IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v48y2000i2p344-347.html
   My bibliography  Save this article

An Assurance Interval for the Non-Archimedean Epsilon in DEA Models

Author

Listed:
  • Saeid Mehrabian

    (Department of Mathematics, University for Teacher Education, Tehran, Iran)

  • Gholam R. Jahanshahloo

    (Department of Mathematics, University for Teacher Education, Tehran, Iran)

  • Mohammad R. Alirezaee

    (Department of Mathematics, University for Teacher Education, Tehran, Iran)

  • Gholam R. Amin

    (Department of Mathematics, Islamic Azad University, Tehran, Iran)

Abstract

This paper clarifies the role of non-Archimedean infinitesimal (epsilon) in DEA models so that the associated linear programs may be infeasible (for the multiplier side) and unbounded (for the envelopment side) for certain values of (epsilon). It is shown that the bound of (epsilon) proposed by Ali and Seiford (1993) is invalid for feasibility and boundedness of the linear programs. A procedure is presented for determining an assurance interval of (epsilon). It is also shown that an assurance value for (epsilon) can be found using a single linear program.

Suggested Citation

  • Saeid Mehrabian & Gholam R. Jahanshahloo & Mohammad R. Alirezaee & Gholam R. Amin, 2000. "An Assurance Interval for the Non-Archimedean Epsilon in DEA Models," Operations Research, INFORMS, vol. 48(2), pages 344-347, April.
    • Handle: RePEc:inm:oropre:v:48:y:2000:i:2:p:344-347
    DOI: 10.1287/opre.48.2.344.12381
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.48.2.344.12381
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.48.2.344.12381?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
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Ali, Agha Iqbal, 1993. "Streamlined computation for data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 64(1), pages 61-67, January.
    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. Pishchulov, Grigory & Trautrims, Alexander & Chesney, Thomas & Gold, Stefan & Schwab, Leila, 2019. "The Voting Analytic Hierarchy Process revisited: A revised method with application to sustainable supplier selection," International Journal of Production Economics, Elsevier, vol. 211(C), pages 166-179.
    2. Podinovski, Victor V. & Bouzdine-Chameeva, Tatiana, 2017. "Solving DEA models in a single optimization stage: Can the non-Archimedean infinitesimal be replaced by a small finite epsilon?," European Journal of Operational Research, Elsevier, vol. 257(2), pages 412-419.
    3. Adel Hatami-Marbini & Per J. Agrell & Hirofumi Fukuyama & Kobra Gholami & Pegah Khoshnevis, 2017. "The role of multiplier bounds in fuzzy data envelopment analysis," Annals of Operations Research, Springer, vol. 250(1), pages 249-276, March.
    4. Hamid Kiaei & Reza Kazemi Matin, 2022. "New common set of weights method in black-box and two-stage data envelopment analysis," Annals of Operations Research, Springer, vol. 309(1), pages 143-162, February.
    5. Shih-Heng Yu & Chia-Wei Hsu, 2020. "A unified extension of super-efficiency in additive data envelopment analysis with integer-valued inputs and outputs: an application to a municipal bus system," Annals of Operations Research, Springer, vol. 287(1), pages 515-535, April.
    6. Toloo, Mehdi & Ebrahimi, Bohlool & Amin, Gholam R., 2021. "New data envelopment analysis models for classifying flexible measures: The role of non-Archimedean epsilon," European Journal of Operational Research, Elsevier, vol. 292(3), pages 1037-1050.
    7. Charles, Vincent & Kumar, Mukesh & Irene Kavitha, S., 2012. "Measuring the efficiency of assembled printed circuit boards with undesirable outputs using data envelopment analysis," International Journal of Production Economics, Elsevier, vol. 136(1), pages 194-206.
    8. Jiawei Yang & Lei Fang, 2022. "Average lexicographic efficiency decomposition in two-stage data envelopment analysis: an application to China’s regional high-tech innovation systems," Annals of Operations Research, Springer, vol. 312(2), pages 1051-1093, May.
    9. Lin, Ruiyue & Liu, Qian, 2021. "Multiplier dynamic data envelopment analysis based on directional distance function: An application to mutual funds," European Journal of Operational Research, Elsevier, vol. 293(3), pages 1043-1057.
    10. Mehdi Toloo & Atefeh Masoumzadeh & Mona Barat, 2015. "Finding an Initial Basic Feasible Solution for DEA Models with an Application on Bank Industry," Computational Economics, Springer;Society for Computational Economics, vol. 45(2), pages 323-336, February.
    11. Bazargan, Massoud & Vasigh, Bijan, 2003. "Size versus efficiency: a case study of US commercial airports," Journal of Air Transport Management, Elsevier, vol. 9(3), pages 187-193.
    12. Bohlool Ebrahimi & Madjid Tavana & Andreas Kleine & Andreas Dellnitz, 2021. "An epsilon-based data envelopment analysis approach for solving performance measurement problems with interval and ordinal dual-role factors," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(4), pages 1103-1124, December.
    13. Yang, Guo-liang & Yang, Jian-bo & Liu, Wen-bin & Li, Xiao-xuan, 2013. "Cross-efficiency aggregation in DEA models using the evidential-reasoning approach," European Journal of Operational Research, Elsevier, vol. 231(2), pages 393-404.
    14. Mohsen Afsharian & Heinz Ahn, 2017. "Multi-period productivity measurement under centralized management with an empirical illustration to German saving banks," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(3), pages 881-911, July.
    15. Mehdi Toloo & Rahele Jalili, 2016. "LU Decomposition in DEA with an Application to Hospitals," Computational Economics, Springer;Society for Computational Economics, vol. 47(3), pages 473-488, March.
    16. Ebrahimi, Bohlool & Dhamotharan, Lalitha & Ghasemi, Mohammad Reza & Charles, Vincent, 2022. "A cross-inefficiency approach based on the deviation variables framework," Omega, Elsevier, vol. 111(C).
    17. S M Mirhedayatian & R Farzipoor Saen, 2011. "A new approach for weight derivation using data envelopment analysis in the analytic hierarchy process," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(8), pages 1585-1595, August.
    18. Gattoufi, Said & Oral, Muhittin & Reisman, Arnold, 2004. "A taxonomy for data envelopment analysis," Socio-Economic Planning Sciences, Elsevier, vol. 38(2-3), pages 141-158.

