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Distance optimization approach to ratio-form efficiency measures in data envelopment analysis

Author

Listed:
  • Hirofumi Fukuyama
  • Hiroya Masaki
  • Kazuyuki Sekitani
  • Jianming Shi

Abstract

The standard data envelopment analysis measures of the Charnes–Cooper–Rhodes (CCR) and slacks-based measure (SBM) are ratio-form efficiency measures, which do not yield the closest projections. However, because of difficulties implementing projections based on standard measures, the closest projections identified by means of least-distance measures may be preferable. Taking into account the practical significance of closest projection points, Aparicio et al. (J Prod Anal 28:209–218, 2007 ) proposed a least-distance approach based not only on the 1-norm (Manhattan), 2-norm (Euclidean), and ∞-norm (Chebyshev), but also on the procedure presented by Cherchye and Van Puyenbroeck (Eur J Oper Res 132(2):287–295, 2001 ). Recently, Tone (Eur J Oper Res 200(2):901–907, 2010 ) presented a least-distance version of SBM (or equivalently, the enhanced Russell graph measure). However, these authors examined neither the occurrence of multiple optimal projections nor the strong/weak monotonicity of the ratio-form least-distance efficiency measures over the efficient frontier of the production technology. Furthermore, it is not well known that the standard measures of CCR and SBM suffer from the occurrence of multiple optimal solutions or efficient targets. Therefore, the present paper also investigates the possibility of multiple optimal targets and axiomatic properties of ratio-form efficiency measures within a unified p-norm efficiency measurement framework. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Hirofumi Fukuyama & Hiroya Masaki & Kazuyuki Sekitani & Jianming Shi, 2014. "Distance optimization approach to ratio-form efficiency measures in data envelopment analysis," Journal of Productivity Analysis, Springer, vol. 42(2), pages 175-186, October.
    • Handle: RePEc:kap:jproda:v:42:y:2014:i:2:p:175-186
    DOI: 10.1007/s11123-013-0366-7
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    References listed on IDEAS

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    3. Juan Aparicio & Jesus T. Pastor & Jose L. Sainz-Pardo & Fernando Vidal, 2020. "Estimating and decomposing overall inefficiency by determining the least distance to the strongly efficient frontier in data envelopment analysis," Operational Research, Springer, vol. 20(2), pages 747-770, June.
    4. Aparicio, Juan & Cordero, Jose M. & Pastor, Jesus T., 2017. "The determination of the least distance to the strongly efficient frontier in Data Envelopment Analysis oriented models: Modelling and computational aspects," Omega, Elsevier, vol. 71(C), pages 1-10.
    5. Arabi, Behrouz & Munisamy, Susila & Emrouznejad, Ali & Toloo, Mehdi & Ghazizadeh, Mohammad Sadegh, 2016. "Eco-efficiency considering the issue of heterogeneity among power plants," Energy, Elsevier, vol. 111(C), pages 722-735.
    6. Cook, Wade D. & Ruiz, José L. & Sirvent, Inmaculada & Zhu, Joe, 2017. "Within-group common benchmarking using DEA," European Journal of Operational Research, Elsevier, vol. 256(3), pages 901-910.
    7. 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.
    8. Färe, Rolf & Fukuyama, Hirofumi & Grosskopf, Shawna & Zelenyuk, Valentin, 2016. "Cost decompositions and the efficient subset," Omega, Elsevier, vol. 62(C), pages 123-130.
    9. Ruiz, José L. & Sirvent, Inmaculada, 2016. "Common benchmarking and ranking of units with DEA," Omega, Elsevier, vol. 65(C), pages 1-9.
    10. Fukuyama, Hirofumi & Matousek, Roman & Tzeremes, Nickolaos G., 2023. "Estimating the degree of firms’ input market power via data envelopment analysis: Evidence from the global biotechnology and pharmaceutical industry," European Journal of Operational Research, Elsevier, vol. 305(2), pages 946-960.
    11. Ruiz, José L. & Sirvent, Inmaculada, 2019. "Performance evaluation through DEA benchmarking adjusted to goals," Omega, Elsevier, vol. 87(C), pages 150-157.
    12. Kaoru Tone, 2015. "SBM variations revisited," GRIPS Discussion Papers 15-05, National Graduate Institute for Policy Studies.
    13. Mette Asmild & Tomas Baležentis & Jens Leth Hougaard, 2016. "Multi-directional productivity change: MEA-Malmquist," Journal of Productivity Analysis, Springer, vol. 46(2), pages 109-119, December.
    14. Sekitani, Kazuyuki & Zhao, Yu, 2023. "Least-distance approach for efficiency analysis: A framework for nonlinear DEA models," European Journal of Operational Research, Elsevier, vol. 306(3), pages 1296-1310.
    15. Lozano, Sebastián & Khezri, Somayeh, 2021. "Network DEA smallest improvement approach," Omega, Elsevier, vol. 98(C).
    16. Vicente J. Bolós & Rafael Benítez & Vicente Coll-Serrano, 2023. "Continuous models combining slacks-based measures of efficiency and super-efficiency," 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. 31(2), pages 363-391, June.
    17. Kaoru Tone, 2016. "On the Consistency of Slacks-based Measure-Max Model and Super-Slacks-based Measure Model," GRIPS Discussion Papers 16-24, National Graduate Institute for Policy Studies.
    18. Aparicio, Juan & Cordero, Jose M. & Gonzalez, Martin & Lopez-Espin, Jose J., 2018. "Using non-radial DEA to assess school efficiency in a cross-country perspective: An empirical analysis of OECD countries," Omega, Elsevier, vol. 79(C), pages 9-20.
    19. Kao, Chiang, 2022. "Closest targets in the slacks-based measure of efficiency for production units with multi-period data," European Journal of Operational Research, Elsevier, vol. 297(3), pages 1042-1054.
    20. Ando, Kazutoshi & Minamide, Masato & Sekitani, Kazuyuki & Shi, Jianming, 2017. "Monotonicity of minimum distance inefficiency measures for Data Envelopment Analysis," European Journal of Operational Research, Elsevier, vol. 260(1), pages 232-243.
    21. Fangqing Wei & Junfei Chu & Jiayun Song & Feng Yang, 2019. "A cross-bargaining game approach for direction selection in the directional distance function," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 41(3), pages 787-807, September.
    22. Javad Vakili & Hanieh Amirmoshiri & Rashed Khanjani Shiraz & Hirofumi Fukuyama, 2020. "A modified distance friction minimization approach in data envelopment analysis," Annals of Operations Research, Springer, vol. 288(2), pages 789-804, May.

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    More about this item

    Keywords

    Data envelopment analysis (DEA); Least distance; Non-minimum distance; Ratio-form efficiency measure; p-Norm; C43; C61; D21; D24;
    All these keywords.

    JEL classification:

    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

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