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Families of linear efficiency programs based on Debreu’s loss function

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  • Jesus Pastor
  • C. Lovell
  • Juan Aparicio

Abstract

Gerard Debreu introduced a well known radial efficiency measure which he called a “coefficient of resource utilization.” He derived this scalar from a much less well known “dead loss” function that characterizes the monetary value sacrificed to inefficiency, and which is to be minimized subject to a normalization condition. We use Debreu’s loss function, together with a variety of normalization conditions, to generate several popular families of linear efficiency programs. Our methodology also can be employed to generate entirely new families of linear efficiency programs. Copyright Springer Science+Business Media, LLC 2012

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  • Jesus Pastor & C. Lovell & Juan Aparicio, 2012. "Families of linear efficiency programs based on Debreu’s loss function," Journal of Productivity Analysis, Springer, vol. 38(2), pages 109-120, October.
    • Handle: RePEc:kap:jproda:v:38:y:2012:i:2:p:109-120
    DOI: 10.1007/s11123-011-0216-4
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    18. Subhash Ray, 2007. "Shadow profit maximization and a measure of overall inefficiency," Journal of Productivity Analysis, Springer, vol. 27(3), pages 231-236, June.
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    Cited by:

    1. William Cooper & Jesús Pastor & Fernando Borras & Juan Aparicio & Diego Pastor, 2011. "BAM: a bounded adjusted measure of efficiency for use with bounded additive models," Journal of Productivity Analysis, Springer, vol. 35(2), pages 85-94, April.
    2. Aparicio, Juan & Garcia-Nove, Eva M. & Kapelko, Magdalena & Pastor, Jesus T., 2017. "Graph productivity change measure using the least distance to the pareto-efficient frontier in data envelopment analysis," Omega, Elsevier, vol. 72(C), pages 1-14.
    3. Zhongqi Deng & Qianyu Zhao & Helen X. H. Bao, 2020. "The Impact of Urbanization on Farmland Productivity: Implications for China’s Requisition–Compensation Balance of Farmland Policy," Land, MDPI, vol. 9(9), pages 1-24, September.
    4. Pastor, Jesús T. & Zofío, José L. & Aparicio, Juan & Alcaraz, Javier, 2024. "The flexible reverse approach for decomposing economic inefficiency: With an application to Taiwanese banks," Economic Modelling, Elsevier, vol. 139(C).
    5. 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.
    6. Chambers, Robert G., 2024. "Numeraire choice, shadow profit, and inefficiency measurement," European Journal of Operational Research, Elsevier, vol. 319(2), pages 658-668.
    7. Alcaraz, Javier & Anton-Sanchez, Laura & Aparicio, Juan & Monge, Juan F. & Ramón, Nuria, 2021. "Russell Graph efficiency measures in Data Envelopment Analysis: The multiplicative approach," European Journal of Operational Research, Elsevier, vol. 292(2), pages 663-674.
    8. Zofio, Jose Luis & Aparicio, Juan & Barbero, Javier & Zabala-Iturriagagoitia, Jon Mikel, 2024. "Benchmarking performance through efficiency analysis trees: Improvement strategies for colombian higher education institutions," Socio-Economic Planning Sciences, Elsevier, vol. 92(C).
    9. Zhu, Qingyuan & Aparicio, Juan & Li, Feng & Wu, Jie & Kou, Gang, 2022. "Determining closest targets on the extended facet production possibility set in data envelopment analysis: Modeling and computational aspects," European Journal of Operational Research, Elsevier, vol. 296(3), pages 927-939.
    10. Díaz-Hernández, Juan José & Cova-Alonso, David-José & Martínez-Budría, Eduardo, 2025. "Measuring technical efficiency under variable returns to scale using Debreu's loss function," European Journal of Operational Research, Elsevier, vol. 323(3), pages 975-987.
    11. Juan Aparicio & José L. Zofío & Jesús T. Pastor, 2023. "Decomposing Economic Efficiency into Technical and Allocative Components: An Essential Property," Journal of Optimization Theory and Applications, Springer, vol. 197(1), pages 98-129, April.
    12. Raul Moragues & Juan Aparicio & Miriam Esteve, 2023. "Measuring technical efficiency for multi-input multi-output production processes through OneClass Support Vector Machines: a finite-sample study," Operational Research, Springer, vol. 23(3), pages 1-33, September.
    13. Moragues, Raul & Aparicio, Juan & Esteve, Miriam, 2023. "An unsupervised learning-based generalization of Data Envelopment Analysis," Operations Research Perspectives, Elsevier, vol. 11(C).
    14. Halická, Margaréta & Trnovská, Mária, 2021. "A unified approach to non-radial graph models in data envelopment analysis: common features, geometry, and duality," European Journal of Operational Research, Elsevier, vol. 289(2), pages 611-627.
    15. Halická, Margaréta & Trnovská, Mária, 2019. "Duality and profit efficiency for the hyperbolic measure model," European Journal of Operational Research, Elsevier, vol. 278(2), pages 410-421.
    16. Aparicio, Juan & Ortiz, Lidia & Pastor, Jesus T., 2017. "Measuring and decomposing profit inefficiency through the Slacks-Based Measure," European Journal of Operational Research, Elsevier, vol. 260(2), pages 650-654.
    17. Raphaël Fèvre & Thomas Michael Mueller, 2023. "Toward a “Prodigious Revival of French Economics”? Allais, Debreu, and the Dead Loss Controversy (1943–51)," Post-Print hal-04119618, HAL.
    18. Wen, Yao & An, Qingxian & Gong, Yeming & Wu, Pengkun, 2024. "Structural rearrangement of the network system from an efficiency perspective: A silver lining of profit improvement," European Journal of Operational Research, Elsevier, vol. 316(3), pages 1001-1011.
    19. Halická, Margaréta & Trnovská, Mária, 2018. "The Russell measure model: Computational aspects, duality, and profit efficiency," European Journal of Operational Research, Elsevier, vol. 268(1), pages 386-397.
    20. Rafael Benítez & Vicente Coll-Serrano & Vicente J. Bolós, 2021. "deaR-Shiny: An Interactive Web App for Data Envelopment Analysis," Sustainability, MDPI, vol. 13(12), pages 1-19, June.
    21. 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.
    22. Deng, Zhongqi & Song, Shunfeng & Jiang, Nan & Pang, Ruizhi, 2023. "Sustainable development in China? A nonparametric decomposition of economic growth," China Economic Review, Elsevier, vol. 81(C).

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    More about this item

    Keywords

    Loss function; Linear efficiency programs; DEA; C51; C61;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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