    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. 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.
    2. Wen-Chih Chen & Sheng-Yung Lai, 2017. "Determining radial efficiency with a large data set by solving small-size linear programs," Annals of Operations Research, Springer, vol. 250(1), pages 147-166, March.
    3. Premachandra, I. M., 2001. "A note on DEA vs principal component analysis: An improvement to Joe Zhu's approach," European Journal of Operational Research, Elsevier, vol. 132(3), pages 553-560, August.
    4. M Soleimani-damaneh, 2009. "A fast algorithm for determining some characteristics in DEA," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(11), pages 1528-1534, November.
    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. Walter Briec & Kristiaan Kerstens & Ignace Van de Woestyne, 2013. "Nonparametric cost and revenue functions under constant economies of scale: An enumeration approach for the single output or input case," Working Papers 2013-ECO-22, IESEG School of Management.
    7. Reuben Elan & Verma Bharat Bhushan & Bhat Ramesh, 2001. "Hospital Efficiency: An Empirical Analysis of District and Grant-in-Aid Hospitals in Gujarat," IIMA Working Papers WP2001-07-05, Indian Institute of Management Ahmedabad, Research and Publication Department.
    8. Zelenyuk, Valentin, 2020. "Aggregation of inputs and outputs prior to Data Envelopment Analysis under big data," European Journal of Operational Research, Elsevier, vol. 282(1), pages 172-187.
    9. Franz R. Hahn, 2007. "Determinants of Bank Efficiency in Europe. Assessing Bank Performance Across Markets," WIFO Studies, WIFO, number 31499, April.
    10. Alperovych, Yan & Hübner, Georges & Lobet, Fabrice, 2015. "How does governmental versus private venture capital backing affect a firm's efficiency? Evidence from Belgium," Journal of Business Venturing, Elsevier, vol. 30(4), pages 508-525.
    11. Wang, Zhao-Hua & Zeng, Hua-Lin & Wei, Yi-Ming & Zhang, Yi-Xiang, 2012. "Regional total factor energy efficiency: An empirical analysis of industrial sector in China," Applied Energy, Elsevier, vol. 97(C), pages 115-123.
    12. Ruiqing Yuan & Xiangyang Xu & Yanli Wang & Jiayi Lu & Ying Long, 2024. "Evaluating Carbon-Emission Efficiency in China’s Construction Industry: An SBM-Model Analysis of Interprovincial Building Heating," Sustainability, MDPI, vol. 16(6), pages 1-16, March.
    13. Azarnoosh Kafi & Behrouz Daneshian & Mohsen Rostamy-Malkhalifeh, 2021. "Forecasting the confidence interval of efficiency in fuzzy DEA," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 31(1), pages 41-59.
    14. Costa, Marcelo Azevedo & Lopes, Ana Lúcia Miranda & de Pinho Matos, Giordano Bruno Braz, 2015. "Statistical evaluation of Data Envelopment Analysis versus COLS Cobb–Douglas benchmarking models for the 2011 Brazilian tariff revision," Socio-Economic Planning Sciences, Elsevier, vol. 49(C), pages 47-60.
    15. Ahmad, Usman, 2011. "Financial Reforms and Banking Efficiency: Case of Pakistan," MPRA Paper 34220, University Library of Munich, Germany.
    16. Ashrafi, Ali & Seow, Hsin-Vonn & Lee, Lai Soon & Lee, Chew Ging, 2013. "The efficiency of the hotel industry in Singapore," Tourism Management, Elsevier, vol. 37(C), pages 31-34.
    17. Büschken, Joachim, 2009. "When does data envelopment analysis outperform a naïve efficiency measurement model?," European Journal of Operational Research, Elsevier, vol. 192(2), pages 647-657, January.
    18. Jahangoshai Rezaee, Mustafa & Jozmaleki, Mehrdad & Valipour, Mahsa, 2018. "Integrating dynamic fuzzy C-means, data envelopment analysis and artificial neural network to online prediction performance of companies in stock exchange," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 489(C), pages 78-93.
    19. Suhyeon Han & Shinyoung Park & Sejin An & Wonjun Choi & Mina Lee, 2023. "Research on Analyzing the Efficiency of R&D Projects for Climate Change Response Using DEA–Malmquist," Sustainability, MDPI, vol. 15(10), pages 1-23, May.
    20. Chenini Hajer & Jarboui Anis, 2018. "Analysis of the Impact of Governance on Bank Performance: Case of Commercial Tunisian Banks," Journal of the Knowledge Economy, Springer;Portland International Center for Management of Engineering and Technology (PICMET), vol. 9(3), pages 871-895, September.

    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:inm:oropre:v:48:y:2000:i:2:p:344-347. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.