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

Author

Listed:
  • 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.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ormnsc:v:37:y:1991:i:6:p:733-738
    DOI: 10.1287/mnsc.37.6.733
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    Citations

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    Cited by:

    1. Antreas D. Athanassopoulos, 1998. "Decision Support for Target-Based Resource Allocation of Public Services in Multiunit and Multilevel Systems," Management Science, INFORMS, vol. 44(2), pages 173-187, February.
    2. Wade Cook & Dan Chai & John Doyle & Rodney Green, 1998. "Hierarchies and Groups in DEA," Journal of Productivity Analysis, Springer, vol. 10(2), pages 177-198, October.
    3. William W. Cooper & Kyung Sam Park & Gang Yu, 2001. "An Illustrative Application of Idea (Imprecise Data Envelopment Analysis) to a Korean Mobile Telecommunication Company," Operations Research, INFORMS, vol. 49(6), pages 807-820, December.
    4. 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.
    5. Ströhl, Florian & Borsch, Erik & Souren, Rainer, 2018. "Integration von Gewichtsrestriktionen in das DEA-Modell nach Charnes, Cooper und Rhodes: Exemplarische Optionen und Auswirkungen," Ilmenauer Schriften zur Betriebswirtschaftslehre, Technische Universität Ilmenau, Institut für Betriebswirtschaftslehre, volume 3, number 32018.
    6. 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.
    7. 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.
    8. Kaoru Tone, 2001. "On Returns to Scale under Weight Restrictions in Data Envelopment Analysis," Journal of Productivity Analysis, Springer, vol. 16(1), pages 31-47, July.
    9. Peter Bogetoft, 2000. "DEA and Activity Planning under Asymmetric Information," Journal of Productivity Analysis, Springer, vol. 13(1), pages 7-48, January.
    10. 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.
    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.
    12. 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.
    13. Pereira, Miguel Alves & Camanho, Ana Santos & Figueira, José Rui & Marques, Rui Cunha, 2021. "Incorporating preference information in a range directional composite indicator: The case of Portuguese public hospitals," European Journal of Operational Research, Elsevier, vol. 294(2), pages 633-650.
    14. T Joro & E-J Viitala, 2004. "Weight-restricted DEA in action: from expert opinions to mathematical models," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(8), pages 814-821, August.
    15. Peter Bogetoft & Kurt Nielsen, 2005. "Internet Based Benchmarking," Group Decision and Negotiation, Springer, vol. 14(3), pages 195-215, May.
    16. Francisco Pedraja-Chaparro & Javier Salinas-Jimenez & Peter Smith, 1997. "On the Role of Weight Restrictions in Data Envelopment Analysis," Journal of Productivity Analysis, Springer, vol. 8(2), pages 215-230, May.
    17. William W. Cooper & Kyung Sam Park & Gang Yu, 1999. "IDEA and AR-IDEA: Models for Dealing with Imprecise Data in DEA," Management Science, INFORMS, vol. 45(4), pages 597-607, April.
    18. 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.
    19. De Luca Cardillo, Dorotea & Fortuna, Tiziana, 2000. "A DEA model for the efficiency evaluation of nondominated paths on a road network," European Journal of Operational Research, Elsevier, vol. 121(3), pages 549-558, March.
    20. Michael O. Nyong, 2017. "Relative Efficiency of Commercial Banks in Nigeria: A Nonparametric Mathematical Optimization Analysis," Noble International Journal of Economics and Financial Research, Noble Academic Publsiher, vol. 2(2), pages 27-49, February.
    21. 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.
    22. Yu Yu & Weiwei Zhu & Qian Zhang, 2019. "DEA cross-efficiency evaluation and ranking method based on interval data," Annals of Operations Research, Springer, vol. 278(1), pages 159-175, July.
    23. Bogetoft, Peter, 1999. "Process Aggregation and Efficiency," Unit of Economics Working Papers 24190, Royal Veterinary and Agricultural University, Food and Resource Economic Institute.

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