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Use of Piecewise Linear Value Functions in Interactive Multicriteria Decision Support: A Monte Carlo Study

Author

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  • Theodor J. Stewart

    (Department of Statistical Sciences, University of Cape Town, Rondebosch 7700, South Africa)

Abstract

This paper describes a Monte Carlo study conducted to evaluate the effects of modelling assumptions and design parameters on the behaviour of interactive methods for the discrete choice MCDM problem, based on explicit value function models. The purpose of the study is to identify those assumptions and parameters which lead to the most efficient use of preference judgements made by the decision maker, and to the greatest robustness to judgmental errors. It is concluded that nonlinearities in the value function need to be modelled, achieved here by use of a piecewise linear form. It was also found that search for indifference points, rather than using simple preference judgements alone, is of great advantage, best realized by expressing judgements in terms of pairwise trade-offs. Methods incorporating these features are highly robust to judgmental errors. Interactive methods of this class are compared with a priori fitting of similar value functions, and found to give a very similar quality of solution.

Suggested Citation

  • Theodor J. Stewart, 1993. "Use of Piecewise Linear Value Functions in Interactive Multicriteria Decision Support: A Monte Carlo Study," Management Science, INFORMS, vol. 39(11), pages 1369-1381, November.
    • Handle: RePEc:inm:ormnsc:v:39:y:1993:i:11:p:1369-1381
    DOI: 10.1287/mnsc.39.11.1369
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    Citations

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    Cited by:

    1. Ron Janssen & Marjan van Herwijnen & Theodor J Stewart & Jeroen C J H Aerts, 2008. "Multiobjective Decision Support for Land-Use Planning," Environment and Planning B, , vol. 35(4), pages 740-756, August.
    2. Lahdelma, Risto & Salminen, Pekka, 2009. "Prospect theory and stochastic multicriteria acceptability analysis (SMAA)," Omega, Elsevier, vol. 37(5), pages 961-971, October.
    3. Menou, Abdellah & Benallou, Abdelhanine & Lahdelma, Risto & Salminen, Pekka, 2010. "Decision support for centralizing cargo at a Moroccan airport hub using stochastic multicriteria acceptability analysis," European Journal of Operational Research, Elsevier, vol. 204(3), pages 621-629, August.
    4. Stewart, Theodor J. & Losa, Fabio B., 2003. "Towards reconciling outranking and value measurement practice," European Journal of Operational Research, Elsevier, vol. 145(3), pages 645-659, March.
    5. Durbach, Ian N. & Stewart, Theodor J., 2009. "Using expected values to simplify decision making under uncertainty," Omega, Elsevier, vol. 37(2), pages 312-330, April.
    6. Mats Danielson & Love Ekenberg, 2017. "A Robustness Study of State-of-the-Art Surrogate Weights for MCDM," Group Decision and Negotiation, Springer, vol. 26(4), pages 677-691, July.
    7. Doumpos, Michael & Zopounidis, Constantin & Galariotis, Emilios, 2014. "Inferring robust decision models in multicriteria classification problems: An experimental analysis," European Journal of Operational Research, Elsevier, vol. 236(2), pages 601-611.
    8. de Almeida Filho, Adiel T. & Clemente, Thárcylla R.N. & Morais, Danielle Costa & de Almeida, Adiel Teixeira, 2018. "Preference modeling experiments with surrogate weighting procedures for the PROMETHEE method," European Journal of Operational Research, Elsevier, vol. 264(2), pages 453-461.
    9. Mats Danielson & Love Ekenberg, 2016. "The CAR Method for Using Preference Strength in Multi-criteria Decision Making," Group Decision and Negotiation, Springer, vol. 25(4), pages 775-797, July.

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