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Note---Ordinal Ranking and Intensity of Preference: A Linear Programming Approach

Author

Listed:
  • Iqbal Ali

    (Department of General Business, University of Texas, Austin, Texas 78712)

  • Wade D. Cook

    (Faculty of Administrative Studies, York University, Toronto, Ontario, Canada M3J 2R6)

  • Moshe Kress

    (CEMA, P.O. Box 2250, Haifa, Israel)

Abstract

Cook and Kress (Cook, Wade D., Moshe Kress. 1985. Ordinal ranking with intensity of preference. Management Sci. 31 (1) 26--32.) present a model for representing ordinal preference rankings, where the voter can express intensity or degree of preference. The consensus of a set of m rankings is that ranking whose distance from this set is minimal. The consensus problem is then shown to be an integer programming problem with a piecewise linear convex objective function. In the present note we prove that the constraint matrix for this integer problem is totally unimodular. In addition, it is shown that the problem can be expressed as an equivalent integer linear programming problem. These two facts allow us to represent the consensus problem as a linear programming model. To further facilitate an efficient solution procedure to the consensus problem, it is shown that the number of columns in the L.P. model can generally be reduced significantly. Computational results on a wide range of problems is presented.

Suggested Citation

  • Iqbal Ali & Wade D. Cook & Moshe Kress, 1986. "Note---Ordinal Ranking and Intensity of Preference: A Linear Programming Approach," Management Science, INFORMS, vol. 32(12), pages 1642-1647, December.
    • Handle: RePEc:inm:ormnsc:v:32:y:1986:i:12:p:1642-1647
    DOI: 10.1287/mnsc.32.12.1642
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    Cited by:

    1. Juan Carlos Leyva-López, 2024. "A consistency and consensus model for group decision support based on the outranking approach," Operational Research, Springer, vol. 24(2), pages 1-29, June.
    2. Ahmed Ghoniem & Agha Iqbal Ali & Mohammed Al-Salem & Wael Khallouli, 2017. "Prescriptive analytics for FIFA World Cup lodging capacity planning," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(10), pages 1183-1194, October.
    3. Dorit S. Hochbaum & Asaf Levin, 2006. "Methodologies and Algorithms for Group-Rankings Decision," Management Science, INFORMS, vol. 52(9), pages 1394-1408, September.
    4. Malcolm J. Beynon, 2006. "The Role of the DS/AHP in Identifying Inter-Group Alliances and Majority Rule Within Group Decision Making," Group Decision and Negotiation, Springer, vol. 15(1), pages 21-42, January.
    5. Tavana, M. & Kennedy, D. T. & Joglekar, P., 1996. "A group decision support framework for consensus ranking of technical manager candidates," Omega, Elsevier, vol. 24(5), pages 523-538, October.

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