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An interactive MCDM weight space reduction method utilizing a tchebycheff utility function

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  • Robert F. Dell
  • Mark H. Karwan

Abstract

Employing a Tchebycheff utility function to locally approximate the underlying utility function, we develop an interactive method to solve multiple‐objective linear programming problems involving a single decision maker. We utilize selected and consistent weights in an augmented Tchebycheff linear programming formulation to obtain nondominated alternatives. Based on pairwise comparisons between alternatives, we generate constraints on the weights used to combine the decision maker's objectives. The constraints, formed to be consistent with a Tchebycheff function, lead to multiple disjoint convex regions in weight space. An algorithm is presented, and its performance is compared to the Zionts‐Walenius method for various true underlying utility functions.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:37:y:1990:i:2:p:263-277
    DOI: 10.1002/1520-6750(199004)37:23.0.CO;2-6
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Murat Köksalan & Mark H. Karwan & Stanley Zionts, 1988. "An approach for solving discrete alternative multiple criteria problems involving ordinal criteria," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(6), pages 625-641, December.
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    Cited by:

    1. 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.
    2. Sun, Minghe, 2005. "Some issues in measuring and reporting solution quality of interactive multiple objective programming procedures," European Journal of Operational Research, Elsevier, vol. 162(2), pages 468-483, April.
    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. Bilge Bozkurt & John W. Fowler & Esma S. Gel & Bosun Kim & Murat Köksalan & Jyrki Wallenius, 2010. "Quantitative Comparison of Approximate Solution Sets for Multicriteria Optimization Problems with Weighted Tchebycheff Preference Function," Operations Research, INFORMS, vol. 58(3), pages 650-659, June.
    5. Karakaya, G. & Köksalan, M., 2023. "Finding preferred solutions under weighted Tchebycheff preference functions for multi-objective integer programs," European Journal of Operational Research, Elsevier, vol. 308(1), pages 215-228.
    6. Karakaya, G. & Köksalan, M., 2021. "Evaluating solutions and solution sets under multiple objectives," European Journal of Operational Research, Elsevier, vol. 294(1), pages 16-28.

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