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Strict vs. Weak Ordinal Relations for Multipliers in Data Envelopment Analysis

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Author Info

  • Agha Iqbal Ali

    (School of Management, University of Massachusetts, Amherst, Massachusetts 01003)

  • Wade D. Cook

    (Faculty of Administrative Studies, York University, Toronto, Ontario, Canada)

  • Lawrence M. Seiford

    (Department of Industrial Engineering and Operations Research, University of Massachusetts, Amherst, Massachusetts 01003)

Abstract

In a recent paper, Golany (1988) proposes an interesting extension of Data Envelopment Analysis to the situation where ordinal relations among weights corresponding to certain dimensions exist. However, the development of the extended model contains mathematical errors and the proposed equivalence is incorrect. We establish the correct model equivalence and prove that weak ordinal relations require a nonstandard DEA model. We also show that the case of strict ordinal relations can be handled with the standard DEA model. These results hold for the CCR, BCC, additive, and multiplicative models and for relations involving both input and output multipliers.

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File URL: http://dx.doi.org/10.1287/mnsc.37.6.733
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Bibliographic Info

Article provided by INFORMS in its journal Management Science.

Volume (Year): 37 (1991)
Issue (Month): 6 (June)
Pages: 733-738

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Handle: RePEc:inm:ormnsc:v:37:y:1991:i:6:p:733-738

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Related research

Keywords: data envelopment analysis; ordinal relationships; orderings; relative efficiency;

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Cited by:
  1. T. Joro & E-J. Viitala, 1999. "The Efficiency of Public Forestry Organizations: A Comparison of Different Weight Restriction Approaches," Working Papers ir99059, International Institute for Applied Systems Analysis.
  2. Agrell, Per J. & Bogetoft, Peter, 2001. "DEA-Based Incentive Regimes in Health-Care Provision," Unit of Economics Working papers 24182, Royal Veterinary and Agricultural University, Food and Resource Economic Institute.
  3. Troutt, Marvin D. & Ehie, Ike C. & Brandyberry, Alan A., 2007. "Maximally productive input-output units," European Journal of Operational Research, Elsevier, vol. 178(2), pages 359-373, April.
  4. Green, Rodney H. & Doyle, John R. & Cook, Wade D., 1996. "Preference voting and project ranking using DEA and cross-evaluation," European Journal of Operational Research, Elsevier, vol. 90(3), pages 461-472, May.
  5. Despotis, Dimitris K. & Smirlis, Yiannis G., 2002. "Data envelopment analysis with imprecise data," European Journal of Operational Research, Elsevier, vol. 140(1), pages 24-36, July.
  6. 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.
  7. Bogetoft, Peter & Nielsen, Kurt, 2002. "Internet Based Benchmarking," Unit of Economics Working papers 24215, Royal Veterinary and Agricultural University, Food and Resource Economic Institute.
  8. Krishna Kumar, C. & Sinha, Bani K., 1999. "Efficiency based production planning and control models," European Journal of Operational Research, Elsevier, vol. 117(3), pages 450-469, September.
  9. Peter Bogetoft, 2000. "DEA and Activity Planning under Asymmetric Information," Journal of Productivity Analysis, Springer, vol. 13(1), pages 7-48, January.
  10. Bogetoft, Peter, 1999. "Process Aggregation and Efficiency," Unit of Economics Working papers 24190, Royal Veterinary and Agricultural University, Food and Resource Economic Institute.
  11. Bozec, Richard & Dia, Mohamed, 2007. "Board structure and firm technical efficiency: Evidence from Canadian state-owned enterprises," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1734-1750, March.

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