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Preference Structure Representation Using Convex Cones in Multicriteria Integer Programming

Author

Listed:
  • R. Ramesh

    (School of Management, State University of New York, Buffalo, New York 14260)

  • Mark H. Karwan

    (Department of Industrial Engineering, State University of New York, Buffalo, New York 14260)

  • Stanley Zionts

    (School of Management, State University of New York, Buffalo, New York 14260)

Abstract

A new efficient system of representing the decision-maker's preference structure in solving multicriteria integer programming problems is developed. The problem is solved by an interactive branch-and-bound method that employs the procedure of Zionts and Wallenius (Zionts, S., J. Wallenius. 1983. An interactive multiple objective linear programming method for a class of underlying nonlinear utility functions. Management Sci. 29(5).) for multicriteria linear programming. The decision-maker's underlying utility function is assumed to be pseudoconcave, and his pairwise comparisons of decision alternatives are used to determine his preference structure in terms of certain convex cones in the objective function space and constraints on the weights on the objectives in the weight space. The two forms of preference structure representation are interrelated, and their underlying theory is developed. The primary objective of a representation scheme is exactness, and, in this respect, it is shown that the constraints on the weights are not adequate for representing nonlinear utility functions. On the other hand, the convex cones exactly represent any quasiconcave utility function and clearly avoid the approximations and inaccuracies in other utility assessment systems. Accordingly, an efficient ordered representation using convex cones is developed. An algorithmic framework for multicriteria integer programming that integrates the representation using convex cones with the branch-and-bound solution procedure is developed. Computational experience with bicriteria problems having up to 80 variables and 40 constraints is presented.

Suggested Citation

  • R. Ramesh & Mark H. Karwan & Stanley Zionts, 1989. "Preference Structure Representation Using Convex Cones in Multicriteria Integer Programming," Management Science, INFORMS, vol. 35(9), pages 1092-1105, September.
  • Handle: RePEc:inm:ormnsc:v:35:y:1989:i:9:p:1092-1105
    DOI: 10.1287/mnsc.35.9.1092
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    Citations

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    Cited by:

    1. Karaivanova, Jasmina & Korhonen, Pekka & Narula, Subhash & Wallenius, Jyrki & Vassilev, Vassil, 1995. "A reference direction approach to multiple objective integer linear programming," European Journal of Operational Research, Elsevier, vol. 81(1), pages 176-187, February.
    2. Lotfi, Vahid, 1995. "Implementing flexible automation: A multiple criteria decision making approach," International Journal of Production Economics, Elsevier, vol. 38(2-3), pages 255-268, March.
    3. 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.
    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. Angur, Madhukar G. & Lotfi, Vahid & Sarkis, Joseph, 1996. "A hybrid conjoint measurement and bi-criteria model for a two group negotiation problem," Socio-Economic Planning Sciences, Elsevier, vol. 30(3), pages 195-206, September.
    6. 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.
    7. 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.
    8. Mavrotas, G. & Diakoulaki, D., 1998. "A branch and bound algorithm for mixed zero-one multiple objective linear programming," European Journal of Operational Research, Elsevier, vol. 107(3), pages 530-541, June.

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