IDEAS home Printed from https://ideas.repec.org/p/hal/wpaper/hal-02144705.html
   My bibliography  Save this paper

Mixed Stochastic Input Oriented Data Envelopment Analysis Model

Author

Listed:
  • Nahia Mourad

    (CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - ENPC - École des Ponts ParisTech)

  • Assem Tharwat

Abstract

Data envelopment analysis (DEA) is a mathematical tool used to evaluate relative efficiency of decision making units (DMUs). It is a bench-marking method for these units. To measure this relative efficiency, data related to a set of inputs and outputs are provided from all the DMUs under analysis, and then implemented in a suitable DEA model. Stochastic DEA allows the inputs or outputs to be stochastic random variables. In this article, we consider combination of deterministic and stochastic inputs following Normal and/or Poisson distribution. To the best of our knowledge, variables following Poisson distribution are not yet considered in these methods. We introduce the stochastic input oriented data envelopment analysis (SIODEA) model. The random inputs, following either normal or Poisson distributions, are controlled by chance constrained. Using functional analysis techniques, the chance constrained with Poisson variables is replaced by difference of Marcum functions evaluated at points related to the parameters of these variables. Consequently, we formulate a deter-ministic equivalent model with mixed random inputs. Finally, a numerical example is presented and the efficiencies of different DMUs are calculated using the obtained equivalent model to test its validity.

Suggested Citation

  • Nahia Mourad & Assem Tharwat, 2019. "Mixed Stochastic Input Oriented Data Envelopment Analysis Model," Working Papers hal-02144705, HAL.
    • Handle: RePEc:hal:wpaper:hal-02144705
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    References listed on IDEAS

    as
    1. Joe Zhu, 2014. "Quantitative Models for Performance Evaluation and Benchmarking," International Series in Operations Research and Management Science, Springer, edition 3, number 978-3-319-06647-9, September.
    2. Emrouznejad, Ali & Yang, Guo-liang, 2018. "A survey and analysis of the first 40 years of scholarly literature in DEA: 1978–2016," Socio-Economic Planning Sciences, Elsevier, vol. 61(C), pages 4-8.
    3. Khoshnevisan, Benyamin & Shariati, Hanifreza Motamed & Rafiee, Shahin & Mousazadeh, Hossein, 2014. "Comparison of energy consumption and GHG emissions of open field and greenhouse strawberry production," Renewable and Sustainable Energy Reviews, Elsevier, vol. 29(C), pages 316-324.
    4. Cooper, William W. & Deng, H. & Huang, Zhimin & Li, Susan X., 2004. "Chance constrained programming approaches to congestion in stochastic data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 155(2), pages 487-501, June.
    5. Joe Zhu, 2014. "Data Envelopment Analysis," International Series in Operations Research & Management Science, in: Quantitative Models for Performance Evaluation and Benchmarking, edition 3, chapter 1, pages 1-9, Springer.
    6. Léopold Simar & Valentin Zelenyuk, 2011. "Stochastic FDH/DEA estimators for frontier analysis," Journal of Productivity Analysis, Springer, vol. 36(1), pages 1-20, August.
    7. Costa, A.O. & Oliveira, L.B. & Lins, M.P.E. & Silva, A.C.M. & Araujo, M.S.M. & Pereira Jr., A.O. & Rosa, L.P., 2013. "Sustainability analysis of biodiesel production: A review on different resources in Brazil," Renewable and Sustainable Energy Reviews, Elsevier, vol. 27(C), pages 407-412.
    8. Lee, Seong Kon & Mogi, Gento & Hui, K.S., 2013. "A fuzzy analytic hierarchy process (AHP)/data envelopment analysis (DEA) hybrid model for efficiently allocating energy R&D resources: In the case of energy technologies against high oil prices," Renewable and Sustainable Energy Reviews, Elsevier, vol. 21(C), pages 347-355.
    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. W W Cooper & H Deng & Z Huang & S X Li, 2002. "Chance constrained programming approaches to technical efficiencies and inefficiencies in stochastic data envelopment analysis," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 53(12), pages 1347-1356, December.
    Full references (including those not matched with items on IDEAS)

