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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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    1. Cherchye, Laurens & Van Puyenbroeck, Tom, 2001. "Product mixes as objects of choice in non-parametric efficiency measurement," European Journal of Operational Research, Elsevier, vol. 132(2), pages 287-295, July.
    2. Briec, W., 2000. "An extended Fare-Lovell technical efficiency measure," International Journal of Production Economics, Elsevier, vol. 65(2), pages 191-199, April.
    3. Ray,Subhash C., 2012. "Data Envelopment Analysis," Cambridge Books, Cambridge University Press, number 9781107405264.
    4. 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.
    5. Frances Frei & Patrick Harker, 1999. "Projections Onto Efficient Frontiers: Theoretical and Computational Extensions to DEA," Journal of Productivity Analysis, Springer, vol. 11(3), pages 275-300, June.
    6. Seiford, Lawrence M. & Thrall, Robert M., 1990. "Recent developments in DEA : The mathematical programming approach to frontier analysis," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 7-38.
    7. Fukuyama, Hirofumi & Weber, William L., 2009. "A directional slacks-based measure of technical inefficiency," Socio-Economic Planning Sciences, Elsevier, vol. 43(4), pages 274-287, December.
    8. Walter Briec & Kristiaan Kerstens & Hervé Leleu & Philippe Eeckaut, 2000. "Returns to Scale on Nonparametric Deterministic Technologies: Simplifying Goodness-of-Fit Methods Using Operations on Technologies," Journal of Productivity Analysis, Springer, vol. 14(3), pages 267-274, November.
    9. R. Robert Russell & William Schworm, 2009. "Axiomatic Foundations of Inefficiency Measurement on Space," Discussion Papers 2009-07, School of Economics, The University of New South Wales.
    10. Juan Aparicio & José Ruiz & Inmaculada Sirvent, 2007. "Closest targets and minimum distance to the Pareto-efficient frontier in DEA," Journal of Productivity Analysis, Springer, vol. 28(3), pages 209-218, December.
    11. Pastor, J. T. & Ruiz, J. L. & Sirvent, I., 1999. "An enhanced DEA Russell graph efficiency measure," European Journal of Operational Research, Elsevier, vol. 115(3), pages 596-607, June.
    12. R. G. Chambers & Y. Chung & R. Färe, 1998. "Profit, Directional Distance Functions, and Nerlovian Efficiency," Journal of Optimization Theory and Applications, Springer, vol. 98(2), pages 351-364, August.
    13. Gonzalez, Eduardo & Alvarez, Antonio, 2001. "From efficiency measurement to efficiency improvement: The choice of a relevant benchmark," European Journal of Operational Research, Elsevier, vol. 133(3), pages 512-520, September.
    14. 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.
    15. Tone, Kaoru, 2001. "A slacks-based measure of efficiency in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 130(3), pages 498-509, May.
    16. Tone, Kaoru & Tsutsui, Miki, 2009. "Network DEA: A slacks-based measure approach," European Journal of Operational Research, Elsevier, vol. 197(1), pages 243-252, August.
    17. William Cooper & Kyung Park & Jesus Pastor, 1999. "RAM: A Range Adjusted Measure of Inefficiency for Use with Additive Models, and Relations to Other Models and Measures in DEA," Journal of Productivity Analysis, Springer, vol. 11(1), pages 5-42, February.
    18. Fukuyama, Hirofumi & Sekitani, Kazuyuki, 2012. "Decomposing the efficient frontier of the DEA production possibility set into a smallest number of convex polyhedrons by mixed integer programming," European Journal of Operational Research, Elsevier, vol. 221(1), pages 165-174.
    19. tone, Kaoru, 2010. "Variations on the theme of slacks-based measure of efficiency in DEA," European Journal of Operational Research, Elsevier, vol. 200(3), pages 901-907, February.
    20. Tone, Kaoru & Tsutsui, Miki, 2010. "Dynamic DEA: A slacks-based measure approach," Omega, Elsevier, vol. 38(3-4), pages 145-156, June.
    21. Sueyoshi, Toshiyuki & Sekitani, Kazuyuki, 2009. "An occurrence of multiple projections in DEA-based measurement of technical efficiency: Theoretical comparison among DEA models from desirable properties," European Journal of Operational Research, Elsevier, vol. 196(2), pages 764-794, July.
    22. Fare, Rolf & Grosskopf, Shawna & Noh, Dong-Woon & Weber, William, 2005. "Characteristics of a polluting technology: theory and practice," Journal of Econometrics, Elsevier, vol. 126(2), pages 469-492, June.
    23. William W. Cooper & Lawrence M. Seiford & Kaoru Tone, 2007. "Data Envelopment Analysis," Springer Books, Springer, edition 0, number 978-0-387-45283-8, December.
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    Cited by:

    1. 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.
    2. 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.
    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. Ruiz, José L. & Sirvent, Inmaculada, 2016. "Common benchmarking and ranking of units with DEA," Omega, Elsevier, vol. 65(C), pages 1-9.
    5. 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.
    6. Färe, Rolf & Fukuyama, Hirofumi & Grosskopf, Shawna & Zelenyuk, Valentin, 2016. "Cost decompositions and the efficient subset," Omega, Elsevier, vol. 62(C), pages 123-130.
    7. Lozano, Sebastián & Khezri, Somayeh, 2021. "Network DEA smallest improvement approach," Omega, Elsevier, vol. 98(C).
    8. 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.
    9. 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.
    10. Shogo Eguchi & Hirotaka Takayabu & Mitsuki Kaneko & Shigemi Kagawa & Shunichi Hienuki, 2021. "Proposing effective strategies for meeting an environmental regulation with attainable technology improvement targets," Business Strategy and the Environment, Wiley Blackwell, vol. 30(7), pages 2907-2921, November.
    11. Juan Aparicio & Magdalena Kapelko & Bernhard Mahlberg & Jose L. Sainz-Pardo, 2017. "Measuring input-specific productivity change based on the principle of least action," Journal of Productivity Analysis, Springer, vol. 47(1), pages 17-31, February.
    12. 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.
    13. 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.
    14. Ruiz, José L. & Sirvent, Inmaculada, 2019. "Performance evaluation through DEA benchmarking adjusted to goals," Omega, Elsevier, vol. 87(C), pages 150-157.
    15. Kaoru Tone, 2015. "SBM variations revisited," GRIPS Discussion Papers 15-05, National Graduate Institute for Policy Studies.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. 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.
    21. 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.
    22. 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.

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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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