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IDEA and AR-IDEA: Models for Dealing with Imprecise Data in DEA

  • William W. Cooper

    (Graduate School of Business, The University of Texas at Austin, Austin, Texas 78712)

  • Kyung Sam Park

    (Graduate School of Management, KAIST, 207-43 Cheongryang, Dongdaemun, Seoul 130-012, Korea)

  • Gang Yu

    (MSIS Department and Center for Management of Operations & Logistics, Graduate School of Business, The University of Texas at Austin, Austin, Texas 78712)

Registered author(s):

    Data Envelopment Analysis (DEA) is a nonparametric approach to evaluating the relative efficiency of decision making units (DMUs) that use multiple inputs to produce multiple outputs. An assumption underlying DEA is that all the data assume the form of specific numerical values. In some applications, however, the data may be imprecise. For instance, some of the data may be known only within specified bounds, while other data may be known only in terms of ordinal relations. DEA with imprecise data or, more compactly, the Imprecise Data Envelopment Analysis (IDEA) method developed in this paper permits mixtures of imprecisely- and exactly-known data, which the IDEA models transform into ordinary linear programming forms. This is carried even further in the present paper to comprehend the now extensively employed Assurance Region (AR) concepts in which bounds are placed on the variables rather than the data. We refer to this approach as AR-IDEA, because it replaces conditions on the variables with transformations of the data and thus also aligns the developments we describe in this paper with what are known as cone-ratio envelopments in DEA. As a result, one unified approach, referred to as the AR-IDEA model, is achieved which includes not only imprecise data capabilities but also assurance region and cone-ratio envelopment concepts.

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    File URL: http://dx.doi.org/10.1287/mnsc.45.4.597
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    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 45 (1999)
    Issue (Month): 4 (April)
    Pages: 597-607

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    Handle: RePEc:inm:ormnsc:v:45:y:1999:i:4:p:597-607
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    1. Wade D. Cook & Moshe Kress, 1990. "A Data Envelopment Model for Aggregating Preference Rankings," Management Science, INFORMS, vol. 36(11), pages 1302-1310, November.
    2. Boaz Golany, 1988. "Note---A Note on Including Ordinal Relations Among Multipliers in Data Envelopment Analysis," Management Science, INFORMS, vol. 34(8), pages 1029-1033, August.
    3. Agha Iqbal Ali & Wade D. Cook & Lawrence M. Seiford, 1991. "Strict vs. Weak Ordinal Relations for Multipliers in Data Envelopment Analysis," Management Science, INFORMS, vol. 37(6), pages 733-738, June.
    4. 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.
    5. Schaffnit, Claire & Rosen, Dan & Paradi, Joseph C., 1997. "Best practice analysis of bank branches: An application of DEA in a large Canadian bank," European Journal of Operational Research, Elsevier, vol. 98(2), pages 269-289, April.
    6. Cook, Wade D. & Kress, Moshe, 1991. "A multiple criteria decision model with ordinal preference data," European Journal of Operational Research, Elsevier, vol. 54(2), pages 191-198, September.
    7. Roll, Y & Golany, B., 1993. "Alternate methods of treating factor weights in DEA," Omega, Elsevier, vol. 21(1), pages 99-109, January.
    8. Cook, Wade D. & Doyle, John & Green, Rodney & Kress, Moshe, 1997. "Multiple criteria modelling and ordinal data: Evaluation in terms of subsets of criteria," European Journal of Operational Research, Elsevier, vol. 98(3), pages 602-609, May.
    9. Thompson, Russell G. & Langemeier, Larry N. & Lee, Chih-Tah & Lee, Euntaik & Thrall, Robert M., 1990. "The role of multiplier bounds in efficiency analysis with application to Kansas farming," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 93-108.
    10. Thompson, Russell G. & Dharmapala, P. S. & Thrall, Robert M., 1995. "Linked-cone DEA profit ratios and technical efficiency with application to Illinois coal mines," International Journal of Production Economics, Elsevier, vol. 39(1-2), pages 99-115, April.
    11. 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.
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