and try to obtain their anchor points. This paper uses a variant of super-efficiency model to characterize all extreme efficient decision making units and anchor points of the free replication hull models. A necessary and sufficient conditions for a decision making unit to be anchor point of the production possibility set of the free replication hull models are stated and proved. Since the set of anchor points is a subset of the set of extreme units, a definition of extreme units and a new method for obtaining these units in non-convex technologies are given. To illustrate the applicability of the proposed model, some numerical examples are finally provided.

Performance Ranking Method Based on Superefficiency with Directional Distance Function in DEA

In data envelopment analysis (DEA) methodology, superefficiency models eliminate the DMU to be evaluated from the production possibility set (PPS) to investigate whether its performance is superefficient. However, the infeasibility has been found in the superefficiency models when variable return-to-scale (VRS) technology is assumed. In recent developments, directional distance functions (DDF) are introduced into VRS superefficiency models to address the infeasibility, and the obtained efficiency scores from the DDF-based VRS superefficiency measure are used to rank all DMUs. In this study, we discuss conditions on selecting some proper reference bundles for feasible DDF and suggest a new DDF-based VRS superefficiency measure, which is unit-invariant and does not need to specify additional parameters. Two example illustrations are evaluated to demonstrate the feasibility and usefulness of our proposed DDF-based VRS superefficiency ranking method.