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Solving the Discrete Multiple Criteria Problem using Convex Cones


Author Info

  • Pekka Korhonen

    (Helsinki School of Economics and Business Administration, Runeberginkatu 14-16, 00100 Helsinki, Finland)

  • Jyrki Wallenius

    (Department of Economics and Management, University of Jyvaskyla, Jyvaskyla, Finland)

  • Stanley Zionts

    (School of Management, State University of New York, Buffalo, New York 14214)


An interactive method employing pairwise comparisons of attainable solutions is developed for solving the discrete, deterministic multiple criteria problem assuming a single decision maker who has an implicit quasi-concave increasing utility (or value) function. The method chooses an arbitrary set of positive multipliers to generate a proxy composite linear objective function which is then maximized over the set of solutions. The maximizing solution is compared with several solutions using pairwise judgments asked of the decision maker. Responses are used to eliminate alternatives using convex cones based on expressed preferences, and then a new set of weights is found that satisfies the indicated preferences. The requisite theory and proofs as well as a detailed numerical example are included. In addition, the results of some computational experiments to test the effectiveness of the method are described.

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Bibliographic Info

Article provided by INFORMS in its journal Management Science.

Volume (Year): 30 (1984)
Issue (Month): 11 (November)
Pages: 1336-1345

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Handle: RePEc:inm:ormnsc:v:30:y:1984:i:11:p:1336-1345

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Keywords: decision analysis; utility/preference: multiattribute; programming: multiple criteria; convex cones;


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Cited by:
  1. Moshkovich, Helen M. & Mechitov, Alexander I. & Olson, David L., 2002. "Ordinal judgments in multiattribute decision analysis," European Journal of Operational Research, Elsevier, vol. 137(3), pages 625-641, March.
  2. Kallio, Markku & Halme, Merja, 2013. "Cone contraction and reference point methods for multi-criteria mixed integer optimization," European Journal of Operational Research, Elsevier, vol. 229(3), pages 645-653.
  3. Vetschera, Rudolf, 2000. "A multi-criteria agency model with incomplete preference information," European Journal of Operational Research, Elsevier, vol. 126(1), pages 152-165, October.
  4. Ringuest, Jeffrey L. & Graves, Samuel B., 2000. "A sampling-based method for generating nondominated solutions in stochastic MOMP problems," European Journal of Operational Research, Elsevier, vol. 126(3), pages 651-661, November.
  5. Huang, Zhimin & Li, Susan X. & Raghavan, Veeravalli & Bruce Sun, D., 1995. "Proper efficiency and cardinal utilities in multicriteria decision making," European Journal of Operational Research, Elsevier, vol. 82(3), pages 476-489, May.
  6. 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.
  7. Koksalan, Murat & Ulu, Canan, 2003. "An interactive approach for placing alternatives in preference classes," European Journal of Operational Research, Elsevier, vol. 144(2), pages 429-439, January.
  8. Vetschera, Rudolf, 1992. "Estimating preference cones from discrete choices: Computational techniques and experiences," Discussion Papers, Series 1 259, University of Konstanz, Department of Economics.
  9. Nowak, Maciej, 2007. "Aspiration level approach in stochastic MCDM problems," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1626-1640, March.
  10. Sun, Minghe & Steuer, Ralph E., 1996. "InterQuad: An interactive quad tree based procedure for solving the discrete alternative multiple criteria problem," European Journal of Operational Research, Elsevier, vol. 89(3), pages 462-472, March.
  11. Lee, Dong-Hee & Kim, Kwang-Jae & Köksalan, Murat, 2011. "A posterior preference articulation approach to multiresponse surface optimization," European Journal of Operational Research, Elsevier, vol. 210(2), pages 301-309, April.
  12. P. Korhonen & J. Karaivanova, 1998. "An Algorithm for Projecting a Reference Direction onto the Nondominated Set of Given Points," Working Papers ir98011, International Institute for Applied Systems Analysis.


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