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In economics, a production function relates the outputs of a production process to the inputs of the production. Generally, the production function is not available due to the complexity of the production process, the changes in production technology. Therefore, we have to consider an approximation of the production function. Data Envelopment Analysis (DEA) is a non-parametric methodology for obtaining an approximation of the production function and assessing the relative efficiency of economic units. Sensitivity analysis and sustainability evaluation of Decision Making Units (DMUs) are as the most important concerns of Decision Makers (DM). This study considers the sustainability radius of economic performance of DMUs and then proposes some approaches combined with sensitivity analysis for determining the sustainability radius of cost efficiency, revenue efficiency and profit efficiency of units. The proposed approaches eliminate the unit under evaluation from the observed data and disturb the data of it, based on the sensitivity analysis, to determine the sustainability radius of cost efficiency, revenue efficiency and profit efficiency of decision making units. Potential application of our proposed methods is illustrated with a dataset consisting of 21 medical centers in Taiwan.

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Data Envelopment Analysis (DEA) is a Nonparametric method for measuring of the performance of decision-making units (DMUs) - which do not need to have or compute a firm's production function, which is often difficult to calculate. In this article, we evaluate the units under review in terms of cost efficiency, and the units in terms of spending and production over several periods, and the rate of improvement or regression of each of these units. Considering the minimal use of resources and consuming less money, the improvement or retreat of the recipient's decision unit in terms of cost was examined by presenting a method based on solving linear programming models using the productivity index is Malmquist Global. Finally, by designing and solving a numerical example, we emphasize and test the applicability of the material presented in this article.