Ranking efficient DMUs using cooperative game theory

The problem of ranking Decision Making Units (DMUs) in Data Envelopment Analysis (DEA) has been widely studied in the literature. Some of the proposed approaches use cooperative game theory as a tool to perform the ranking. In this paper, we use the Shapley value of two different cooperative games in which the players are the efficient DMUs and the characteristic function represents the increase in the discriminant power of DEA contributed by each efficient DMU. The idea is that if the efficient DMUs are not included in the modified reference sample then the efficiency score of some inefficient DMUs would be higher. The characteristic function represents, therefore, the change in the efficiency scores of the inefficient DMUs that occurs when a given coalition of efficient units is dropped from the sample. Alternatively, the characteristic function of the cooperative game can be defined as the change in the efficiency scores of the inefficient DMUs that occurs when a given coalition of efficient DMUs are the only efficient DMUs that are included in the sample. Since the two cooperative games proposed are dual games, their corresponding Shapley value coincide and thus lead to the same ranking. The more an ef- ficient DMU impacts the shape of the efficient frontier, the higher the increase in the efficiency scores of the inefficient DMUs its removal brings about and, hence, the higher its contribution to the overall discriminant power of the method. The proposed approach is illustrated on a number of datasets from the literature and compared with existing methods

Measuring Technical Efficiency of Dairy Farms with Imprecise Data: A Fuzzy Data Envelopment Analysis Approach

This article integrates fuzzy set theory in Data Envelopment Analysis (DEA) framework to compute technical efficiency scores when input and output data are imprecise. The underlying assumption in convectional DEA is that inputs and outputs data are measured with precision. However, production agriculture takes place in an uncertain environment and, in some situations, input and output data may be imprecise. We present an approach of measuring efficiency when data is known to lie within specified intervals and empirically illustrate this approach using a group of 34 dairy producers in Pennsylvania. Compared to the convectional DEA scores that are point estimates, the computed fuzzy efficiency scores allow the decision maker to trace the performance of a decision-making unit at different possibility levels.fuzzy set theory, Data Envelopment Analysis, membership function, α-cut level, technical efficiency, Farm Management, Production Economics, Productivity Analysis, Research Methods/ Statistical Methods, Risk and Uncertainty, D24, Q12, C02, C44, C61,

Clasificación de unidades por el método de eficiencia cruzada corregido usando pesos óptimos en el intervalo más pequeño

An important method for ranking of decision making units (DMUs) in data envelopment analysis (DEA) is cross-efficiency method. This study proposes a secondary multi-objective model for calculating optimal weights with least dispersion. Firstly, these weights are placed in the smallest interval. Secondly, the cross-efficiency of each of the other units has the least deviation from the CCR efficiency of the same unit. Therefore, optimal weights are obtained which have the least dispersion. As result, the zero optimal weights which lead to the triviality of the relevant index, are avoided as far as possible. Hence, using the average cross-efficiency, the results of the ranking would be more reasonable. Using the proposed model for ranking of six nursing homes, the results show that this model is more accurate. Finally, in order to improve performance of the emergency department of a hospital, the proposed model is used to rank 11 defined scenarios.Un método importante para clasificar las unidades de toma de decisiones (DMU) en el análisis envolvente de datos (DEA) es el método de eficiencia cruzada. Este estudio propone un modelo secundario multiobjetivo para calcular los pesos óptimos con la menor dispersión. En primer lugar, estos pesos se colocan en el intervalo más pequeño. En segundo lugar, la eficiencia cruzada de cada una de las otras unidades tiene la menor desviación de la eficiencia CCR de la misma unidad. Por tanto, se obtienen pesos óptimos que tienen la menor dispersión. Como resultado, se evitan en la medida de lo posible las ponderaciones óptimas cero que conducen a la trivialidad del índice relevante. Por lo tanto, utilizando la eficiencia cruzada promedio, los resultados de la clasificación serían más razonables. Utilizando el modelo propuesto para la clasificación de seis hogares de ancianos, los resultados muestran que este modelo es más preciso. Finalmente, con el fin de mejorar el desempeño del servicio de urgencias de un hospital, se utiliza el modelo propuesto para clasificar 11 escenarios definidos

Clasificación de unidades por el método de eficiencia cruzada corregido usando pesos óptimos en el intervalo más pequeño

Un método importante para clasificar las unidades de toma de decisiones (DMU) en el análisis envolvente de datos (DEA) es el método de eficiencia cruzada. Este estudio propone un modelo secundario multiobjetivo para calcular los pesos óptimos con la menor dispersión. En primer lugar, estos pesos se colocan en el intervalo más pequeño. En segundo lugar, la eficiencia cruzada de cada una de las otras unidades tiene la menor desviación de la eficiencia CCR de la misma unidad. Por tanto, se obtienen pesos óptimos que tienen la menor dispersión. Como resultado, se evitan en la medida de lo posible las ponderaciones óptimas cero que conducen a la trivialidad del índice relevante. Por lo tanto, utilizando la eficiencia cruzada promedio, los resultados de la clasificación serían más razonables. Utilizando el modelo propuesto para la clasificación de seis hogares de ancianos, los resultados muestran que este modelo es más preciso. Finalmente, con el fin de mejorar el desempeño del servicio de urgencias de un hospital, se utiliza el modelo propuesto para clasificar 11 escenarios definidos

