Essays on the fairer evaluation of units in various network Data Envelopment Analysis structures

Abstract

This thesis sheds new light on proposing and illustrating the use of several alternative modelling approaches and methodological frameworks to attain fairness in the evaluation outcomes of the decision-making units (DMUs) under exploration, being arranged as a network Data Envelopment Analysis (DEA) system. The thesis contains three main chapters. Apart from Chapter 1 (Introduction), in Chapter 2, we initially emphasise that in 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 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 chapter, 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 chapter includes a description of a numerical experiment, illustrating the approach. The evaluation of the performance of a DMU can be measured by its own optimistic and pessimistic multipliers, leading to an interval self-efficiency score. While this concept has been thoroughly studied with regard to single-stage systems, there is still a gap when it is extended to two-stage tandem structures, which better correspond to a real-world scenario. In this spirit, in Chapter 3, we argue that in this context, a meaningful ranking of the DMUs is obtained; this outcome simultaneously considers the optimistic and pessimistic viewpoints within the self-appraisal context, and the most favourable and unfavourable weight sets of each of the other DMUs in a peer-appraisal setting. We initially extend the optimistic-pessimistic DEA models to the specifications of such a two-stage structure. The two opposing self-efficiency measures are merged to a combined self-efficiency measure via the geometric average. Under this framework, the DMUs are further evaluated in a peer setting via the interval cross-efficiency (CE). This methodological tool is applied to evaluate the target DMU in relation to the most favourable and unfavourable weight profiles of each of the other DMUs, while maintaining the combined self-efficiency measure. We, thus, determine an interval individual CE score for each DMU and flow. By treating the interval CE matrix as a multi-criteria decision making problem and by utilising several well-established approaches from the literature, we delineate its remaining elements; these lead us to a meaningful ultimate ranking of the DMUs. A numerical example about the efficiency evaluation of ten bank branches in China illustrates the applicability of our modelling approaches. Many organisations are composed of multiple departments connected either in series or in parallel, which may be further decomposed into a number of functions arranged in a hierarchical structure. Several researchers have successfully used appropriate DEA modelling techniques to assess complex structures. However, to our knowledge, noone has examined the case of measuring and evaluating a parallel network structure combined with a hierarchical one. Chapter 4 discusses the development of the novel multi-function parallel system with embedded hierarchical network structures to eliminate this research gap. A linear additive decomposition DEA model and a non-linear multiplicative aggregation DEA model are proposed as alternatives to evaluate the operating performance of such a structure. The system, the sub-systems, and the efficiencies of their internal units, as well as their relationships, are identified. The system efficiency of the additive model is shown to be greater than or equal to that of the multiplic...

More information

Identifiers

ORCID for Marios Dominikos Kremantzis: orcid.org/0000-0002-9531-404X

ORCID for Patrick Beullens: orcid.org/0000-0001-6156-3550

ORCID for Jonathan Klein: orcid.org/0000-0002-5495-8738

Catalogue record

Export record