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Use of Convex Cones in Interactive Multiple Objective Decision Making

Author

Listed:
  • Srinivas Y. Prasad

    (Department of Management Science, The George Washington University, Washington, DC 20052)

  • Mark H. Karwan

    (Department of Industrial Engineering, SUNY at Buffalo, Buffalo, New York 14260)

  • Stanley Zionts

    (Department of Management Science and Systems, SUNY at Buffalo, Buffalo, New York 14260)

Abstract

One approach for solving decision problems involving multiple objectives is interactive optimization. Methods based on this approach assess the decision maker's preference structure interactively, typically based on pairwise comparisons and tradeoffs, and guide the search process toward identifying improved solutions. A desirable feature of such approaches, that is based on minimizing the preference information requirements, is fast convergence. Toward this end, the use of convex cones as a preference structure representation has been proposed in the literature. In this work, new theory is developed that aids in further reducing preference information requirements and improving convergence. New cones termed p cones are developed. The efficiencies of solution alternatives are evaluated with respect to the p cones, and these are termed p cone efficiencies. Acceleration and Early Termination procedures that are based on these efficiencies are proposed. The procedures are presented within a solution framework for solving Multiple Objective Linear Programming (MOLP) problems along with computational results.

Suggested Citation

  • Srinivas Y. Prasad & Mark H. Karwan & Stanley Zionts, 1997. "Use of Convex Cones in Interactive Multiple Objective Decision Making," Management Science, INFORMS, vol. 43(5), pages 723-734, May.
    • Handle: RePEc:inm:ormnsc:v:43:y:1997:i:5:p:723-734
    DOI: 10.1287/mnsc.43.5.723
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    Citations

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    Cited by:

    1. Pekka Korhonen & Majid Soleimani-damaneh & Jyrki Wallenius, 2017. "The use of quasi-concave value functions in MCDM: some theoretical results," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(2), pages 367-375, October.
    2. Banu Lokman & Murat Köksalan & Pekka J. Korhonen & Jyrki Wallenius, 2016. "An interactive algorithm to find the most preferred solution of multi-objective integer programs," Annals of Operations Research, Springer, vol. 245(1), pages 67-95, October.
    3. M Köksalan & E Karasakal, 2006. "An interactive approach for multiobjective decision making," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(5), pages 532-540, May.
    4. Nikolaos Argyris & Alec Morton & José Rui Figueira, 2014. "CUT: A Multicriteria Approach for Concavifiable Preferences," Operations Research, INFORMS, vol. 62(3), pages 633-642, June.
    5. Lahdelma, Risto & Salminen, Pekka & Kuula, Markku, 2003. "Testing the efficiency of two pairwise comparison methods in discrete multiple criteria problems," European Journal of Operational Research, Elsevier, vol. 145(3), pages 496-508, March.
    6. Korhonen, Pekka & Soleimani-damaneh, Majid & Wallenius, Jyrki, 2016. "Dual cone approach to convex-cone dominance in multiple criteria decision making," European Journal of Operational Research, Elsevier, vol. 249(3), pages 1139-1143.
    7. Peter Reichert & Klemens Niederberger & Peter Rey & Urs Helg & Susanne Haertel-Borer, 2019. "The need for unconventional value aggregation techniques: experiences from eliciting stakeholder preferences in environmental management," EURO Journal on Decision Processes, Springer;EURO - The Association of European Operational Research Societies, vol. 7(3), pages 197-219, November.
    8. Nasim Nasrabadi & Akram Dehnokhalaji & Pekka Korhonen & Jyrki Wallenius, 2019. "Using convex preference cones in multiple criteria decision making and related fields," Journal of Business Economics, Springer, vol. 89(6), pages 699-717, August.
    9. Engau, Alexander, 2009. "Tradeoff-based decomposition and decision-making in multiobjective programming," European Journal of Operational Research, Elsevier, vol. 199(3), pages 883-891, December.

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