The Production Possibility Set (PPS) is defined as the set of all inputs and outputs of a system in which inputs can produce outputs‎. ‎In Data Envelopment Analysis (DEA)‎, ‎it is highly important to identify the defining hyperplanes and especially the strong defining hyperplanes of the empirical PPS‎. ‎Although DEA models can determine the efficiency of a Decision Making Unit (DMU)‎, ‎but they...

In a recent paper in this journal, Yang et al. [Feng Yang, Dexiang Wu,Liang Liang, Gongbing Bi & Desheng Dash Wu (2009), supply chainDEA:production possibility set and performance evaluation model] definedtwo types of supply chain production possibility set which were proved to beequivalent to each other. They also proposed a new model for evaluatingsupply chains. There are, however, some short...

Introduction: Data envelopment analysis (DEA) is a data-oriented method for measuring and benchmarking the relative efficiency of peer decision making units (DMUs) with multiple inputs and multiple outputs. DEA was initiated in 1978 when Charnes, Cooper and Rhodes (CCR) demonstrated how to change a fractional linear measure of efficiency into a linear programming format. This non-parametric app...

Data envelopment analysis (DEA), as originally proposed, is a methodology for evaluating the relative efficiencies of a set of homogeneous decision-making units (DMUs) in the sense that each uses the same input and output measures (in varying amounts from one DMU to another). In some situations, however, the assumption of homogeneity among DMUs may not apply. As an example, consider the case wh...

DEA models treat the DMU as a “black box.” Inputs enter and outputs exit, with no consideration of the intervening steps. Consequently, it is di(cult, if not impossible, to provide individual DMU managers with speci;c information regarding the sources of ine(ciency within their DMUs. We show how to use DEA to look inside the DMU, allowing greater insight as to the sources of organizational ine(...

In the conventional data envelopment analysis (DEA), it is assumed that all decision making units (DMUs) using the same input and output measures, means that DMUs are homogeneous. In some settings, however, this usual assumption of DEA might be violated. A related problem is the problem of textit{missing} textit{data} where a DMU produces a certain output or consumes a certain input but the val...

The production possibility set (PPS) is defined as the set of all inputs and outputs of a system in which inputs can produce outputs. In data envelopment analysis (DEA), identification of the strong defining hyperplanes of the empirical production possibility set (PPS) is important, because they can be used for determining rates of change of outputs with change in inputs. Also, efficient hyperp...

The existing data envelopment analysis (DEA) models for measuring the relative efficiencies of a set of decision making units (DMUs) using various inputs to produce various outputs are limited to crisp data. The notion of fuzziness has been introduced to deal with imprecise data. Fuzzy DEA models are made more powerful for applications. This paper develops the measure of efficiencies in input o...

The ability of determining all defining hyperplanes of DEA production possibility set (efficient frontier) prior to the DEA computations is of extreme importance. Specially, access to efficient frontier permits a complete analysis (e.g. calculation of efficiency scores, returns to scale, sensitivity analysis and so on) in second phase for the corresponding model. This paper presents a linear sy...

In models of data envelopment analysis (DEA), an optimal set of weights is generally assumed to represent the assessed decision making unit(DMU) in the best light in comparison to all the other DMUs, and so there is an optimal set of weights corresponding to each DMU. The present paper, proposes a three stage method to determine one common set of weights for decision making units. Then, we use ...