Evaluating performance of Two-Step Networks Using Fuzzy Data Envelopment Analysis

In order to improve the performance of each decision making unit and identify weaknesses and strengths of them, managers frequently need to compare performance of units under their supervision with performance of other existing homogeneous decision making units. Earlier methods in traditional data envelopment analysis investigate efficiency for single stage decision making units with crisp data which use some inputs X to product final outputs Y. If we envisage multistage decision making units with external inputs, intermediate flows and final outputs which some or all of them are not crisp necessarily, the decision making units can't be easily evaluated. In this paper we promote a new technique based on the composition method to evaluate the efficiency score of two-stage production processes where data are not crisp in specific required model which is unskew and the efficiency scores evaluated by it are unique. The proposed method consider expected interval of fuzzy values and use the convex combination of two end-point of them to measure each stages' efficiency and the overall efficiency score for different α-values. We use multiplicative CCR output-oriented and CCR input-oriented fuzzy models for the first and second stages respectively to assess efficiency scores for the two stages, which are then aggregated to get the overall efficiency score of the evaluated unit. In order to evaluate the performance of the method, the efficiencies of four decision making units are calculated which transform two external inputs to an intermediate measure and then use it to product two final outputs which all data are fuzzy value, and thus it is shown how our method leads in exact results.