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Translation Invariance in Data Envelopment Analysis

In: Data Envelopment Analysis

Author

Listed:
  • Jesus T. Pastor

    (University Miguel Hernandez of Elche)

  • Juan Aparicio

    (University Miguel Hernandez of Elche)

Abstract

In this chapter we present an overview of the different approaches that have considered translation invariant Data Envelopment Analysis (DEA) models. Translation invariance is a relevant property for dealing with non-positive input and/or non-positive output values. We start by considering the classical approach and continue revising recent contributions. We also consider non-translation invariant DEA models that are able to deal with negative data at the expense of modifying the model itself. Finally, we propose to study translation invariance in a general framework through a recently introduced distance function: the linear loss distance function.

Suggested Citation

  • Jesus T. Pastor & Juan Aparicio, 2015. "Translation Invariance in Data Envelopment Analysis," International Series in Operations Research & Management Science, in: Joe Zhu (ed.), Data Envelopment Analysis, edition 127, chapter 8, pages 245-268, Springer.
    • Handle: RePEc:spr:isochp:978-1-4899-7553-9_8
    DOI: 10.1007/978-1-4899-7553-9_8
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    Citations

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    Cited by:

    1. Aparicio, Juan & Kapelko, Magdalena, 2019. "Accounting for slacks to measure dynamic inefficiency in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 278(2), pages 463-471.
    2. Hainan Guo & Yang Zhao & Tie Niu & Kwok-Leung Tsui, 2017. "Hong Kong Hospital Authority resource efficiency evaluation: Via a novel DEA-Malmquist model and Tobit regression model," PLOS ONE, Public Library of Science, vol. 12(9), pages 1-24, September.
    3. Henriques, C.O. & Chavez, J.M. & Gouveia, M.C. & Marcenaro-Gutierrez, O.D., 2022. "Efficiency of secondary schools in Ecuador: A value based DEA approach," Socio-Economic Planning Sciences, Elsevier, vol. 82(PA).
    4. Michalis Doumpos & Alexis Guyot & Emilios Galariotis & Constantin Zopounidis, 2020. "Assessing the quality of life in French municipalities: a multidimensional approach," Annals of Operations Research, Springer, vol. 293(2), pages 789-808, October.
    5. Vaninsky, Alexander, 2018. "Energy-environmental efficiency and optimal restructuring of the global economy," Energy, Elsevier, vol. 153(C), pages 338-348.
    6. Aparicio, Juan & Monge, Juan F. & Ramón, Nuria, 2021. "A new measure of technical efficiency in data envelopment analysis based on the maximization of hypervolumes: Benchmarking, properties and computational aspects," European Journal of Operational Research, Elsevier, vol. 293(1), pages 263-275.
    7. Cova-Alonso, David José & Díaz-Hernández, Juan José & Martínez-Budría, Eduardo, 2021. "A strong efficiency measure for CCR/BCC models," European Journal of Operational Research, Elsevier, vol. 291(1), pages 284-295.
    8. Aparicio, Juan & Kapelko, Magdalena & Ortiz, Lidia, 2023. "Enhancing the measurement of firm inefficiency accounting for corporate social responsibility: A dynamic data envelopment analysis fuzzy approach," European Journal of Operational Research, Elsevier, vol. 306(2), pages 986-997.
    9. Tone, Kaoru & Chang, Tsung-Sheng & Wu, Chen-Hui, 2020. "Handling negative data in slacks-based measure data envelopment analysis models," European Journal of Operational Research, Elsevier, vol. 282(3), pages 926-935.
    10. Pooja Bansal & Aparna Mehra, 2018. "Multi-period additive efficiency measurement in data envelopment analysis with non-positive and undesirable data," OPSEARCH, Springer;Operational Research Society of India, vol. 55(3), pages 642-661, November.
    11. Tavana, Madjid & Izadikhah, Mohammad & Toloo, Mehdi & Roostaee, Razieh, 2021. "A new non-radial directional distance model for data envelopment analysis problems with negative and flexible measures," Omega, Elsevier, vol. 102(C).
    12. Aparicio, Juan & Monge, Juan F., 2022. "The generalized range adjusted measure in data envelopment analysis: Properties, computational aspects and duality," European Journal of Operational Research, Elsevier, vol. 302(2), pages 621-632.
    13. Juan Aparicio & Magdalena Kapelko, 2019. "Enhancing the Measurement of Composite Indicators of Corporate Social Performance," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 144(2), pages 807-826, July.

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