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This paper deals with evaluating congestion in free disposal hull (FDH) models. There are several approaches in data envelopment analysis (DEA) literatures which discuss the theory and application of congestion. However, almost all of these approaches considered convex DEA technologies. So, in the case of nonconvex technologies, including FDH technology, this field is almost nil. This paper makes an attempt to fill in this void. To do so, this study provides a pairwise comparisons-based algorithm to evaluate congestion in FDH model. This algorithm identifies the sources of congestion and estimates its amounts. It is also capable of detecting the losses amounts of output due to congestion. The validity of the proposed model is demonstrated using some numerical and empirical examples.
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Algoritmos , Toma de Decisiones , Modelos Estadísticos , Aglomeración , Humanos , Análisis de RegresiónRESUMEN
This paper studies the inverse data envelopment analysis using the nonradial enhanced Russell model. Necessary and sufficient conditions for inputs/outputs determination are introduced based on Pareto solutions of multiple-objective linear programming. In addition, an approach is investigated to identify extra input/lack output in each of input/output components (maximum/minimum reduction/increase amounts in each a of input/output components). In addition, the following question is addressed: if among a group of DMUs, it is required to increase inputs and outputs to a particular unit and assume that the DMU maintains its current efficiency level with respect to other DMUs, how much should the inputs and outputs of the DMU increase? This question is discussed as inverse data envelopment analysis problems, and a technique is suggested to answer this question. Necessary and sufficient conditions are established by employing Pareto solutions of multiple-objective linear programming as well.
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Matemática/métodos , Modelos Lineales , Cómputos Matemáticos , Modelos Teóricos , Estadísticas no ParamétricasRESUMEN
The main objective of the present study was to develop a valid and appropriate model to evaluate companies' efficiency and environmental performance, concerning health, safety, and environmental management system principles. The proposed model overcomes the shortcomings of the previous models developed in this area. This model has been designed on the basis of a mathematical method known as Data Envelopment Analysis (DEA). In order to differentiate high-performing companies from weak ones, one of DEA nonradial models named as enhanced Russell graph efficiency measure has been applied. Since some of the environmental performance indicators cannot be controlled by companies' managers, it was necessary to develop the model in a way that it could be applied when discretionary and/or nondiscretionary factors were involved. The model, then, has been modified on a real case that comprised 12 oil and gas general contractors. The results showed the relative efficiency, inefficiency sources, and the rank of contractors.