Minor and major consolidations in inverse DEA: Definition and determination

•Defining a major or a minor consolidation when merging two entities.•Proposing a novel method to identify a merger is a major or a minor consolidation.•Developing a new inverse Data Envelopment Analysis for merging.•Applying the proposed model in real data from banks.•Providing insight that the same method can be used in any industries.

Many production systems have acquisition and merge operations to increase productivity. This paper proposes a novel method to anticipate whether a merger in a market is generating a major or a minor consolidation, using Inverse data envelopment analysis (InvDEA) model. A merger between two or more decision making units (DMUs) producing a single merged DMU that affects the efficiency frontier, defined by the pre-consolidation market conditions, is called a major consolidation. The corresponding alternative case is called a minor consolidation. A necessary and sufficient condition to distinguish the two types of consolidations is proven and two numerical illustrations in banking and supply chain management are discussed. The crucial importance of anticipating the magnitude of a consolidation in a market is outlined.