IDEAS home Printed from https://ideas.repec.org/a/kap/jproda/v15y2001i2p95-113.html
   My bibliography  Save this article

Stochastic DEA Models With Different Types of Input-Output Disturbances

Author

Listed:
  • 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

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1023/A:1007874304917
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1023/A:1007874304917?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Forsund, Finn R. & Lovell, C. A. Knox & Schmidt, Peter, 1980. "A survey of frontier production functions and of their relationship to efficiency measurement," Journal of Econometrics, Elsevier, vol. 13(1), pages 5-25, May.
    2. William F. Sharpe, 1963. "A Simplified Model for Portfolio Analysis," Management Science, INFORMS, vol. 9(2), pages 277-293, January.
    3. A. Charnes & W. W. Cooper & E. Rhodes, 1981. "Evaluating Program and Managerial Efficiency: An Application of Data Envelopment Analysis to Program Follow Through," Management Science, INFORMS, vol. 27(6), pages 668-697, June.
    4. Li, Susan X., 1998. "Stochastic models and variable returns to scales in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 104(3), pages 532-548, February.
    5. William Cooper & Zhimin Huang & Vedran Lelas & Susan Li & Ole Olesen, 1998. "Chance Constrained Programming Formulations for Stochastic Characterizations of Efficiency and Dominance in DEA," Journal of Productivity Analysis, Springer, vol. 9(1), pages 53-79, January.
    6. Charnes, A. & Cooper, W. W. & Huang, Z. M. & Sun, D. B., 1990. "Polyhedral Cone-Ratio DEA Models with an illustrative application to large commercial banks," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 73-91.
    7. Seiford, Lawrence M. & Thrall, Robert M., 1990. "Recent developments in DEA : The mathematical programming approach to frontier analysis," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 7-38.
    8. Charnes, A. & Cooper, W. W. & Golany, B. & Seiford, L. & Stutz, J., 1985. "Foundations of data envelopment analysis for Pareto-Koopmans efficient empirical production functions," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 91-107.
    9. R. D. Banker & A. Charnes & W. W. Cooper, 1984. "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, INFORMS, vol. 30(9), pages 1078-1092, September.
    10. Huang, Zhimin & Li, Susan X., 1996. "Dominance stochastic models in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 95(2), pages 390-403, December.
    11. Yehuda Kahane, 1977. "Determination of the Product Mix and the Business Policy of an Insurance Company--A Portfolio Approach," Management Science, INFORMS, vol. 23(10), pages 1060-1069, June.
    12. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    13. Aigner, Dennis & Lovell, C. A. Knox & Schmidt, Peter, 1977. "Formulation and estimation of stochastic frontier production function models," Journal of Econometrics, Elsevier, vol. 6(1), pages 21-37, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Parag Pendharkar & Marvin Troutt, 2014. "Interactive classification using data envelopment analysis," Annals of Operations Research, Springer, vol. 214(1), pages 125-141, March.
    2. Shahsuzan Zakaria, 2023. "The Need to go Beyond Deterministic Data Envelopment Analysis (DEA): A Comparative Analysis with Bootstrapping DEA in Risk Management Efficiency Measurements," Information Management and Business Review, AMH International, vol. 15(4), pages 433-446.
    3. O'Neill, Liam & Rauner, Marion & Heidenberger, Kurt & Kraus, Markus, 2008. "A cross-national comparison and taxonomy of DEA-based hospital efficiency studies," Socio-Economic Planning Sciences, Elsevier, vol. 42(3), pages 158-189, September.
    4. 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.
    5. 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.
    6. Thanh Ngo & Kan Wai Hong Tsui, 2022. "Estimating the confidence intervals for DEA efficiency scores of Asia-Pacific airlines," Operational Research, Springer, vol. 22(4), pages 3411-3434, September.
    7. 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.
    8. 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.
    9. Onorato, Grazia & Pampurini, Francesca & Quaranta, Anna Grazia, 2024. "Lending activity efficiency. A comparison between fintech firms and the banking sector," Research in International Business and Finance, Elsevier, vol. 68(C).
    10. Wei, Guiwu & Chen, Jian & Wang, Jiamin, 2014. "Stochastic efficiency analysis with a reliability consideration," Omega, Elsevier, vol. 48(C), pages 1-9.
    11. Morrison Paul, Catherine J. & Felthoven, Ronald G. & de O. Torres, Marcelo, 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 1-18.
    12. 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.
    13. 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.
    14. Pampurini, Francesca & Pezzola, Annagiulia & Quaranta, Anna Grazia, 2024. "Lending business models and FinTechs efficiency," Finance Research Letters, Elsevier, vol. 65(C).
    15. 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.
