Inverse DEA-R models for merger analysis with negative data

Abstract Data envelopment analysis (DEA) is a mathematical programming technique for efficiency analysis. For dealing with the data in ratio form, the DEA model for ratio data known as DEA-R exists in the literature. However, some ratio data like financial risk may be negative naturally. In this paper, we contribute to the literature in two ways. In the first place, we deal with DEA-R models in the presence of negative ratio data by proposing an inverse DEA model for merger analysis. In the second place, we develop DEA-R models for merger analysis that can deal with negative data. We apply our models in a real-world application of efficiency and merger analysis of an Iranian bank with 66 branches. The proposed models maintain data confidentiality. This motivates managers to participate in the evaluation and merger process. Our models also provide a reasonable endogenous weight restriction framework without restricting weights exogenously.