Non-homogeneous DEA approach in the presence of negative data: a promising prospective approach to enhance decision-making

Data envelopment analysis (DEA) has come to be recognized as an important technique for evaluating the efficiency of decision-making units (DMUs) in recent years. In conventional DEA, it is often assumed that each DMU being assessed for efficiency utilizes the same number of inputs and produces the same number of outputs. In recent years, some academicians have attempted to address the non-homogeneity of the data in DEA; nevertheless, there is a lack of models that take into consideration the non-homogeneity of negative data. To address the issue of data heterogeneity in the presence of negative data, the research suggests a DEA model based on the range directional measure (RDM). More precisely, we are concerned in this study with the heterogeneity of output data generated by a homogeneous set of input data collections. Our objective is to determine the inefficiency of each subunit associated with an output that utilizes the optimal proportion of inputs instead of merely categorizing DMUs according to their output structure, as was the case in previous research. For empirical analysis of the proposed model first, we made a comparison between the proposed model and a representative set of data from earlier studies. We next used synthesized negative data generated uniformly using Matlab software version R2021b to provide an empirical illustration of the proposed model. In addition, we carried out an analysis to assess the research efficiency of 20 institutions.