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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

Suggested Citation

  • 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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    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    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. 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.
    14. 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.
    15. 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).
    16. 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.

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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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