Improving efficiency evaluation in the presence of ratio data: Inverse non-radial enhanced Russell models

In many real-world scenarios, decision makers often rely on data available in ratio form. Under the data envelopment analysis (DEA) framework, radial (R) models, such as DEA-R, do consider ratio data for the efficiency evaluation of decision making units (DMUs). Nevertheless, the omission of the slack values over the evaluation process may lead to inaccurate results. Hence, this paper introduces non-radial Enhanced Russell Models (ERM) with ratio data for more precise and reliable assessments. Furthermore, we develop new inverse non-linear ERM formulations to determine the optimal levels of inputs and outputs for preset ratio-efficiency scores. The validity of the proposed models is demonstrated through illustrative examples and a real-world case study, highlighting their practical relevance across diverse organizational contexts. Our research contributes novel insights and methodologies to the field of efficiency assessment, offering managers robust tools for more accurate decision-making.