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Closest targets and strong monotonicity on the strongly efficient frontier in DEA

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  • Aparicio, Juan
  • Pastor, Jesus T.

Abstract

The determination of closest efficient targets has attracted increasing interest of researchers in recent Data Envelopment Analysis (DEA) literature. Several methods have been introduced in this respect. However, only a few attempts exist that analyze the implications of using closest targets on the technical inefficiency measurement. In particular, least distance measures based on Hölder norms satisfy neither weak nor strong monotonicity on the strongly efficient frontier. In this paper, we study Hölder distance functions and show why strong monotonicity fails. Along this line, we provide a solution for output-oriented models that allows assuring strong monotonicity on the strongly efficient frontier. Our approach may also be extended to the most general case, i.e. non-oriented models, under some conditions of regularity.

Suggested Citation

  • Aparicio, Juan & Pastor, Jesus T., 2014. "Closest targets and strong monotonicity on the strongly efficient frontier in DEA," Omega, Elsevier, vol. 44(C), pages 51-57.
  • Handle: RePEc:eee:jomega:v:44:y:2014:i:c:p:51-57
    DOI: 10.1016/j.omega.2013.10.001
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    References listed on IDEAS

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    1. Maria Silva Portela & Pedro Borges & Emmanuel Thanassoulis, 2003. "Finding Closest Targets in Non-Oriented DEA Models: The Case of Convex and Non-Convex Technologies," Journal of Productivity Analysis, Springer, vol. 19(2), pages 251-269, April.
    2. Jahanshahloo, G.R. & Hosseinzadeh Lotfi, F. & Zhiani Rezai, H. & Rezai Balf, F., 2007. "Finding strong defining hyperplanes of Production Possibility Set," European Journal of Operational Research, Elsevier, vol. 177(1), pages 42-54, February.
    3. Walter Briec & Hervé Leleu, 2003. "Dual Representations of Non-Parametric Technologies and Measurement of Technical Efficiency," Journal of Productivity Analysis, Springer, vol. 20(1), pages 71-96, July.
    4. O. B. Olesen & N. C. Petersen, 1996. "Indicators of Ill-Conditioned Data Sets and Model Misspecification in Data Envelopment Analysis: An Extended Facet Approach," Management Science, INFORMS, vol. 42(2), pages 205-219, February.
    5. Takeda, Akiko & Nishino, Hisakazu, 2001. "On measuring the inefficiency with the inner-product norm in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 133(2), pages 377-393, January.
    6. 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.
    7. Chen, Yao & Morita, Hiroshi & Zhu, Joe, 2003. "Multiplier bounds in DEA via strong complementary slackness condition solution," International Journal of Production Economics, Elsevier, vol. 86(1), pages 11-19, October.
    8. Cook, Wade D. & Seiford, Larry M., 2009. "Data envelopment analysis (DEA) - Thirty years on," European Journal of Operational Research, Elsevier, vol. 192(1), pages 1-17, January.
    9. 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.
    10. Liu, John S. & Lu, Louis Y.Y. & Lu, Wen-Min & Lin, Bruce J.Y., 2013. "Data envelopment analysis 1978–2010: A citation-based literature survey," Omega, Elsevier, vol. 41(1), pages 3-15.
    11. Liu, John S. & Lu, Louis Y.Y. & Lu, Wen-Min & Lin, Bruce J.Y., 2013. "A survey of DEA applications," Omega, Elsevier, vol. 41(5), pages 893-902.
    12. Kleine, A., 2004. "A general model framework for DEA," Omega, Elsevier, vol. 32(1), pages 17-23, February.
    13. Lim, Sungmook & Zhu, Joe, 2013. "Incorporating performance measures with target levels in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 230(3), pages 634-642.
    14. 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.
    15. Green, Rodney H. & Doyle, John R. & Cook, Wade D., 1996. "Efficiency bounds in Data Envelopment Analysis," European Journal of Operational Research, Elsevier, vol. 89(3), pages 482-490, March.
    16. Ole Olesen & N. Petersen, 2003. "Identification and Use of Efficient Faces and Facets in DEA," Journal of Productivity Analysis, Springer, vol. 20(3), pages 323-360, November.
    17. Briec, W. & Lemaire, B., 1999. "Technical efficiency and distance to a reverse convex set," European Journal of Operational Research, Elsevier, vol. 114(1), pages 178-187, April.
    18. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
    19. 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.
    20. 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.
    21. Tarmo Räty, 2002. "Efficient Facet Based Efficiency Index: A Variable Returns to Scale Specification," Journal of Productivity Analysis, Springer, vol. 17(1), pages 65-82, January.
    22. Hinojosa, M.A. & Mármol, A.M., 2011. "Axial solutions for multiple objective linear problems. An application to target setting in DEA models with preferences," Omega, Elsevier, vol. 39(2), pages 159-167, April.
    23. 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.
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    Cited by:

