Imprecise DEA for setting scale efficient targets.

This paper discusses the new aspects of setting scale efficient targets in DEA with imprecise data such as ordinal and interval. The achieved models are non-linear but it can be solved in linear Appa and Yue models with determining a set of exact data from imprecise input and output data. Numerical examples are provided to show the projection of DMUs to their most productive scale size under input minimization and output maximization criteria

Target setting in data envelopment analysis using MOLP.

Data envelopment analysis (DEA) and multiple objective linear programming (MOLP) can be used as tools in management control and planning. The existing models have been established during the investigation of the relations between the output-oriented dual DEA model and the minimax reference point formulations, namely the super-ideal point model, the ideal point model and the shortest distance model. Through these models, the decision makers’ preferences are considered by interactive trade-off analysis procedures in multiple objective linear programming. These models only consider the output-oriented dual DEA model, which is a radial model that focuses more on output increase. In this paper, we improve those models to obtain models that address both inputs and outputs. Our main aim is to decrease total input consumption and increase total output production which results in solving one mathematical programming model instead of n models. Numerical illustration is provided to show some advantages of our method over the previous methods

A full investigation of the directional congestion in data envelopment analysis

One of interesting subjects in Data Envelopment Analysis (DEA) is estimation of congestion of Decision Making Units (DMUs). Congestion is evidenced when decreases (increases) in some inputs result in increases (decreases) in some outputs without worsening (improving) any other input/output. Most of the existing methods for measuring the congestion of DMUs utilize the traditional definition of congestion and assume that inputs and outputs change with the same proportion. Therefore, the important question that arises is whether congestion will occur or not if the decision maker (DM) increases or decreases the inputs dis-proportionally. This means that, the traditional definition of congestion in DEA may be unable to measure the congestion of units with multiple inputs and outputs. This paper focuses on the directional congestion and proposes methods for recognizing the directional congestion using DEA models. To do this, we consider two different scenarios: (i) just the input direction is available. (ii) none of the input and output directions are available. For each scenario, we propose a method consists in systems of inequalities or linear programming problems for estimation of the directional congestion. The validity of the proposed methods are demonstrated utilizing two numerical examples

Modificación de la condición de convexidad en el Análisis Envolvente de Datos (AED)

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.Los modelos de análisis envolvente de datos convencionales (DEA) se basan en un conjunto de posibilidades de producción (PPS) que satisface varios postulados. La extensión o modificación de estos axiomas conduce a diferentes modelos DEA. En este artículo, nuestro enfoque se concentra en el axioma de convexidad, dejando los otros axiomas sin modificar. Modificar o extender la condición de convexidad puede conducir a un PPS diferente. A esta adaptación le sigue un procedimiento de dos pasos para evaluar la eficiencia de una unidad en función del PPS resultante. La frontera propuesta está ubicada entre dos fronteras de la DEA estándar y conocidas. El modelo presentado puede diferenciar entre unidades con mayor precisión que el modelo de retorno a escala variable estándar (VRS). Para ilustrar las fortalezas del modelo propuesto, se utilizó un conjunto de datos reales que describen los bancos iraníes. Los resultados muestran que este modelo alternativo supera al modelo estándar de VRS y aumenta el poder de discriminación de los modelos (VRS)

Modificación de la condición de convexidad en el Análisis Envolvente de Datos (AED)

Los modelos de análisis envolvente de datos convencionales (DEA) se basan en un conjunto de posibilidades de producción (PPS) que satisface varios postulados. La extensión o modificación de estos axiomas conduce a diferentes modelos DEA. En este artículo, nuestro enfoque se concentra en el axioma de convexidad, dejando los otros axiomas sin modificar. Modificar o extender la condición de convexidad puede conducir a un PPS diferente. A esta adaptación le sigue un procedimiento de dos pasos para evaluar la eficiencia de una unidad en función del PPS resultante. La frontera propuesta está ubicada entre dos fronteras de la DEA estándar y conocidas. El modelo presentado puede diferenciar entre unidades con mayor precisión que el modelo de retorno a escala variable estándar (VRS). Para ilustrar las fortalezas del modelo propuesto, se utilizó un conjunto de datos reales que describen los bancos iraníes. Los resultados muestran que este modelo alternativo supera al modelo estándar de VRS y aumenta el poder de discriminación de los modelos (VRS)

Modificación de la condición de convexidad en el Análisis Envolvente de Datos (AED)

