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Stochastic DEA Models With Different Types of Input-Output Disturbances

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  • Zhimin Huang
  • Susan Li

Abstract

This paper presents stochasticmodels in data envelopment analysis (DEA) for the possibilityof variations in inputs and outputs. Efficiency measure of adecision making unit (DMU) is defined via joint probabilisticcomparisons of inputs and outputs with other DMUs and can becharacterized by solving a chance constrained programming problem.By utilizing the theory of chance constrained programming, deterministicequivalents are obtained for both situations of multivariatesymmetric random disturbances and a single random factor in theproduction relationships. The linear deterministic equivalentand its dual form are obtained via the goal programming theoryunder the assumption of the single random factor. An analysisof stochastic variable returns to scale is developed using theidea of stochastic supporting hyperplanes. The relationshipsof our stochastic DEA models with some conventional DEA modelsare also discussed. Copyright Kluwer Academic Publishers 2001

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  • Zhimin Huang & Susan Li, 2001. "Stochastic DEA Models With Different Types of Input-Output Disturbances," Journal of Productivity Analysis, Springer, vol. 15(2), pages 95-113, March.
    • Handle: RePEc:kap:jproda:v:15:y:2001:i:2:p:95-113
    DOI: 10.1023/A:1007874304917
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    7. Wu, Desheng (Dash) & Lee, Chi-Guhn, 2010. "Stochastic DEA with ordinal data applied to a multi-attribute pricing problem," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1679-1688, December.
    8. 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.
    9. Prakashan Veettil & Stijn Speelman & Guido Huylenbroeck, 2013. "Estimating the Impact of Water Pricing on Water Use Efficiency in Semi-arid Cropping System: An Application of Probabilistically Constrained Nonparametric Efficiency Analysis," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 27(1), pages 55-73, January.
    10. Mohammad Izadikhah & Elnaz Azadi & Majid Azadi & Reza Farzipoor Saen & Mehdi Toloo, 2022. "Developing a new chance constrained NDEA model to measure performance of sustainable supply chains," Annals of Operations Research, Springer, vol. 316(2), pages 1319-1347, September.
    11. Luis R. Murillo‐Zamorano, 2004. "Economic Efficiency and Frontier Techniques," Journal of Economic Surveys, Wiley Blackwell, vol. 18(1), pages 33-77, February.
    12. Catherine J. Morrison Paul & Ronald G. Felthoven & Marcelo de O. Torres, 2010. "Productive performance in fisheries: modeling, measurement, and management," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 54(3), pages 343-360, July.
    13. Habtamu Alem, 2021. "A Metafrontier Analysis on the Performance of Grain-Producing Regions in Norway," Economies, MDPI, vol. 9(1), pages 1-10, February.
    14. Wanke, Peter & Barros, C.P. & Figueiredo, Otávio, 2016. "Efficiency and productive slacks in urban transportation modes: A two-stage SDEA-Beta Regression approach," Utilities Policy, Elsevier, vol. 41(C), pages 31-39.
    15. Panagiotis Mitropoulos & Panagiotis D. Zervopoulos & Ioannis Mitropoulos, 2020. "Measuring performance in the presence of noisy data with targeted desirable levels: evidence from healthcare units," Annals of Operations Research, Springer, vol. 294(1), pages 537-566, November.
    16. Balak, Sima & Behzadi, Mohammad Hassan & Nazari, Ali, 2021. "Stochastic copula-DEA model based on the dependence structure of stochastic variables: An application to twenty bank branches," Economic Analysis and Policy, Elsevier, vol. 72(C), pages 326-341.
    17. Nathaniel D. Bastian & Tahir Ekin & Hyojung Kang & Paul M. Griffin & Lawrence V. Fulton & Benjamin C. Grannan, 2017. "Stochastic multi-objective auto-optimization for resource allocation decision-making in fixed-input health systems," Health Care Management Science, Springer, vol. 20(2), pages 246-264, June.
    18. Tsionas, Efthymios G. & Papadakis, Emmanuel N., 2010. "A Bayesian approach to statistical inference in stochastic DEA," Omega, Elsevier, vol. 38(5), pages 309-314, October.
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    20. Haibo Zhou & Hanhui Hu, 2017. "Sustainability Evaluation of Railways in China Using a Two-Stage Network DEA Model with Undesirable Outputs and Shared Resources," Sustainability, MDPI, vol. 9(1), pages 1-23, January.

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