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Probabilistically constrained models for efficiency and dominance in DEA

Author

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  • Bruni, M.E.
  • Conforti, D.
  • Beraldi, P.
  • Tundis, E.

Abstract

This paper proposes a stochastic model for data envelopment analysis (DEA), based on the theory of joint probabilistic constraints, which can be used with general multivariate distribution functions. The key assumption is that the random variables representative of the uncertain data follow a discrete distribution or that a discrete approximation of continuous distribution is available. Under this assumption, mixed integer linear models are formulated to tackle, rather originally, dependencies among DMUs inputs, outputs and inputs-outputs through the theory of joint probabilistic constraints. The features of the model are illustrated through an application for the performance evaluation of screening units.

Suggested Citation

  • Bruni, M.E. & Conforti, D. & Beraldi, P. & Tundis, E., 2009. "Probabilistically constrained models for efficiency and dominance in DEA," International Journal of Production Economics, Elsevier, vol. 117(1), pages 219-228, January.
    • Handle: RePEc:eee:proeco:v:117:y:2009:i:1:p:219-228
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    References listed on IDEAS

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    Cited by:

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    4. Mitropoulos, Panagiotis & Talias, Μichael A. & Mitropoulos, Ioannis, 2015. "Combining stochastic DEA with Bayesian analysis to obtain statistical properties of the efficiency scores: An application to Greek public hospitals," European Journal of Operational Research, Elsevier, vol. 243(1), pages 302-311.
    5. Rashed Khanjani Shiraz & Madjid Tavana & Hirofumi Fukuyama, 2021. "A joint chance-constrained data envelopment analysis model with random output data," Operational Research, Springer, vol. 21(2), pages 1255-1277, June.
    6. Quirós Romero, Cipriano & Rodríguez Rodríguez, Diego, 2010. "E-commerce and efficiency at the firm level," International Journal of Production Economics, Elsevier, vol. 126(2), pages 299-305, August.
    7. Gianpaolo Iazzolino & Maria Elena Bruni & Patrizia Beraldi, 2013. "Using DEA and financial ratings for credit risk evaluation: an empirical analysis," Applied Economics Letters, Taylor & Francis Journals, vol. 20(14), pages 1310-1317, September.
    8. 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.
    9. Jinpeng Liu & Yun Long & Xiaohua Song, 2017. "A Study on the Conduction Mechanism and Evaluation of the Comprehensive Efficiency of Photovoltaic Power Generation in China," Energies, MDPI, vol. 10(5), pages 1-22, May.
    10. Chen, Kun & Zhu, Joe, 2019. "Computational tractability of chance constrained data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 274(3), pages 1037-1046.
    11. 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.
    12. Wang, Ying-Ming & Chin, Kwai-Sang, 2010. "Some alternative models for DEA cross-efficiency evaluation," International Journal of Production Economics, Elsevier, vol. 128(1), pages 332-338, November.
    13. Khodadadipour, M. & Hadi-Vencheh, A. & Behzadi, M.H. & Rostamy-malkhalifeh, M., 2021. "Undesirable factors in stochastic DEA cross-efficiency evaluation: An application to thermal power plant energy efficiency," Economic Analysis and Policy, Elsevier, vol. 69(C), pages 613-628.
    14. Angus Jeang, 2019. "Robust DEA methodology via computer model for conceptual design under uncertainty," Journal of Intelligent Manufacturing, Springer, vol. 30(3), pages 1221-1245, March.
    15. Ruiling Sun & Yi Zhou & Jie Wu & Zaiwu Gong, 2019. "Influencing Factors of PM 2.5 Pollution: Disaster Points of Meteorological Factors," IJERPH, MDPI, vol. 16(20), pages 1-31, October.
    16. Wai‐Peng Wong & Qiang Deng & Ming-Lang Tseng & Loo‐Hay Lee & Chee‐Wooi Hooy, 2014. "A Stochastic Setting To Bank Financial Performance For Refining Efficiency Estimates," Intelligent Systems in Accounting, Finance and Management, John Wiley & Sons, Ltd., vol. 21(4), pages 225-245, October.
    17. Udhayakumar, A. & Charles, V. & Kumar, Mukesh, 2011. "Stochastic simulation based genetic algorithm for chance constrained data envelopment analysis problems," Omega, Elsevier, vol. 39(4), pages 387-397, August.
    18. Kao, Chiang & Liu, Shiang-Tai, 2019. "Stochastic efficiency measures for production units with correlated data," European Journal of Operational Research, Elsevier, vol. 273(1), pages 278-287.
    19. Wei, Guiwu & Chen, Jian & Wang, Jiamin, 2014. "Stochastic efficiency analysis with a reliability consideration," Omega, Elsevier, vol. 48(C), pages 1-9.
    20. Vincent Charles & Ioannis E. Tsolas & Tatiana Gherman, 2018. "Satisficing data envelopment analysis: a Bayesian approach for peer mining in the banking sector," Annals of Operations Research, Springer, vol. 269(1), pages 81-102, October.
    21. Rashed Khanjani Shiraz & Adel Hatami-Marbini & Ali Emrouznejad & Hirofumi Fukuyama, 2020. "Chance-constrained cost efficiency in data envelopment analysis model with random inputs and outputs," Operational Research, Springer, vol. 20(3), pages 1863-1898, September.
    22. Davtalab-Olyaie, Mostafa & Asgharian, Masoud & Nia, Vahid Partovi, 2019. "Stochastic ranking and dominance in DEA," International Journal of Production Economics, Elsevier, vol. 214(C), pages 125-138.

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