A fairer assessment of DMUs in a generalised two-stage DEA structure

Abstract

In Data Envelopment Analysis (DEA), a variety of approaches have been used in the context of single-stage and basic serial two-stage systems to attain fairness in the evaluation of decision-making units (DMUs). Little work, however, has been done to address this challenge in a generalised two-stage structure featuring additional inputs in the second stage and a proportion of first-stage outputs as final outputs. In this paper, we argue that in this context, fairness is enhanced by increasing measures related to the discriminatory power and the weighting scheme of the method. We describe a mechanism that gives prominence to a more contemporary concept of fairness, incorporating diversity and inclusion of minority opinions. These aspects have, to our knowledge, not yet received explicit attention in the methodological development of DEA. We propose a novel combination of an additive self-efficiency aggregation model, a minimax secondary goal model, and the CRiteria Importance Through Inter-criteria Correlation (CRITIC) method, in order to promote these aspects of fairness, and thus achieve a better degree of cooperation between the stages of a DMU and among DMUs. The additive aggregation model is chosen over the alternative multiplicative approach for a variety of reasons relating to the emphasis on the intermediate products exchanged and the simplification. The minimax model offers peer evaluation in which each DMU aims to evaluate the worst of the others in the best possible light. Application of the CRITIC method to DEA addresses the aggregation problem within the cross-efficiency concept. Practical applications of this approach could include supporting the determination of training needs in job rotation manufacturing, or evaluation of sustainable supply chains. The paper includes a description of a numerical experiment, illustrating the approach.