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Slacks-based measures of efficiency and super-efficiency in presence of nonpositive data

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  • Lee, Hsuan-Shih

Abstract

SBM and Super-SBM models will not function correctly when zero data or negative data appear in the inputs or outputs. This paper generalizes the SBM model and Super-SBM model so that zero data and negative data can be dealt with. Nonpositive SBM extends SBM, and Nonpositive Super-SBM extends Super-SBM. Both Nonpositive SBM and Nonpositive Super-SBM can deal with negative data and zero data. If the data are positive, Nonpositive SBM and Nonpositive Super-SBM are the same as SBM and Super-SBM, respectively. Nonpositive Super-SBM does not guarantee that the projection is Pareto efficient. A two-stage approach like that in [7] is proposed to resolve this issue. Nonpositive Super-SBM is employed to identify input savings and output surpluses, which are incorporated into the Modified Nonpositive SBM so that the Pareto efficient projection can be determined. The super-efficiency measure proposed by Fang et al. [7] and Lin et al. [11] do not account for the slacks identified at the second stage when the super-efficiency obtained at the first stage is larger than one. We will propose a composite super-efficiency index to resolve such issue.

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  • Lee, Hsuan-Shih, 2021. "Slacks-based measures of efficiency and super-efficiency in presence of nonpositive data," Omega, Elsevier, vol. 103(C).
    • Handle: RePEc:eee:jomega:v:103:y:2021:i:c:s0305048321000049
    DOI: 10.1016/j.omega.2021.102395
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    Cited by:

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    3. Duoxun Ba & Jing Zhang & Suocheng Dong & Bing Xia & Lin Mu, 2022. "Spatial-Temporal Characteristics and Driving Factors of the Eco-Efficiency of Tourist Hotels in China," IJERPH, MDPI, vol. 19(18), pages 1-24, September.
    4. Lin, Boqiang & Xie, Yongjing, 2023. "Does digital transformation improve the operational efficiency of Chinese power enterprises?," Utilities Policy, Elsevier, vol. 82(C).
    5. 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.
    6. Guo-Ya Gan & Hsuan-Shih Lee, 2021. "Resolving the infeasibility of the super-efficiency DEA based on DDF," Annals of Operations Research, Springer, vol. 307(1), pages 139-152, December.

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