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Interactive multicriteria linear programming: An extension of the method of Zionts and Wallenius

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  • R. Ramesh
  • Mark H. Karwan
  • Stanley Zionts

Abstract

This article presents an extension of the interactive multicriteria linear‐programming method of Zionts and Wallenius [see Management Science, 29(5) (1983)]. The decision maker's underlying utility function is assumed to be pseudoconcave, and his preference structure is assessed through pairwise comparison questions. In the method of Zionts and Wallenius, the decision maker's preference structure is represented as constraints on the weights on the objectives derived from his responses. This representation is only a linear approximation to the underlying nonlinear utility function. Accordingly, inconsistency among the constraints on the weights arises while solving the problem. Therefore, some of the constraints have to be dropped, resulting in a loss of information on the preference structure, and hence an increase in the total number of questions. In this article we develop a hybrid representation scheme to avoid this problem. The proposed scheme is implemented within the algorithmic framework of the method of Zionts and Wallenius, and its underlying theory is developed. Computational results show that the number of questions required by the Zionts and Wallenius method can be sinificantly reduced using the proposed scheme.

Suggested Citation

  • R. Ramesh & Mark H. Karwan & Stanley Zionts, 1989. "Interactive multicriteria linear programming: An extension of the method of Zionts and Wallenius," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(3), pages 321-335, June.
    • Handle: RePEc:wly:navres:v:36:y:1989:i:3:p:321-335
    DOI: 10.1002/1520-6750(198906)36:33.0.CO;2-F
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    References listed on IDEAS

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    1. Stanley Zionts & Jyrki Wallenius, 1980. "Identifying Efficient Vectors: Some Theory and Computational Results," Operations Research, INFORMS, vol. 28(3-part-ii), pages 785-793, June.
    2. Ramesh, R. & Zionts, Stanley & Karwan, Mark H., 1986. "A class of practical interactive branch and bound algorithms for multicriteria integer programming," European Journal of Operational Research, Elsevier, vol. 26(1), pages 161-172, July.
    3. 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.
    4. Steuer, Ralph E & Oliver, Richard L, 1976. "An application of multiple objective linear programming to media selection," Omega, Elsevier, vol. 4(4), pages 455-462.
    5. Gerald W. Evans, 1984. "An Overview of Techniques for Solving Multiobjective Mathematical Programs," Management Science, INFORMS, vol. 30(11), pages 1268-1282, November.
    6. Stanley Zionts & Jyrki Wallenius, 1983. "An Interactive Multiple Objective Linear Programming Method for a Class of Underlying Nonlinear Utility Functions," Management Science, INFORMS, vol. 29(5), pages 519-529, May.
    7. Ralph E. Steuer, 1976. "Multiple Objective Linear Programming with Interval Criterion Weights," Management Science, INFORMS, vol. 23(3), pages 305-316, November.
    8. Stanley Zionts & Jyrki Wallenius, 1976. "An Interactive Programming Method for Solving the Multiple Criteria Problem," Management Science, INFORMS, vol. 22(6), pages 652-663, February.
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    Cited by:

    1. Robert F. Dell & Mark H. Karwan, 1990. "An interactive MCDM weight space reduction method utilizing a tchebycheff utility function," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(2), pages 263-277, April.
    2. 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.

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