Extension of Ranking Method Based On Effectiveness Of units In Society by Common Weights Approach in stochastic DEA

The aim of this paper is to modify the suggested method by Noura et al. (A. A. Noura, F. Hosseinzadeh Lotfi, G. R. Jahanshahloo, S. Fanati Rashidi, Super-efficiency in DEA by effectiveness of each unit in society, Applied Mathematics Letters, 24, 2010, 623-626), that is a ranking method based on the effectiveness of each unit in society. They utilized the assigned weights for ranking DMUs, but this is not a conventional method for determining the weights. This paper proposes common weights approach for improving its method. A multi-objective linear fractional is derived and then it was converted to a multi-objective linear programming by Taylor series. The model is solved by Max Min method. Based on the obtained optimal solution, common weights are acquired and then DMUs will be ranked. And we introduce stochastic version of this model in DEA. The deterministic equivalent of this stochastic model will be obtained. The proposed method is illustrated by ranking Taiwan forests after reorganization.