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Continuity of DEA Efficiency Measures

Author

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  • Holger Scheel

    (Universität Dortmund, Operations Research und Wirtschaftsinformatik, D-44221 Dortmund, Germany)

  • Stefan Scholtes

    (University of Cambridge, Judge Institute of Management, Cambridge CB2 1AG, England)

Abstract

Data envelopment analysis (DEA) is a methodology that allows, in one way or other, the assignment of efficiency scores to members of a group of decision-making units. We call an efficiency measure “continuous” if small perturbations of the input-output data cause only small changes in the score. Continuity is a desirable property of an efficiency measure, in particular in the presence of measurement tolerances. Continuity is also desirable from a numerical point of view because the scores are computed by linear programming software.Focusing on convex production possibility sets, we give examples where radial DEA measures fail to be continuous, i.e., they “jump” under small data perturbations. We present necessary and sufficient conditions for continuity in terms of the data and show that these conditions are satisfied for “almost all” data. We also discuss continuity of nonradial measures and identify possible problems of “multistage approaches” to compute mix efficiencies.

Suggested Citation

  • Holger Scheel & Stefan Scholtes, 2003. "Continuity of DEA Efficiency Measures," Operations Research, INFORMS, vol. 51(1), pages 149-159, February.
    • Handle: RePEc:inm:oropre:v:51:y:2003:i:1:p:149-159
    DOI: 10.1287/opre.51.1.149.12803
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    References listed on IDEAS

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    2. Lamb, John D. & Tee, Kai-Hong, 2012. "Data envelopment analysis models of investment funds," European Journal of Operational Research, Elsevier, vol. 216(3), pages 687-696.
    3. Lamb, John D. & Tee, Kai-Hong, 2012. "Resampling DEA estimates of investment fund performance," European Journal of Operational Research, Elsevier, vol. 223(3), pages 834-841.
    4. Podinovski, Victor V. & Bouzdine-Chameeva, Tatiana, 2017. "Solving DEA models in a single optimization stage: Can the non-Archimedean infinitesimal be replaced by a small finite epsilon?," European Journal of Operational Research, Elsevier, vol. 257(2), pages 412-419.
    5. Timo Kuosmanen, 2007. "Performance measurement and best-practice benchmarking of mutual funds: combining stochastic dominance criteria with data envelopment analysis," Journal of Productivity Analysis, Springer, vol. 28(1), pages 71-86, October.
    6. Cooper, W.W. & Huang, Zhimin & Li, Susan X. & Parker, Barnett R. & Pastor, Jesus T., 2007. "Efficiency aggregation with enhanced Russell measures in data envelopment analysis," Socio-Economic Planning Sciences, Elsevier, vol. 41(1), pages 1-21, March.
    7. Chong Wu & Jiahua Gan & Zhuo Jiang & Anding Jiang & Wenlong Zheng, 2022. "Ecological Efficiency Evaluation, Spatial Difference, and Trend Analysis of Logistics Industry and Manufacturing Industry Linkage in the Northeast Old Industrial Base," Sustainability, MDPI, vol. 14(19), pages 1-20, October.
    8. Chien-Ming Chen, 2014. "Evaluating eco-efficiency with data envelopment analysis: an analytical reexamination," Annals of Operations Research, Springer, vol. 214(1), pages 49-71, March.
    9. Chen, Chien-Ming & van Dalen, Jan, 2010. "Measuring dynamic efficiency: Theories and an integrated methodology," European Journal of Operational Research, Elsevier, vol. 203(3), pages 749-760, June.
    10. 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.
    11. Delimiro Visbal-Cadavid & Mónica Martínez-Gómez & Francisco Guijarro, 2017. "Assessing the Efficiency of Public Universities through DEA. A Case Study," Sustainability, MDPI, vol. 9(8), pages 1-19, August.
    12. Sueyoshi, Toshiyuki & Shang, Jennifer & Chiang, Wen-Chyuan, 2009. "A decision support framework for internal audit prioritization in a rental car company: A combined use between DEA and AHP," European Journal of Operational Research, Elsevier, vol. 199(1), pages 219-231, November.

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