Minor and major consolidations in inverse DEA: Definition and determination

Gholam R Amin,Ali Emrouznejad,Said Gattoufi

doi:10.1016/j.cie.2016.11.029

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.

Highlights

An inverse optimization problem for a given feasible solution of an optimization problem consists of determining the least perturbation in the objective function’s coefficients of the optimization problem in order to make the given feasible solution optimal for the perturbed model, as suggested in Ahuja and Orlin (2001)
The interest in this paper goes to the inverse data envelopment analysis (InvDEA) introduced in
This paper develops an InvDEA method to anticipate the type of consolidation generated by a merger, a major or a minor, for the decision makers to plan the appropriate actions required by the post-consolidation market conditions

Summary

Introduction

An inverse optimization problem for a given feasible solution of an optimization problem consists of determining the least perturbation in the objective function’s coefficients of the optimization problem in order to make the given feasible solution optimal for the perturbed model, as suggested in Ahuja and Orlin (2001) Though it is relatively recent concept, inverse optimization became a popular method to the extend it generated a new research stream in the optimization theory. This paper develops an InvDEA method to anticipate the type of consolidation generated by a merger, a major or a minor, for the decision makers to plan the appropriate actions required by the post-consolidation market conditions.

Basic concept

Minor and major consolidations

Mergers in banking

Mergers in supply chain industry

Concluding remarks and direction for future studies