    1. Gawiejnowicz, Stanisław & Kurc, Wiesław, 2015. "Structural properties of time-dependent scheduling problems with the lp norm objective," Omega, Elsevier, vol. 57(PB), pages 196-202.
    2. 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.
    3. 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.
    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. Aparicio, Juan & Pastor, Jesús T. & Vidal, Fernando & Zofío, José L., 2017. "Evaluating productive performance: A new approach based on the product-mix problem consistent with Data Envelopment Analysis," Omega, Elsevier, vol. 67(C), pages 134-144.
    6. Juan Aparicio & Magdalena Kapelko & Juan F. Monge, 2020. "A Well-Defined Composite Indicator: An Application to Corporate Social Responsibility," Journal of Optimization Theory and Applications, Springer, vol. 186(1), pages 299-323, July.
    7. Atwood, Joseph & Shaik, Saleem, 2020. "Theory and statistical properties of Quantile Data Envelopment Analysis," European Journal of Operational Research, Elsevier, vol. 286(2), pages 649-661.
    8. Tone, Kaoru & Chang, Tsung-Sheng & Wu, Chen-Hui, 2020. "Handling negative data in slacks-based measure data envelopment analysis models," European Journal of Operational Research, Elsevier, vol. 282(3), pages 926-935.
    9. 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.
    10. Aparicio, Juan & Pastor, Jesus T. & Vidal, Fernando, 2016. "The directional distance function and the translation invariance property," Omega, Elsevier, vol. 58(C), pages 1-3.
    11. Lozano, S. & Hinojosa, M.A. & Mármol, A.M., 2015. "Set-valued DEA production games," Omega, Elsevier, vol. 52(C), pages 92-100.
    12. 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.
    13. Ruiz, José L. & Sirvent, Inmaculada, 2016. "Common benchmarking and ranking of units with DEA," Omega, Elsevier, vol. 65(C), pages 1-9.
    14. Léopold Simar & Valentin Zelenyuk, 2018. "Improving Finite Sample Approximation by Central Limit Theorems for DEA and FDH efficiency scores," CEPA Working Papers Series WP072018, School of Economics, University of Queensland, Australia.
    15. Ruiz, José L. & Sirvent, Inmaculada, 2019. "Performance evaluation through DEA benchmarking adjusted to goals," Omega, Elsevier, vol. 87(C), pages 150-157.
    16. Xiaohong Liu & Qingyuan Zhu & Junfei Chu & Xiang Ji & Xingchen Li, 2019. "Environmental Performance and Benchmarking Information for Coal-Fired Power Plants in China: A DEA Approach," Computational Economics, Springer;Society for Computational Economics, vol. 54(4), pages 1287-1302, December.
    17. Lozano, Sebastián & Khezri, Somayeh, 2021. "Network DEA smallest improvement approach," Omega, Elsevier, vol. 98(C).
    18. Lozano, Sebastián & Calzada-Infante, Laura, 2018. "Computing gradient-based stepwise benchmarking paths," Omega, Elsevier, vol. 81(C), pages 195-207.
    19. 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.
    20. Zhu, Qingyuan & Wu, Jie & Ji, Xiang & Li, Feng, 2018. "A simple MILP to determine closest targets in non-oriented DEA model satisfying strong monotonicity," Omega, Elsevier, vol. 79(C), pages 1-8.
    21. J. Vakili, 2017. "New Models for Computing the Distance of DMUs to the Weak Efficient Boundary of Convex and Nonconvex PPSs in DEA," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(06), pages 1-20, December.
    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.
    23. Jie Wu & Jun-Fei Chu & Liang Liang, 2016. "Target setting and allocation of carbon emissions abatement based on DEA and closest target: an application to 20 APEC economies," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 84(1), pages 279-296, November.

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