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Qualitative and quantitative data envelopment analysis with interval data

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  • Masahiro Inuiguchi
  • Fumiki Mizoshita

Abstract

In this paper, we investigate DEA with interval input-output data. First we show various extensions of efficiency and that 25 of them are essential. Second we formulate the efficiency test problems as mixed integer programming problems. We prove that 14 among 25 problems can be reduced to linear programming problems and that the other 11 efficiencies can be tested by solving a finite sequence of linear programming problems. Third, in order to obtain efficiency scores, we extend SBM model to interval input-output data. Fourth, to moderate a possible positive overassessment by DEA, we introduce the inverted DEA model with interval input-output data. Using efficiency and inefficiency scores, we propose a classification of DMUs. Finally, we apply the proposed approach to Japanese Bank Data and demonstrate its advantages. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Masahiro Inuiguchi & Fumiki Mizoshita, 2012. "Qualitative and quantitative data envelopment analysis with interval data," Annals of Operations Research, Springer, vol. 195(1), pages 189-220, May.
    • Handle: RePEc:spr:annopr:v:195:y:2012:i:1:p:189-220:10.1007/s10479-011-0988-y
    DOI: 10.1007/s10479-011-0988-y
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    References listed on IDEAS

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    Cited by:

    1. A. K. Bhurjee & G. Panda, 2016. "Sufficient optimality conditions and duality theory for interval optimization problem," Annals of Operations Research, Springer, vol. 243(1), pages 335-348, August.
    2. Konstantinos Petridis & Alexander Chatzigeorgiou & Emmanouil Stiakakis, 2016. "A spatiotemporal Data Envelopment Analysis (S-T DEA) approach: the need to assess evolving units," Annals of Operations Research, Springer, vol. 238(1), pages 475-496, March.
    3. Amin Mostafaee & Milan Hladík, 2020. "Optimal value bounds in interval fractional linear programming and revenue efficiency measuring," 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. 28(3), pages 963-981, September.
    4. Konstantinos Petridis & Alexander Chatzigeorgiou & Emmanouil Stiakakis, 2016. "A spatiotemporal Data Envelopment Analysis (S-T DEA) approach: the need to assess evolving units," Annals of Operations Research, Springer, vol. 238(1), pages 475-496, March.
    5. Zahra Mohmmad Nejad & Alireza Ghaffari-Hadigheh, 2018. "A novel DEA model based on uncertainty theory," Annals of Operations Research, Springer, vol. 264(1), pages 367-389, May.

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