    16. Luis R. Murillo‐Zamorano, 2004. "Economic Efficiency and Frontier Techniques," Journal of Economic Surveys, Wiley Blackwell, vol. 18(1), pages 33-77, February.
    17. 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.
    18. Oduro, Richard A. & Taylor, Peter G., 2023. "Future pathways for energy networks: A review of international experiences in high income countries," Renewable and Sustainable Energy Reviews, Elsevier, vol. 171(C).
    19. 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.
    20. 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.
    21. Habtamu Alem, 2021. "A Metafrontier Analysis on the Performance of Grain-Producing Regions in Norway," Economies, MDPI, vol. 9(1), pages 1-10, February.
    22. Habtamu Alem, 2021. "The Role of Technical Efficiency Achieving Sustainable Development: A Dynamic Analysis of Norwegian Dairy Farms," Sustainability, MDPI, vol. 13(4), pages 1-11, February.
    23. Alireza Amirteimoori & Biresh K. Sahoo & Saber Mehdizadeh, 2023. "Data envelopment analysis for scale elasticity measurement in the stochastic case: with an application to Indian banking," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 9(1), pages 1-36, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Li, Susan X., 1998. "Stochastic models and variable returns to scales in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 104(3), pages 532-548, February.
    2. Huang, Zhimin & Li, Susan X., 1996. "Dominance stochastic models in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 95(2), pages 390-403, December.
    3. William Cooper & Zhimin Huang & Vedran Lelas & Susan Li & Ole Olesen, 1998. "Chance Constrained Programming Formulations for Stochastic Characterizations of Efficiency and Dominance in DEA," Journal of Productivity Analysis, Springer, vol. 9(1), pages 53-79, January.
    4. Mai, Nhat Chi, 2015. "Efficiency of the banking system in Vietnam under financial liberalization," OSF Preprints qsf6d, Center for Open Science.
    5. Alireza Amirteimoori & Biresh K. Sahoo & Saber Mehdizadeh, 2023. "Data envelopment analysis for scale elasticity measurement in the stochastic case: with an application to Indian banking," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 9(1), pages 1-36, December.
    6. Cherchye, L. & Post, G.T., 2001. "Methodological Advances in Dea," ERIM Report Series Research in Management ERS-2001-53-F&A, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    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. Zhimin Huang & Waiman Cheung & Huiwen Wang, 2006. "Cone dominance and efficiency in DEA," Annals of Operations Research, Springer, vol. 145(1), pages 89-103, July.
    9. Glover, Fred & Sueyoshi, Toshiyuki, 2009. "Contributions of Professor William W. Cooper in Operations Research and Management Science," European Journal of Operational Research, Elsevier, vol. 197(1), pages 1-16, August.
    10. Ali, Agha Iqbal & Lerme, Catherine S. & Seiford, Lawrence M., 1995. "Components of efficiency evaluation in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 80(3), pages 462-473, February.
    11. Kuosmanen, Timo & Post, Thierry & Scholtes, Stefan, 2007. "Non-parametric tests of productive efficiency with errors-in-variables," Journal of Econometrics, Elsevier, vol. 136(1), pages 131-162, January.
    12. Zhong, Wei & Yuan, Wei & Li, Susan X. & Huang, Zhimin, 2011. "The performance evaluation of regional R&D investments in China: An application of DEA based on the first official China economic census data," Omega, Elsevier, vol. 39(4), pages 447-455, August.
    13. Po, Rung-Wei & Guh, Yuh-Yuan & Yang, Miin-Shen, 2009. "A new clustering approach using data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 199(1), pages 276-284, November.
    14. Olesen, O. B., 1995. "Some unsolved problems in data envelopment analysis: A survey," International Journal of Production Economics, Elsevier, vol. 39(1-2), pages 5-36, April.
    15. Haslem, John A. & Scheraga, Carl A. & Bedingfield, James P., 1999. "DEA efficiency profiles of U.S. banks operating internationally," International Review of Economics & Finance, Elsevier, vol. 8(2), pages 165-182, June.
    16. Luis R. Murillo‐Zamorano, 2004. "Economic Efficiency and Frontier Techniques," Journal of Economic Surveys, Wiley Blackwell, vol. 18(1), pages 33-77, February.
    17. Cook, Wade D. & Seiford, Larry M., 2009. "Data envelopment analysis (DEA) - Thirty years on," European Journal of Operational Research, Elsevier, vol. 192(1), pages 1-17, January.
    18. Adler, Nicole & Friedman, Lea & Sinuany-Stern, Zilla, 2002. "Review of ranking methods in the data envelopment analysis context," European Journal of Operational Research, Elsevier, vol. 140(2), pages 249-265, July.
    19. 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.
    20. Bolós, V.J. & Benítez, R. & Coll-Serrano, V., 2024. "Chance constrained directional models in stochastic data envelopment analysis," Operations Research Perspectives, Elsevier, vol. 12(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kap:jproda:v:15:y:2001:i:2:p:95-113. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.