In this study using an input-oriented data envelopment analysis (DEA) model with undesirable outputs a new stochastic model called Expected Ranking Criterion is proposed. The proposed model employs statistical techniques to evaluate the efficiency of decision making units (DMUs) with stochastic data. Based on the proposed model, a stochastic DEA (SDEA) cross-efficiency model is suggested for ranking and discrimination of DMUs. Then, given the non-uniqueness of resulting optimal solution, a stochastic model is introduced for rating priorities by which cross-efficiency evaluation is performed using aggressive approach. Finally, the proposed models are implemented for evaluating 32 thermal power plants. The results show the applicability of the proposed models.

在这项研究中，使用具有不期望的输出的面向输入的数据包络分析（DEA）模型，提出了一种新的随机模型，称为期望排名标准。所提出的模型采用统计技术来评估具有随机数据的决策单位（DMU）的效率。基于所提出的模型，提出了一种随机DEA（SDEA）交叉效率模型来对DMU进行排名和区分。然后，考虑到所得最优解的非唯一性，引入了一种随机模型来评估优先级，通过该模型可以使用积极的方法进行交叉效率评估。最后，所提出的模型用于评估32个火力发电厂。结果表明了所提模型的适用性。