Inverse DEA-R models for merger analysis of electricity distribution units

This study addresses a significant gap in the existing literature on Data Envelopment Analysis (DEA) by introducing a novel approach for handling ratio data in merger and acquisition analysis. Traditional DEA models often struggle with ratio data, which are common in many real-world applications, such as electricity distribution. To tackle this issue, we propose an advanced Inverse DEA (Inve-DEA) framework specifically designed for ratio data, termed Inve-DEA-R. Our approach includes both input-oriented and output-oriented Inve-DEA-R models under the assumption of variable returns to scale. The primary contribution of this research is the development of these models to estimate the required input levels and producible output levels in the context of mergers and acquisitions, incorporating ratio data effectively. We apply our proposed models to the performance assessment and merger analysis of 39 electricity distribution units in Iran, where some of the data are in ratio form. Our results reveal that the application of the Inve-DEA-R models offers significant insights into potential merger gains. Specifically, the analysis indicates that merging distribution units could lead to improved service provision and operational efficiency. The developed Inve-DEA-R models not only address the theoretical gap in DEA for ratio data but also provide practical tools for merger analysis across various sectors dealing with ratio-form data. This research extends the applicability of DEA methodologies and offers a robust framework for evaluating efficiency and potential benefits in merger scenarios.