In conventional DEA methods, all inputs and outputs are assumed to be continuous. However, the implied presumption of continuous data may not maintain an acceptable level of precision in practical data. Many practical situations such as number of teachers in a school, number of students in a college, or research papers only take integer values. Presented work presumes subsets of input and output variables in traditional five-pronged axioms in DEA model to be integer values for the first time in the field. An additional effort in this work expands axioms and a new model is presented. This paper presents a novel two phase model that in the first phase produces more precise efficiency values and the best benchmark in its second phase, i.e. the nearest integer point to the efficiency boundary is selected based on constant returns to scale. A case study is presented that demonstrates a comparison of efficiency values obtained with this model compared to prior models that is show in table 1. And in Table 2, the values of the slack are compared with each other. Manuscript profile

Conventional data envelopment analysis (DEA) models are used to measure efficiency score of production systems when they are considered as black boxes and their internal relationship is ignored. This paper deals with a common special case of network systems which is called multi-stage production system and can be generalized to many organizations. A multi stage production system has some stages in which the outputs of each stage are used as the inputs of the next stage to produce the final outputs of the system. Most of the approaches handling multi-stage systems in DEA evaluate efficiency measure of a production system considering the interrelationship between its stages; however, they do not present their ranking or impact of each stage in ranking of a special multi-stage system through comparison with the others. In this paper, considering the series internal structure of the multi-stage systems and their efficiency measure, we propose some new ratio-based DEA models to determine the best and the worst rank of the multi-stage systems over all sets of feasible weights. In order to improve the performance of the whole system, the proposed models are used to recognize the stages with the most important role in the system’s inefficiency. Some numerical examples are presented to illustrate the approach. Manuscript profile

Traditional data envelopment analysis (DEA) models deal with measurement of relative efficiency of decision making units (DMUs) in which multiple-inputs consumed to produce multiple-outputs. One of the drawbacks of these models is neglecting internal processes of each system, which may have intermediate products and/or independent inputs and/or outputs. In this paper some methods which are usable for network systems are briefly reviewed. A new unified model is also introduced which can be easily applied for performance measurement of all type of network production process. As an application of network DEA models, performance evaluation of wheat production in Iran provinces is considered and the results are compared.Traditional data envelopment analysis (DEA) models deal with measurement of relative efficiency of decision making units (DMUs) in which multiple-inputs consumed to produce multiple-outputs. One of the drawbacks of these models is neglecting internal processes of each system, which may have intermediate products and/or independent inputs and/or outputs. In this paper some methods which are usable for network systems are briefly reviewed. A new unified model is also introduced which can be easily applied for performance measurement of all type of network production process. As an application of network DEA models, performance evaluation of wheat production in Iran provinces is considered and the results are compared. Manuscript profile

In production theory, it is necessary to be capable of predicting the production func- tion’s long-run behaviors. Hereof, returns to scale is a helpful concept. Returns to scale describes the reaction of a production function to the proportionally scaling all its input variables. In this regard, Data envelopment analysis (DEA) provides a com- prehensive framework for returns to scale evaluation. A sequence of attempts has been made on the subject of returns to scale in DEA literature which cause DEA to be ex- panded to widespread applications. Centralization of carried out studies in firm level, on one hand, and the importance of economical inter-operation in performance analysis in industry level, on the other hand, were the main motivation to start a new range of studies around identifying the return to scale in industry level. This paper collaborates interesting relations between firms and industry technology with performance analysis techniques to extract a relation between returns to scale status of firms and system-wide unit based on the reference set method. Manuscript profile