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.Los modelos de análisis envolvente de datos convencionales (DEA) se basan en un conjunto de posibilidades de producción (PPS) que satisface varios postulados. La extensión o modificación de estos axiomas conduce a diferentes modelos DEA. En este artículo, nuestro enfoque se concentra en el axioma de convexidad, dejando los otros axiomas sin modificar. Modificar o extender la condición de convexidad puede conducir a un PPS diferente. A esta adaptación le sigue un procedimiento de dos pasos para evaluar la eficiencia de una unidad en función del PPS resultante. La frontera propuesta está ubicada entre dos fronteras de la DEA estándar y conocidas. El modelo presentado puede diferenciar entre unidades con mayor precisión que el modelo de retorno a escala variable estándar (VRS). Para ilustrar las fortalezas del modelo propuesto, se utilizó un conjunto de datos reales que describen los bancos iraníes. Los resultados muestran que este modelo alternativo supera al modelo estándar de VRS y aumenta el poder de discriminación de los modelos (VRS)

Using slacks-based model to solve inverse DEA with integer intervals for input estimation

This paper deals with an inverse data envelopment analysis (DEA) based on the non-radial slacks-based model in the presence of uncertainty employing both integer and continuous interval data. To this matter, suitable technology and formulation for the DEA are proposed using arithmetic and partial orders for interval numbers. The inverse DEA is discussed from the following question: if the output of DMUo increases from Y-o to /beta(o), such the new DMU is given by (alpha(o)& lowast;, /3) belongs to the technology, and its inefficiency score is not less than t-percent, how much should the inputs of the DMU increase? A new model of inverse DEA is offered to respond to the previous question, whose interval Pareto solutions are characterized using the Pareto solution of a related multiple-objective nonlinear programming (MONLP). Necessary and sufficient conditions for input estimation are proposed when output is increased. A functional example is presented on data to illustrate the new model and methodology, with continuous and integer interval variables

Portfolio optimization with asset preselection using data envelopment analysis

This paper uses data envelopment analysis (DEA) approach as a nonparametric efficiency analysis tool to preselect efficient assets in large-scale portfolio problems. Thus, we reduce the dimensionality of portfolio problems, considering multiple asset performance criteria in a linear DEA model. We first introduce several reward/risk criteria that are typically used in portfolio literature to identify features of financial returns. Secondly, we suggest some DEA input/output sets for preselecting efficient assets in a large-scale portfolio framework. Then, we evaluate the impact of the preselected assets in different portfolio optimization strategies. In particular, we propose an ex-post empirical analysis based on two alternative datasets: the components of S &P500 and the Fama and French 100 portfolio formed on size and book to market. According to this empirical analysis we observe better performances of the DEA preselection than the classic PCA factor models for large scale portfolio selection problems. Moreover, the proposed model outperform the S &P500 index and the strategy based on the fully diversified portfolio.Web of Scienc

An Extension of Cross Redundancy of Interval Scale Outputs and Inputs in DEA

It is well known that data envelopment analysis (DEA) models are sensitive to selection of input and output variables. As the number of variables increases, the ability to discriminate between the decision making units (DMUs) decreases. Thus, to preserve the discriminatory power of a DEA model, the number of inputs and outputs should be kept at a reasonable level. There are many cases in which an interval scale output in the sample is derived from the subtraction of nonnegative linear combination of ratio scale outputs and nonnegative linear combination of ratio scale inputs. There are also cases in which an interval scale input is derived from the subtraction of nonnegative linear combination of ratio scale inputs and nonnegative linear combination of ratio scale outputs. Lee and Choi (2010) called such interval scale output and input a cross redundancy. They proved that the addition or deletion of a cross-redundant output variable does not affect the efficiency estimates yielded by the CCR or BCC models. In this paper, we present an extension of cross redundancy of interval scale outputs and inputs in DEA models. We prove that the addition or deletion of a cross-redundant output and input variable does not affect the efficiency estimates yielded by the CCR or BCC models

Funciones ejecutables de las representaciones en el aprendizaje de los conceptos algebraicos

This study aimed to examine the role of multiple representations in learning algebraic concepts for high school students. Using the semiexperimental research method for teaching of numerical, symbolic, and graphical representations, and traditional teaching, 83 female students were selected from the tenth grade of a high school in Tehran. We concluded that there is a significant difference between the mean scores of mathematics in the control and experimental groups. Using the method based on different representations helped the students to become creative and provide similar Algebra examples; thereby analysis power will be increased.Este estudio tiene como objetivo examinar el papel de las representaciones múltiples en el aprendizaje de los conceptos algebraicos en estudiantes de educación secundaria. Se desarrolló una investigación semiexperimental para la enseñanza de representaciones numéricas, simbólicas y gráficas y la enseñanza tradicional, en este estudio participaron 83 estudiantes femeninas del décimo grado de una escuela secundaria en Teherán. Se concluyó que hay una diferencia significativa entre los puntajes promedio de matemáticas en el grupo control y los grupos experimentales. El uso del método basado en diferentes representaciones ayudó a las estudiantes a ser creativas y proporcionar ejemplos de álgebra similares; por lo tanto, la capacidad de análisis aumentará