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Facet Analysis in Data Envelopment Analysis

In: Data Envelopment Analysis

Author

Listed:
  • Ole B. Olesen

    (The University of Southern Denmark)

  • Niels Chr. Petersen

    (The University of Southern Denmark)

Abstract

Data Envelopment Analysis (DEA) employs mathematical programming to measure the relative efficiency of Decision Making Units (DMUs). One of the topics of this chapter is concerned with development of indicators to determine whether or not the specification of the input and output space is supported by data in the sense that the variation in data is sufficient for estimation of a frontier of the same dimension as the input output space. Insufficient variation in data implies that some inputs/outputs can be substituted along the efficient frontier but only in fixed proportions. Data thus locally support variation in a subspace of a lower dimension rather than in the input output space of full dimension. The proposed indicators are related to the existence of so-called Full Dimensional Efficient Facets (FDEFs). To characterize the facet structure of the CCR- or the BCC-estimators, (Charnes et al. Eur J Oper Res 2:429–444, 1978; Banker et al. Manage Sci 30(9):1078–1092, 1984) of the efficient frontier we derive a dual representation of the technologies. This dual representation is derived from polar cones. Relying on the characterization of efficient faces and facets in Steuer (Multiple criteria optimization. Theory, computation and application, 1986), we use the dual representation to define the FDEFs. We provide small examples where no FDEFs exist, both for the CCR- and the BCC estimator. Thrall (Ann Oper Res 66:109–138, 1996) introduces a distinction between interior and exterior facets. In this chapter we discuss the relationship between this classification of facets and the distinction in Olesen and Petersen (Manage Sci 42:205–219, 1996) between non-full dimensional and full dimensional efficient facets. Procedures for identification of all interior and exterior facets are discussed and a specific small example using Qhull to generate all facets is presented. In Appendix B we present the details of the input to and the output from Qhull. It is shown that the existence of well-defined marginal rates of substitution along the estimated strongly efficient frontier segments requires the existence of FDEFs. A test for the existence of FDEFs is developed, and a technology called EXFA that relies only on FDEFs and the extension of these facets is proposed, both in the context of the CCR-model and the BCC-model. This technology is related to the Cone-Ratio DEA. The EXFA technology is used to define the EXFA efficiency index providing a lower bound on the efficiency rating of the DMU under evaluation. An upper bound on the efficiency rating is provided by a technology defined as the (non-convex) union of the input output sets generated from FDEFs only. Finally, we review recent uses of efficient faces and facets in the literature.

Suggested Citation

  • Ole B. Olesen & Niels Chr. Petersen, 2015. "Facet Analysis in Data Envelopment Analysis," International Series in Operations Research & Management Science, in: Joe Zhu (ed.), Data Envelopment Analysis, edition 127, chapter 6, pages 145-190, Springer.
    • Handle: RePEc:spr:isochp:978-1-4899-7553-9_6
    DOI: 10.1007/978-1-4899-7553-9_6
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    Citations

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    Cited by:

    1. K Hervé Dakpo & Philippe Jeanneaux & Laure Latruffe & Claire Mosnier & Patrick Veysset, 2018. "Three decades of productivity change in French beef production: a Färe‐Primont index decomposition," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 62(3), pages 352-372, July.
    2. Ramón, Nuria & Ruiz, José L. & Sirvent, Inmaculada, 2020. "Cross-benchmarking for performance evaluation: Looking across best practices of different peer groups using DEA," Omega, Elsevier, vol. 92(C).
    3. Panagiotis Ravanos & Giannis Karagiannis, 2022. "In search for the Most Preferred Solution in Value Efficiency Analysis," Discussion Paper Series 2022_05, Department of Economics, University of Macedonia, revised Jul 2022.
    4. Mehdiloo, Mahmood & Podinovski, Victor V., 2021. "Strong, weak and Farrell efficient frontiers of technologies satisfying different production assumptions," European Journal of Operational Research, Elsevier, vol. 294(1), pages 295-311.
    5. Giannis Karagiannis & Panagiotis Ravanos, 2023. "On Value Efficiency Analysis and Cone-Ratio Data Envelopment Analysis models," Discussion Paper Series 2023_03, Department of Economics, University of Macedonia, revised Mar 2023.
    6. Maietta, Ornella Wanda & De Devitiis, Biagia & Destefanis, Sergio & Suppa, Domenico, 2019. "Human capital and rural development policy: evidence from European FADN regions," Bio-based and Applied Economics Journal, Italian Association of Agricultural and Applied Economics (AIEAA), vol. 8(3), December.
    7. Panagiotis Ravanos & Giannis Karagiannis, 2022. "In search for the most preferred solution in value efficiency analysis," Journal of Productivity Analysis, Springer, vol. 58(2), pages 203-220, December.
    8. Andreas Dellnitz & Elmar Reucher & Andreas Kleine, 2021. "Efficiency evaluation in data envelopment analysis using strong defining hyperplanes," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(2), pages 441-465, June.
    9. Heesche, Emil & Asmild, Mette, 2022. "Incorporating quality in economic regulatory benchmarking," Omega, Elsevier, vol. 110(C).
    10. Emil Heesche & Mette Asmild, 2022. "Implications of Aggregation Uncertainty in DEA," IFRO Working Paper 2022/02, University of Copenhagen, Department of Food and Resource Economics.
    11. Dakpo, K Herve & Jeanneaux, Philippe & Latruffe, Laure & Mosnier, Claire & Veysset, Patrick, 2018. "Three decades of productivity change in French beef production: a F€are-Primont index decomposition," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 62(3), July.
    12. Hirofumi Fukuyama & Yong Tan, 2021. "Corporate social behaviour: Is it good for efficiency in the Chinese banking industry?," Annals of Operations Research, Springer, vol. 306(1), pages 383-413, November.
    13. Victor V. Podinovski & Tatiana Bouzdine-Chameeva, 2021. "Optimal solutions of multiplier DEA models," Journal of Productivity Analysis, Springer, vol. 56(1), pages 45-68, August.
    14. Dakpo, K.H. & Vincent, M. & Boussemart, J.-P., 2018. "Spatial aggregation of land uses allocation and pesticide efficiency at landscape level A Multi-ware production approach," 2018 Conference, July 28-August 2, 2018, Vancouver, British Columbia 277258, International Association of Agricultural Economists.
    15. Emil Heesche & Mette Asmild, 2020. "Incorporating quality in economic regulatory benchmarking," IFRO Working Paper 2020/13, University of Copenhagen, Department of Food and Resource Economics.

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