Efficiency evaluation with cross-efficiency in the presence of undesirable outputs in stochastic environment

Abstract

Data envelopment analysis (DEA) is a useful tool for efficiency evaluation of decision making units (DMUs). The classical DEA models deal with exact data while in real world problems we concern with uncertain data such as fuzzy, stochastic and etc. In this paper, using input oriented CCR model (ICCR) in the presence of undesirable outputs with specific risk (α), a new stochastic model called Expected Ranking Criterion is proposed. Based on this, the stochastic cross-efficiency evaluation is presented for robust ranking and discrimination of DMUs. Given the non-uniqueness of resulting optimal solutions, a model is introduced for ranking by which stochastic cross-efficiency is performed using aggressive approach. The proposed model provides ranking of all DMUs whereas current stochastic DEA models in literature fail in this regard. Finally, the proposed models are implemented for 32 thermal power plants with stochastic inputs and undesirable outputs. The results show the applicability of proposed models.