Stage interval ratio DEA models and applications

Data envelopment analysis (DEA) is a crucial method for assessing the efficiency of decision-making units (DMUs). In practice, it is common to encounter situations where the performance of a DMU at a certain stage is evaluated, especially in policy effect evaluation. The key to stage performance evaluation is to eliminate the influence of pre-stage inputs (outputs) on stage performance. This paper proposes stage ratio DEA models that consider two types of inputs and outputs: accurate ratio data and interval ratio data. The first form considers the evaluation of stage efficiency when accurate ratios of inputs and outputs are used at the beginning and end of the stage. The second form assesses stage efficiency using interval ratio data for interval inputs and outputs. To verify the validity of the proposed models, the numerical example validates the first form of stage ratio DEA models. And the second form is applied to evaluate the sustainable efficiency of 14 energy saving and environmental protection clean enterprises (ESEPCEs). The empirical results demonstrate that the proposed models provide a more accurate assessment of stage efficiency compared to the traditional DEA-CCR model.