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Modeling CRS bounded additive DEA models and characterizing their Pareto-efficient points

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  • Jesus Pastor
  • Juan Aparicio
  • Juan Monge
  • Diego Pastor

Abstract

Dealing with weighted additive models in Data Envelopment Analysis guarantees that any projection of an inefficient unit belongs to the strong efficient frontier, among other interesting properties. Recently, constant returns to scale (CRS) range-bounded models have been introduced for defining a new additive-type efficiency measure (see Cooper et al. in J Prod Anal 35(2):85–94, 2011 ). This paper continues such earlier work further, considering a more general setting. In particular, we show that under free disposability of inputs and outputs, CRS bounded additive models require a double set of slacks. The second set of slacks allows us to properly characterize all the Pareto-efficient points associated to the bounded technology. We further introduce the CRS partially-bounded additive models. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Jesus Pastor & Juan Aparicio & Juan Monge & Diego Pastor, 2013. "Modeling CRS bounded additive DEA models and characterizing their Pareto-efficient points," Journal of Productivity Analysis, Springer, vol. 40(3), pages 285-292, December.
    • Handle: RePEc:kap:jproda:v:40:y:2013:i:3:p:285-292
    DOI: 10.1007/s11123-012-0324-9
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    References listed on IDEAS

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    1. Ray,Subhash C., 2012. "Data Envelopment Analysis," Cambridge Books, Cambridge University Press, number 9781107405264.
    2. Fried, Harold O. & Lovell, C. A. Knox & Schmidt, Shelton S. (ed.), 1993. "The Measurement of Productive Efficiency: Techniques and Applications," OUP Catalogue, Oxford University Press, number 9780195072181.
    3. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    4. 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.
    5. R. D. Banker & A. Charnes & W. W. Cooper, 1984. "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, INFORMS, vol. 30(9), pages 1078-1092, September.
    6. B. Hollingsworth & P. Smith, 2003. "Use of ratios in data envelopment analysis," Applied Economics Letters, Taylor & Francis Journals, vol. 10(11), pages 733-735.
    7. Charnes, A. & Cooper, W. W. & Golany, B. & Seiford, L. & Stutz, J., 1985. "Foundations of data envelopment analysis for Pareto-Koopmans efficient empirical production functions," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 91-107.
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    Citations

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    Cited by:

    1. Pastor, Jesus T. & Aparicio, Juan & Alcaraz, Javier & Vidal, Fernando & Pastor, Diego, 2015. "An enhanced BAM for unbounded or partially bounded CRS additive models," Omega, Elsevier, vol. 56(C), pages 16-24.
    2. Papaioannou, Grammatoula & Podinovski, Victor V., 2023. "Production technologies with ratio inputs and outputs," European Journal of Operational Research, Elsevier, vol. 310(3), pages 1164-1178.
    3. Jesus T. Pastor & Juan Aparicio & Javier Alcaraz & Fernando Vidal & Diego Pastor, 2018. "Bounded directional distance function models," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 26(4), pages 985-1004, December.
    4. Miao, Zhuang & Chen, Xiaodong & Baležentis, Tomas, 2021. "Improving energy use and mitigating pollutant emissions across “Three Regions and Ten Urban Agglomerations”: A city-level productivity growth decomposition," Applied Energy, Elsevier, vol. 283(C).
    5. Ole Bent Olesen & Niels Christian Petersen & Victor V. Podinovski, 2022. "Scale characteristics of variable returns-to-scale production technologies with ratio inputs and outputs," Annals of Operations Research, Springer, vol. 318(1), pages 383-423, November.
    6. Juan Du & Jiazhen Huo & Joe Zhu, 2016. "Data Envelopment Analysis with Output-Bounded Data," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(06), pages 1-17, December.
    7. Le, Minh Hanh & Afsharian, Mohsen & Ahn, Heinz, 2021. "Inverse Frontier-based Benchmarking for Investigating the Efficiency and Achieving the Targets in the Vietnamese Education System," Omega, Elsevier, vol. 103(C).

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    More about this item

    Keywords

    Data envelopment analysis; Additive models; Bounded technology; 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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