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

Author

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Ali, Agha Iqbal, 1993. "Streamlined computation for data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 64(1), pages 61-67, January.
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    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.
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    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.
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