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A Mathematical Programming Approach for Measuring Technical Efficiency in a Fuzzy Environment

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  • Konstantinos Triantis
  • Olivier Girod

Abstract

A three stage approach is proposed to measure technical efficiency in a fuzzy environment. This approach uses the traditional data envelopment analysis framework and then merges concepts developed in fuzzy parametric programming (Carlsson and Korhonen, 1986). In the first stage, vague input and output variables are expressed in terms of their risk-free and impossible bounds and a membership function. This membership function represents the degree to which a production scenario is plausible. In the second stage, conventional efficiency measurement models (Banker, Charnes and Cooper, 1984; Deprins, Simar and Tulkens, 1984) are re-formulated in terms of the risk-free and impossible bounds and the membership function for each of the fuzzy input and output variables. In the third stage, technical efficiency scores are computed for different values of the membership function so as to identify uniquely sensitive decision making units. The approach is illustrated in the context of a preprint and packaging manufacturing line which inserts commercial pamphlets into newspapers. Copyright Kluwer Academic Publishers 1998

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  • Konstantinos Triantis & Olivier Girod, 1998. "A Mathematical Programming Approach for Measuring Technical Efficiency in a Fuzzy Environment," Journal of Productivity Analysis, Springer, vol. 10(1), pages 85-102, July.
    • Handle: RePEc:kap:jproda:v:10:y:1998:i:1:p:85-102
    DOI: 10.1023/A:1018350516517
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    References listed on IDEAS

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    1. R. E. Bellman & L. A. Zadeh, 1970. "Decision-Making in a Fuzzy Environment," Management Science, INFORMS, vol. 17(4), pages 141-164, December.
    2. Henry Tulkens, 2006. "On FDH Efficiency Analysis: Some Methodological Issues and Applications to Retail Banking, Courts and Urban Transit," Springer Books, in: Parkash Chander & Jacques Drèze & C. Knox Lovell & Jack Mintz (ed.), Public goods, environmental externalities and fiscal competition, chapter 0, pages 311-342, Springer.
    3. 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.
    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. 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.
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    Cited by:

    1. Qin, Rui & Liu, Yan-Kui, 2010. "Modeling data envelopment analysis by chance method in hybrid uncertain environments," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(5), pages 922-950.
    2. Mugera, Amin W., 2013. "Measuring Technical Efficiency of Dairy Farms with Imprecise Data: A Fuzzy Data Envelopment Analysis Approach," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 57(4), pages 1-19.
    3. Aparicio, Juan & Cordero, Jose M. & Ortiz, Lidia, 2019. "Measuring efficiency in education: The influence of imprecision and variability in data on DEA estimates," Socio-Economic Planning Sciences, Elsevier, vol. 68(C).
    4. Hatami-Marbini, Adel & Emrouznejad, Ali & Tavana, Madjid, 2011. "A taxonomy and review of the fuzzy data envelopment analysis literature: Two decades in the making," European Journal of Operational Research, Elsevier, vol. 214(3), pages 457-472, November.
    5. Jens Leth Hougaard & Pieter Jan Kerstens & Kurt Nielsen, 2019. "Benchmarking with uncertain data: a simulation study comparing alternative methods," IFRO Working Paper 2019/05, University of Copenhagen, Department of Food and Resource Economics.
    6. Waichon Lio & Baoding Liu, 2018. "Uncertain data envelopment analysis with imprecisely observed inputs and outputs," Fuzzy Optimization and Decision Making, Springer, vol. 17(3), pages 357-373, September.
    7. Kao, Chiang, 2006. "Interval efficiency measures in data envelopment analysis with imprecise data," European Journal of Operational Research, Elsevier, vol. 174(2), pages 1087-1099, October.
    8. Konstantinos Triantis & Philippe Eeckaut, 2000. "Fuzzy Pair-wise Dominance and Implications for Technical Efficiency Performance Assessment," Journal of Productivity Analysis, Springer, vol. 13(3), pages 207-230, May.
    9. Stefanos A. Nastis & Thomas Bournaris & Dimitrios Karpouzos, 2019. "Fuzzy data envelopment analysis of organic farms," Operational Research, Springer, vol. 19(2), pages 571-584, June.
    10. Avninder Gill, 2011. "Measurement and Comparison of Productivity Performance Under Fuzzy Imprecise Data," International Journal of Business Research and Management (IJBRM), Computer Science Journals (CSC Journals), vol. 2(1), pages 19-32, April.
    11. Triantis, Konstantinos & Sarangi, Sudipta & Kuchta, Dorota, 2003. "Fuzzy pair-wise dominance and fuzzy indices: An evaluation of productive performance," European Journal of Operational Research, Elsevier, vol. 144(2), pages 412-428, January.
    12. Utsav Pandey & Sanjeet Singh, 2022. "Data envelopment analysis in hierarchical category structure with fuzzy boundaries," Annals of Operations Research, Springer, vol. 315(2), pages 1517-1549, August.
    13. Lampe, Hannes W. & Hilgers, Dennis, 2015. "Trajectories of efficiency measurement: A bibliometric analysis of DEA and SFA," European Journal of Operational Research, Elsevier, vol. 240(1), pages 1-21.
    14. Lee, Chia-Yen & Johnson, Andrew L., 2014. "Proactive data envelopment analysis: Effective production and capacity expansion in stochastic environments," European Journal of Operational Research, Elsevier, vol. 232(3), pages 537-548.
    15. Nafiseh Javaherian & Ali Hamzehee & Hossein Sayyadi Tooranloo, 2021. "A compositional approach to two-stage Data Envelopment Analysis in intuitionistic fuzzy environment," Operations Research and Decisions, Wroclaw University of Science Technology, Faculty of Management, vol. 31, pages 21-39.
    16. Nafiseh Javaherian & Ali Hamzehee & Hossein Sayyadi Tooranloo, 2021. "A compositional approach to two-stage Data Envelopment Analysis in intuitionistic fuzzy environment," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 31(1), pages 21-39.
    17. Ali Asghar Foroughi & Roohollah Abbasi Shureshjani, 2017. "Solving generalized fuzzy data envelopment analysis model: a parametric approach," 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. 25(4), pages 889-905, December.
    18. Adel Hatami-Marbini & Per J. Agrell & Hirofumi Fukuyama & Kobra Gholami & Pegah Khoshnevis, 2017. "The role of multiplier bounds in fuzzy data envelopment analysis," Annals of Operations Research, Springer, vol. 250(1), pages 249-276, March.
    19. Florica LUBAN, 2009. "Measuring efficiency of a hierarchical organization with fuzzy DEA method," Economia. Seria Management, Faculty of Management, Academy of Economic Studies, Bucharest, Romania, vol. 12(1), pages 87-97, June.
    20. Ali Ebrahimnejad & Madjid Tavana & Seyed Hadi Nasseri & Omid Gholami, 2019. "A New Method for Solving Dual DEA Problems with Fuzzy Stochastic Data," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 18(01), pages 147-170, January.
    21. Adel Hatami-Marbini & Zahra Ghelej Beigi & Jens Leth Hougaard & Kobra Gholami, 2014. "Estimating Returns to Scale in Imprecise Data Envelopment Analysis," MSAP Working Paper Series 07_2014, University of Copenhagen, Department of Food and Resource Economics.
    22. Lovell, Knox, 2001. "Future Research Opportunities in Efficiency and Productivity Analysis," Efficiency Series Papers 2001/01, University of Oviedo, Department of Economics, Oviedo Efficiency Group (OEG).

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