Clasificación de unidades por el método de eficiencia cruzada corregido usando pesos óptimos en el intervalo más pequeño

An important method for ranking of decision making units (DMUs) in data envelopment analysis (DEA) is cross-efficiency method. This study proposes a secondary multi-objective model for calculating optimal weights with least dispersion. Firstly, these weights are placed in the smallest interval. Secondly, the cross-efficiency of each of the other units has the least deviation from the CCR efficiency of the same unit. Therefore, optimal weights are obtained which have the least dispersion. As result, the zero optimal weights which lead to the triviality of the relevant index, are avoided as far as possible. Hence, using the average cross-efficiency, the results of the ranking would be more reasonable. Using the proposed model for ranking of six nursing homes, the results show that this model is more accurate. Finally, in order to improve performance of the emergency department of a hospital, the proposed model is used to rank 11 defined scenarios.Un método importante para clasificar las unidades de toma de decisiones (DMU) en el análisis envolvente de datos (DEA) es el método de eficiencia cruzada. Este estudio propone un modelo secundario multiobjetivo para calcular los pesos óptimos con la menor dispersión. En primer lugar, estos pesos se colocan en el intervalo más pequeño. En segundo lugar, la eficiencia cruzada de cada una de las otras unidades tiene la menor desviación de la eficiencia CCR de la misma unidad. Por tanto, se obtienen pesos óptimos que tienen la menor dispersión. Como resultado, se evitan en la medida de lo posible las ponderaciones óptimas cero que conducen a la trivialidad del índice relevante. Por lo tanto, utilizando la eficiencia cruzada promedio, los resultados de la clasificación serían más razonables. Utilizando el modelo propuesto para la clasificación de seis hogares de ancianos, los resultados muestran que este modelo es más preciso. Finalmente, con el fin de mejorar el desempeño del servicio de urgencias de un hospital, se utiliza el modelo propuesto para clasificar 11 escenarios definidos

Defuzzification of groups of fuzzy numbers using data envelopment analysis

Defuzzification is a critical process in the implementation of fuzzy systems that converts fuzzy numbers to crisp representations. Few researchers have focused on cases where the crisp outputs must satisfy a set of relationships dictated in the original crisp data. This phenomenon indicates that these crisp outputs are mathematically dependent on one another. Furthermore, these fuzzy numbers may exist as a group of fuzzy numbers. Therefore, the primary aim of this thesis is to develop a method to defuzzify groups of fuzzy numbers based on Charnes, Cooper, and Rhodes (CCR)-Data Envelopment Analysis (DEA) model by modifying the Center of Gravity (COG) method as the objective function. The constraints represent the relationships and some additional restrictions on the allowable crisp outputs with their dependency property. This leads to the creation of crisp values with preserved relationships and/or properties as in the original crisp data. Comparing with Linear Programming (LP) based model, the proposed CCR-DEA model is more efficient, and also able to defuzzify non-linear fuzzy numbers with accurate solutions. Moreover, the crisp outputs obtained by the proposed method are the nearest points to the fuzzy numbers in case of crisp independent outputs, and best nearest points to the fuzzy numbers in case of dependent crisp outputs. As a conclusion, the proposed CCR-DEA defuzzification method can create either dependent crisp outputs with preserved relationship or independent crisp outputs without any relationship. Besides, the proposed method is a general method to defuzzify groups or individuals fuzzy numbers under the assumption of convexity with linear and non-linear membership functions or relationships

A TOPSIS and DEA Based Approach to Evaluate the Operational Efficiency of Sponge City

As an innovative means to promote low-carbon and ecological development of cities, sponge cities have attracted extensive attention from industry and scholars. Measuring the operation efficiency of a sponge city can effectively measure whether the current input and output are reasonable, whether the management and operation are scientific, etc., which can find out the weaknesses in the current process and management. This paper proposes an evaluation method of interval cross-efficiency combined with TOPSIS and DEA to measure the operating efficiency of a sponge city. Specifically, an evaluation system, that includes three inputs and six outputs, is established at first from the perspective of input and output. Secondly, due to the uncertainty of the natural environment, two DEA models of benevolent and aggressive models are adopted to obtain the cross-efficiency interval value of a sponge city. Next, the cross-efficiency interval values are aggregated based on TOPSIS, and then, the descending principle is introduced to rank sponge cities to obtain the optimal operation efficiency cities. Finally, a case is used to verify the effectiveness of the proposed method. The research idea of this paper is clear, the research method is simple, and the research results can provide a basis for building an efficient and high-level sponge city