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A ranking framework based on interval self and cross-efficiencies in a two-stage DEA system

A ranking framework based on interval self and cross-efficiencies in a two-stage DEA system
A ranking framework based on interval self and cross-efficiencies in a two-stage DEA system

The evaluation of the performance of a decision-making unit (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 paper, 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 Data Envelopment Analysis (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; we show how 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.

Data envelopment analysis, interval cross-efficiency, interval self-efficiency, network, ranking
1293-1319
Kremantzis, Marios Dominikos
59c7026c-01a6-475f-9774-12efea43d86a
Beullens, Patrick
893ad2e2-0617-47d6-910b-3d5f81964a9c
Klein, Jonathan
639e04f0-059a-4566-9361-a4edda0dba7d
Kremantzis, Marios Dominikos
59c7026c-01a6-475f-9774-12efea43d86a
Beullens, Patrick
893ad2e2-0617-47d6-910b-3d5f81964a9c
Klein, Jonathan
639e04f0-059a-4566-9361-a4edda0dba7d

Kremantzis, Marios Dominikos, Beullens, Patrick and Klein, Jonathan (2022) A ranking framework based on interval self and cross-efficiencies in a two-stage DEA system. RAIRO - Operations Research, 56 (3), 1293-1319. (doi:10.1051/ro/2022056).

Record type: Article

Abstract

The evaluation of the performance of a decision-making unit (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 paper, 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 Data Envelopment Analysis (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; we show how 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.

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Accepted/In Press date: 20 April 2022
Published date: 2 June 2022
Additional Information: Funding Information: Acknowledgements. The work was supported by the Engineering and Physical Sciences Research Council (Industrial CASE award) under grant 5162031105656, and BAE Systems. Publisher Copyright: © 2022 EDP Sciences. All rights reserved.
Keywords: Data envelopment analysis, interval cross-efficiency, interval self-efficiency, network, ranking

Identifiers

Local EPrints ID: 469030
URI: http://eprints.soton.ac.uk/id/eprint/469030
PURE UUID: 79f918c3-111e-4b08-bf2c-5605d978fee2
ORCID for Marios Dominikos Kremantzis: ORCID iD orcid.org/0000-0002-9531-404X
ORCID for Patrick Beullens: ORCID iD orcid.org/0000-0001-6156-3550
ORCID for Jonathan Klein: ORCID iD orcid.org/0000-0002-5495-8738

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Date deposited: 05 Sep 2022 16:55
Last modified: 19 Dec 2023 02:45

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