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Efficiency bounds and efficiency classifications in DEA with imprecise data

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  • K S Park

    (Korea University, Business School)

Abstract

This paper is concerned with the use of imprecise data in data envelopment analysis (DEA). Imprecise data means that some data are known only to the extent that the true values lie within prescribed bounds while other data are known only in terms of ordinal relations. Imprecise data envelopment analysis (IDEA) has been developed to measure the relative efficiency of decision-making units (DMUs) whose input and/or output data are imprecise. In this paper, we show two distinct strategies to arrive at an upper and lower bound of efficiency that the evaluated DMU can have within the given imprecise data. The optimistic strategy pursues the best score among various possible scores of efficiency and the conservative strategy seeks the worst score. In doing so, we do not limit our attention to the treatment of special forms of imprecise data only, as done in some of the studies associated with IDEA. We target how to deal with imprecise data in a more general form and, under this circumstance, we make it possible to grasp an upper and lower bound of efficiency. The generalized method we develop in this paper also gives rise to a new scheme of efficiency classifications that is more detailed and informative than the standard efficient and inefficient partition.

Suggested Citation

  • K S Park, 2007. "Efficiency bounds and efficiency classifications in DEA with imprecise data," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(4), pages 533-540, April.
    • Handle: RePEc:pal:jorsoc:v:58:y:2007:i:4:d:10.1057_palgrave.jors.2602178
    DOI: 10.1057/palgrave.jors.2602178
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    References listed on IDEAS

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    1. K S Park, 2004. "Simplification of the transformations and redundancy of assurance regions in IDEA (imprecise DEA)," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(12), pages 1363-1366, December.
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    3. W W Cooper & K S Park & G Yu, 2001. "IDEA (Imprecise Data Envelopment Analysis) with CMDs (Column Maximum Decision Making Units)," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 52(2), pages 176-181, February.
    4. Joe Zhu, 2004. "Imprecise DEA via Standard Linear DEA Models with a Revisit to a Korean Mobile Telecommunication Company," Operations Research, INFORMS, vol. 52(2), pages 323-329, April.
    5. Zhu, Joe, 2003. "Imprecise data envelopment analysis (IDEA): A review and improvement with an application," European Journal of Operational Research, Elsevier, vol. 144(3), pages 513-529, February.
    6. 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.
    7. Soyster, A. L., 1979. "Inexact linear programming with generalized resource sets," European Journal of Operational Research, Elsevier, vol. 3(4), pages 316-321, July.
    8. William W. Cooper & Kyung Sam Park & Gang Yu, 1999. "IDEA and AR-IDEA: Models for Dealing with Imprecise Data in DEA," Management Science, INFORMS, vol. 45(4), pages 597-607, April.
    9. A. L. Soyster, 1973. "Technical Note—Convex Programming with Set-Inclusive Constraints and Applications to Inexact Linear Programming," Operations Research, INFORMS, vol. 21(5), pages 1154-1157, October.
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    11. Park, Kyung Sam & Kim, Soung Hie, 1997. "Tools for interactive multiattribute decisionmaking with incompletely identified information," European Journal of Operational Research, Elsevier, vol. 98(1), pages 111-123, April.
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    Cited by:

    1. Nazila Aghayi & Madjid Tavana & Mohammad Ali Raayatpanah, 2016. "Robust efficiency measurement with common set of weights under varying degrees of conservatism and data uncertainty," European Journal of Industrial Engineering, Inderscience Enterprises Ltd, vol. 10(3), pages 385-405.
    2. Anna Labijak-Kowalska & Miłosz Kadziński, 2023. "Exact and stochastic methods for robustness analysis in the context of Imprecise Data Envelopment Analysis," Operational Research, Springer, vol. 23(1), pages 1-34, March.
    3. Kao, Chiang & Lin, Pei-Huang, 2011. "Qualitative factors in data envelopment analysis: A fuzzy number approach," European Journal of Operational Research, Elsevier, vol. 211(3), pages 586-593, June.
    4. Toloo, Mehdi & Mensah, Emmanuel Kwasi & Salahi, Maziar, 2022. "Robust optimization and its duality in data envelopment analysis," Omega, Elsevier, vol. 108(C).
    5. Azadi, Majid & Farzipoor Saen, Reza, 2013. "A combination of QFD and imprecise DEA with enhanced Russell graph measure: A case study in healthcare," Socio-Economic Planning Sciences, Elsevier, vol. 47(4), pages 281-291.
    6. Shabani, Amir & Visani, Franco & Barbieri, Paolo & Dullaert, Wout & Vigo, Daniele, 2019. "Reliable estimation of suppliers’ total cost of ownership: An imprecise data envelopment analysis model with common weights," Omega, Elsevier, vol. 87(C), pages 57-70.
    7. Emmanuel Kwasi Mensah, 2020. "Robust data envelopment analysis via ellipsoidal uncertainty sets with application to the Italian banking industry," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(2), pages 491-518, December.
    8. HATAMI-MARBINI, Adel & AGRELL, Per & AGHAYI, Nazila, 2013. "Imprecise data envelopment analysis for the two-stage process," LIDAM Discussion Papers CORE 2013004, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. Park, K. Sam, 2010. "Duality, efficiency computations and interpretations in imprecise DEA," European Journal of Operational Research, Elsevier, vol. 200(1), pages 289-296, January.
    10. R Farzipoor Saen, 2011. "Media selection in the presence of flexible factors and imprecise data," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(9), pages 1695-1703, September.

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