Measuring productivity change in DEA-R: A ratio-based profit efficiency model

The main purpose of the present study is to evaluate the productivity change of decision making units (DMUs) over time based on ratio data envelopment analysis (DEA-R). To achieve this aim, we formulate a ratio-based profit efficiency model that is inspired by the ratio form of the profit efficiency. Also, a non-oriented DEA-R model is presented to define DEA-R allocative efficiency of DMUs which by using it the proposed productivity index can be decomposed into four components. Finally, a numerical example is presented to compare the results of the proposed approach with DEA approach.