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Notes on ‘Hit-And-Run enables efficient weight generation for simulation-based multiple criteria decision analysis’

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  • van Valkenhoef, Gert
  • Tervonen, Tommi
  • Postmus, Douwe

Abstract

In our previous work published in this journal, we showed how the Hit-And-Run (HAR) procedure enables efficient sampling of criteria weights from a space formed by restricting a simplex with arbitrary linear inequality constraints. In this short communication, we note that the method for generating a basis of the sampling space can be generalized to also handle arbitrary linear equality constraints. This enables the application of HAR to sampling spaces that do not coincide with the simplex, thereby allowing the combined use of imprecise and precise preference statements. In addition, it has come to our attention that one of the methods we proposed for generating a starting point for the Markov chain was flawed. To correct this, we provide an alternative method that is guaranteed to produce a starting point that lies within the interior of the sampling space.

Suggested Citation

  • van Valkenhoef, Gert & Tervonen, Tommi & Postmus, Douwe, 2014. "Notes on ‘Hit-And-Run enables efficient weight generation for simulation-based multiple criteria decision analysis’," European Journal of Operational Research, Elsevier, vol. 239(3), pages 865-867.
    • Handle: RePEc:eee:ejores:v:239:y:2014:i:3:p:865-867
    DOI: 10.1016/j.ejor.2014.06.036
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    References listed on IDEAS

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    1. Tervonen, Tommi & Lahdelma, Risto, 2007. "Implementing stochastic multicriteria acceptability analysis," European Journal of Operational Research, Elsevier, vol. 178(2), pages 500-513, April.
    2. Kadziński, Miłosz & Tervonen, Tommi, 2013. "Robust multi-criteria ranking with additive value models and holistic pair-wise preference statements," European Journal of Operational Research, Elsevier, vol. 228(1), pages 169-180.
    3. Robert L. Smith, 1984. "Efficient Monte Carlo Procedures for Generating Points Uniformly Distributed over Bounded Regions," Operations Research, INFORMS, vol. 32(6), pages 1296-1308, December.
    4. Greco, Salvatore & Mousseau, Vincent & Slowinski, Roman, 2008. "Ordinal regression revisited: Multiple criteria ranking using a set of additive value functions," European Journal of Operational Research, Elsevier, vol. 191(2), pages 416-436, December.
    5. Kadziński, Miłosz & Greco, Salvatore & Słowiński, Roman, 2012. "Selection of a representative value function in robust multiple criteria ranking and choice," European Journal of Operational Research, Elsevier, vol. 217(3), pages 541-553.
    6. Tervonen, Tommi & van Valkenhoef, Gert & Baştürk, Nalan & Postmus, Douwe, 2013. "Hit-And-Run enables efficient weight generation for simulation-based multiple criteria decision analysis," European Journal of Operational Research, Elsevier, vol. 224(3), pages 552-559.
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    Cited by:

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    2. Vetschera, Rudolf, 2017. "Deriving rankings from incomplete preference information: A comparison of different approaches," European Journal of Operational Research, Elsevier, vol. 258(1), pages 244-253.
    3. Luca Anzilli & Silvio Giove, 2020. "Multi-criteria and medical diagnosis for application to health insurance systems: a general approach through non-additive measures," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(2), pages 559-582, December.
    4. Durbach, Ian N. & Calder, Jon M., 2016. "Modelling uncertainty in stochastic multicriteria acceptability analysis," Omega, Elsevier, vol. 64(C), pages 13-23.
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    7. Liu, Jiapeng & Liao, Xiuwu & Huang, Wei & Liao, Xianzhao, 2019. "Market segmentation: A multiple criteria approach combining preference analysis and segmentation decision," Omega, Elsevier, vol. 83(C), pages 1-13.
    8. Angilella, Silvia & Corrente, Salvatore & Greco, Salvatore & Słowiński, Roman, 2016. "Robust Ordinal Regression and Stochastic Multiobjective Acceptability Analysis in multiple criteria hierarchy process for the Choquet integral preference model," Omega, Elsevier, vol. 63(C), pages 154-169.
    9. Corrente, Salvatore & Figueira, José Rui & Greco, Salvatore & Słowiński, Roman, 2017. "A robust ranking method extending ELECTRE III to hierarchy of interacting criteria, imprecise weights and stochastic analysis," Omega, Elsevier, vol. 73(C), pages 1-17.
    10. Corrente, S. & Figueira, J.R. & Greco, S., 2021. "Pairwise comparison tables within the deck of cards method in multiple criteria decision aiding," European Journal of Operational Research, Elsevier, vol. 291(2), pages 738-756.
    11. van Valkenhoef, Gert & Tervonen, Tommi, 2016. "Entropy-optimal weight constraint elicitation with additive multi-attribute utility models," Omega, Elsevier, vol. 64(C), pages 1-12.
    12. Ciomek, Krzysztof & Kadziński, Miłosz & Tervonen, Tommi, 2017. "Heuristics for prioritizing pair-wise elicitation questions with additive multi-attribute value models," Omega, Elsevier, vol. 71(C), pages 27-45.
    13. Costa, Ana Sara & Corrente, Salvatore & Greco, Salvatore & Figueira, José Rui & Borbinha, José, 2020. "A robust hierarchical nominal multicriteria classification method based on similarity and dissimilarity," European Journal of Operational Research, Elsevier, vol. 286(3), pages 986-1001.

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