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Solving the Discrete Multiple Criteria Problem using Convex Cones

Author

Listed:
  • 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)

Abstract

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.

Suggested Citation

  • Pekka Korhonen & Jyrki Wallenius & Stanley Zionts, 1984. "Solving the Discrete Multiple Criteria Problem using Convex Cones," Management Science, INFORMS, vol. 30(11), pages 1336-1345, November.
    • Handle: RePEc:inm:ormnsc:v:30:y:1984:i:11:p:1336-1345
    DOI: 10.1287/mnsc.30.11.1336
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