Minor and major consolidations in inverse DEA: Definition and determination

Abstract

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.

A two‐stage inverse data envelopment analysis approach for estimating potential merger gains in the US banking sector

“…The returns to scale of the inverse DEA models in this paper is from the base DEA models. Following the inverse DEA models for estimating merger gains in the literature (Amin & Al‐Muharrami, 2018; Amin, Al‐Muharrami, & Toloo, 2019; Amin, Emrouznejad, & Gattoufi, 2017a, 2017b; Gattoufi, Amin, & Emrouznejad, 2014), the above inverse DEA models developed in this paper assumed variable returns to scale. The type of returns to scale can be changed to other appropriate forms of returns to scale depending on the application.…”

“…Amin, Emrouznejad, and Gattoufi (2017a) extended the concept of M&A and firms' restructuring and introduced the concept of generalized restructuring using inverse DEA. Amin, Emrouznejad, and Gattoufi (2017b) identified minor and major consolidations using inverse DEA models. A merger that affects the preconsolidation efficiency frontier is called a major consolidation; otherwise, the merger is called a minor consolidation.…”

A novel inverse DEA model with application to allocate the CO2 emissions quota to different regions in Chinese manufacturing industries

“…Despite the potential applicability of the standard DEA in different contexts, there are few applications of inverse DEA that are reported in the literature such as application in resource allocation suggested in Hadi-Vencheh et al (2008). Further recent of inverse DEA studies can be found in Jahanshahloo et al (2015), Ghobadi and Jahangiri (2015), Ghiyasi (2017) and Amin et al (2017a). In addition, Zhang and Cui (2016) discussed an extension of the inverse DEA model and Lim (2016) addressed the frontier change for setting a new product target using a new inverse DEA method.…”

New inverse DEA models for budgeting and planning

“…(Amin & Emrouznejad, 2007) applied the inverse optimization for forecasting and provided a streamlined approach to time series analysis using inverse linear programming. (Amin, Emrouznejad, & Gattoufi, 2017) proposed inverse DEA models for modeling generalized firms' restructuring and anticipating the minor and major consolidation for a merger in a market. (M. dealt with cost and revenue efficiency in the inverse DEA context.…”