This paper introduces discretionary imprecise data in Data Envelopment Analysis (DEA) and discusses the efficiency evaluation of Decision Making Units (DMUs) with non-discretionary imprecise data. Then, suggests a method for evaluation the efficiency of DMUs with non-discretionary imprecise data.When some inputs and outputs are imprecise and non-discretionary, the DEA model becomes non-linear programming problem. By a Theorem, we use the translation of imprecise data into exact data and then use the standard linear DEA model for evaluating DMUs with non-discretionary and imprecise data, which is the generalized form of envelopment form in input oriented of CCR model. To illustrate the proposed method, a numerical example with non-discretionary imprecise data is solved.

In this paper, with the priority of measuring and promoting productivity in energy sector, we presented a model for evaluating the technical efficiency of oil refineries, as huge producers of energy and different fuels. The basis of evaluation in this research was Math modeling by using new and advanced operational research techniques such as data envelopment analysis, goal programming, analytical hierarchy process and designing combined models. The formulating process was made under two different scenarios and assumptions: consumption-production and cost-income. The final results ranked the order and sort of each refinery as a decision making unit. In addition to calculation of each unit's score, we also made a comparison between the units, their weaknesses and the favorite score of each unit in real situation. This research focuses on the optimized utilization of refining processes with less refining cost and ability to make more valuable products considering the present availabilities and capacities.

Data envelopment analysis (DEA) is a non-parametric technique for evaluation of relative efficiency of decision making units described by multiple inputs and outputs. It is based on solving linear programming problems. Since 1978 when basic DEA model was introduced many its modifications were formulated. Among them are two or multi-stage models with serial or parallel structure often called network DEA models that are widely discussed in professional community in the last years. The exact known inputs and outputs are required in these DEA models. However, in the real world, the concern is systems with interval (bounded) data. When we incorporate such interval data into multi-stage DEA models, the resulting DEA model becomes a non-linear programming problem. In this study, we suggest an approach to measure the efficiency of series and parallel systems with interval data that preserves the linearity of DEA model. Also, the interval DEA models are proposed to measure the lower and upper bounds of the efficiency of each DMU with interval data.

The main reasons for developing countries to support small and medium-scale industries are their high flexibility, lower investment necessity, targeting specific entrepreneurs, and dynamic management. These characteristics are important for creating jobs, bringing equitable distribution of income, and overall higher-gross domestic products. The main purpose of this study is to measure the efficiency of small -scale industries by data envelopment analysis within different provinces of the country with special reference to Hamedan province. The results show that, during the years 1381-1386, the average efficiency of small industries in the country was around 96 percent. The sensitivity analysis shows that the most important factors affecting performance are employment rate, quantity of investment, and value of production. Hamedan province has been equal to the average score of the country (92 percent), ranking 12 among all the provinces. However, the trend of efficiency and productivity growth was not positive as expected.