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Shortest paths with ordinal weights

Author

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  • Schäfer, Luca E.
  • Dietz, Tobias
  • Fröhlich, Nicolas
  • Ruzika, Stefan
  • Figueira, José R.

Abstract

We investigate the single-source-single-destination “shortest” path problem in directed, acyclic graphs with ordinal weighted arc costs. We define the concepts of ordinal dominance and efficiency for paths and their associated ordinal levels, respectively. Further, we show that the number of ordinally non-dominated path vectors from the source node to every other node in the graph is polynomially bounded and we propose a polynomial time labeling algorithm for solving the problem of finding the set of ordinally non-dominated path vectors from source to sink.

Suggested Citation

  • Schäfer, Luca E. & Dietz, Tobias & Fröhlich, Nicolas & Ruzika, Stefan & Figueira, José R., 2020. "Shortest paths with ordinal weights," European Journal of Operational Research, Elsevier, vol. 280(3), pages 1160-1170.
    • Handle: RePEc:eee:ejores:v:280:y:2020:i:3:p:1160-1170
    DOI: 10.1016/j.ejor.2019.08.008
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    Cited by:

    1. Klamroth, Kathrin & Stiglmayr, Michael & Sudhoff, Julia, 2023. "Ordinal optimization through multi-objective reformulation," European Journal of Operational Research, Elsevier, vol. 311(2), pages 427-443.
    2. Schäfer, Luca E. & Dietz, Tobias & Barbati, Maria & Figueira, José Rui & Greco, Salvatore & Ruzika, Stefan, 2021. "The binary knapsack problem with qualitative levels," European Journal of Operational Research, Elsevier, vol. 289(2), pages 508-514.

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