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Meta-frontier: literature review and toolkit

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Abstract

Introduced in the 1970s and refined at the beginning of the 2000s, the concept of meta-frontier is now recognized as the most popular operations research technique to deal with technology heterogeneity when conducting an efficiency analysis. As proof, the number of publications has followed an exponential trend with almost 800 publications overall. In short, the concept is based on partitioning DMUs into groups where each group uses its technology. The meta-frontier is defined as the envelopment of the group-specific counterparts. Technology gap ratios are evaluated to distinguish inefficiency behaviours from technological differences. After 20 years of applications and extensions, it is now time to assess the impact of the meta-frontier in the efficiency analysis literature. In this paper, we present a systematic literature review of the concept of meta-frontier. We cover several important aspects such as its origins, developments, and applications, and discuss technical considerations. An important focus will be made on how the partitioning of the DMUs into groups is made in practice; a crucial aspect of the meta-frontier technique. Beyond a simple literature review, this paper represents a guideline and toolkit for practitioners.

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Notes

  1. We highlight the existence of the Free Disposable Hull (FDH after Tulkens 1993) that, contrary to DEA, is not based on a convex technology. Nevertheless, the popularity of DEA is incomparable to the one of FDH.

  2. We highlight that Web of Science is now owned by Clarivate. We have mainly used three sub-datasets since they are directly relevant to our research topic: Science Citation Index Expanded (SCIE), Social Sciences Citation Index, and Arts & Humanities Citation Index (A &HCI).

  3. Fields are those given by Scimago. For better readability, we adopt the following categories: A: Business, Management and Accounting; B: Energy; C: Engineering; D: Environmental Science; E: Computer Science; F: Social Sciences; G: Economics, Econometrics and Finance; H: Decision Sciences; I: Mathematics; J: Medicine; K: Agricultural and Biological Sciences; L: Psychology; M: Multidisciplinary; N: Health Professions; O: Nursing; P: Biochemistry, Genetics and Molecular Biology; Q: Earth and Planetary Sciences; R: Arts and Humanities; S: Psychology.

  4. The averages, 760.75 and 2954.05, respectively, are less informative in that case because of applications using very large samples.

  5. The following groups appear only in one paper: branch, career, collaboration, complexity, gene, playing position, risk, sex, star number, and water use.

  6. The following DMUs appear only in one paper: buildings, CEOs, chains, children, councils, departments, distributors, districts, equity funds, fisheries, franchises, greenhouses, management systems, meals, menus, owners, parcels, pharmacies, platforms, players, programs, projects, providers, regencies, responses, services, shops, smartphones, terminals, towns, vessels, villages, years, and zones.

  7. Note that we only present the group criteria that appear at least in three publications in Table 10, i.e. the group criteria of Table 5.

  8. Note that Table 12 covers technical aspects from 2009 to 2022. Technical aspects before 2008 are discussed in Sect. 3.1.

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Acknowledgements

We wish to thank the Editor-In-Chief Nikolaos Fragkiskos Matsatsinis, the anonymous referees, and Thibault Piron for their comments that substantially improved the paper. This work is supported by the Fonds de la Recherche Scientifique (FNRS) under Grant No. J.0193.23.

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  1. HEC Liège, Université de Liège, Liège, Belgium

    Barnabe Walheer

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  1. Barnabe Walheer
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Correspondence to Barnabe Walheer.

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Appendix

Appendix

References related to the literature review about the concept of meta-frontier for the period 1969–2021 are given per year in the attached Online Appendix.

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Walheer, B. Meta-frontier: literature review and toolkit. Oper Res Int J 24, 20 (2024). https://doi.org/10.1007/s12351-024-00830-z

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