    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. Mardani, Abbas & Zavadskas, Edmundas Kazimieras & Streimikiene, Dalia & Jusoh, Ahmad & Khoshnoudi, Masoumeh, 2017. "A comprehensive review of data envelopment analysis (DEA) approach in energy efficiency," Renewable and Sustainable Energy Reviews, Elsevier, vol. 70(C), pages 1298-1322.
    2. Thyago C. C. Nepomuceno & Ana Paula C. S. Costa, 2019. "Resource allocation with Time Series DEA applied to Brazilian Federal Saving banks," Economics Bulletin, AccessEcon, vol. 39(2), pages 1384-1392.
    3. 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.
    4. Sueyoshi, Toshiyuki & Yuan, Yan & Goto, Mika, 2017. "A literature study for DEA applied to energy and environment," Energy Economics, Elsevier, vol. 62(C), pages 104-124.
    5. Valentin Zelenyuk, 2019. "Data Envelopment Analysis and Business Analytics: The Big Data Challenges and Some Solutions," CEPA Working Papers Series WP072019, School of Economics, University of Queensland, Australia.
    6. Francisco Javier Santos Arteaga & Debora Di Caprio & David Cucchiari & Josep M Campistol & Federico Oppenheimer & Fritz Diekmann & Ignacio Revuelta, 2021. "Modeling patients as decision making units: evaluating the efficiency of kidney transplantation through data envelopment analysis," Health Care Management Science, Springer, vol. 24(1), pages 55-71, March.
    7. 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.
    8. Kaffash, Sepideh & Azizi, Roza & Huang, Ying & Zhu, Joe, 2020. "A survey of data envelopment analysis applications in the insurance industry 1993–2018," European Journal of Operational Research, Elsevier, vol. 284(3), pages 801-813.
    9. Jradi, Samah & Bouzdine Chameeva, Tatiana & Aparicio, Juan, 2019. "The measurement of revenue inefficiency over time: An additive perspective," Omega, Elsevier, vol. 83(C), pages 167-180.
    10. Abbas Mardani & Dalia Streimikiene & Tomas Balezentis & Muhamad Zameri Mat Saman & Khalil Md Nor & Seyed Meysam Khoshnava, 2018. "Data Envelopment Analysis in Energy and Environmental Economics: An Overview of the State-of-the-Art and Recent Development Trends," Energies, MDPI, vol. 11(8), pages 1-21, August.
    11. 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.
    12. Nyankomo Marwa, 2014. "Efficiency and Profitability of Tanzanian saving and Credit Cooperatives: Who is a Star?," Journal of Economics and Behavioral Studies, AMH International, vol. 6(8), pages 658-669.
    13. Yongjun Li & Xiao Shi & Min Yang & Liang Liang, 2017. "Variable selection in data envelopment analysis via Akaike’s information criteria," Annals of Operations Research, Springer, vol. 253(1), pages 453-476, June.
    14. Chen, Ya & Tsionas, Mike G. & Zelenyuk, Valentin, 2021. "LASSO+DEA for small and big wide data," Omega, Elsevier, vol. 102(C).
    15. Lam, Chor Man & Hsu, Shu-Chien & Alvarado, Valeria & Li, Wing Man, 2020. "Integrated life-cycle data envelopment analysis for techno-environmental performance evaluation on sludge-to-energy systems," Applied Energy, Elsevier, vol. 266(C).
    16. Fazıl Gökgöz & Mustafa Taylan Güvercin, 2018. "Investigating the total factor productivity changes in the top ICT companies worldwide," Electronic Commerce Research, Springer, vol. 18(4), pages 791-811, December.
    17. Liu, John S. & Lu, Louis Y.Y. & Lu, Wen-Min, 2016. "Research fronts in data envelopment analysis," Omega, Elsevier, vol. 58(C), pages 33-45.
    18. Nomita Pachar & Jyoti Dhingra Darbari & Kannan Govindan & P. C. Jha, 2022. "Sustainable performance measurement of Indian retail chain using two-stage network DEA," Annals of Operations Research, Springer, vol. 315(2), pages 1477-1515, August.
    19. Le, Minh Hanh & Afsharian, Mohsen & Ahn, Heinz, 2021. "Inverse Frontier-based Benchmarking for Investigating the Efficiency and Achieving the Targets in the Vietnamese Education System," Omega, Elsevier, vol. 103(C).
    20. Sahoo, Biresh & Singh, Ramadhar & Mishra, Bineet & Sankaran, Krithiga, 2015. "Research Productivity in Management Schools of India: A Directional Benefit-of-Doubt Model Analysis," MPRA Paper 67046, University Library of Munich, Germany.

    More about this item

    Keywords

    mathematical programming; performance; efficiency; decision making; data envelopment analysis; input oriented DEA; stochastic inputs; chance constrained;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:hal:wpaper:hal-02144705. 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.