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The binary knapsack problem with qualitative levels

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  • Schäfer, Luca E.
  • Dietz, Tobias
  • Barbati, Maria
  • Figueira, José Rui
  • Greco, Salvatore
  • Ruzika, Stefan

Abstract

A variant of the classical knapsack problem is considered in which each item is associated with an integer weight and a qualitative level. We define a dominance relation over the feasible subsets of the given item set and show that this relation defines a preorder. We propose a dynamic programming algorithm to compute the entire set of non-dominated rank cardinality vectors and we state two greedy algorithms, which efficiently compute a single efficient solution.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:289:y:2021:i:2:p:508-514
    DOI: 10.1016/j.ejor.2020.07.040
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    References listed on IDEAS

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    1. 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.
    2. Sbihi, Abdelkader, 2010. "A cooperative local search-based algorithm for the Multiple-Scenario Max-Min Knapsack Problem," European Journal of Operational Research, Elsevier, vol. 202(2), pages 339-346, April.
    3. Liesiö, Juuso & Mild, Pekka & Salo, Ahti, 2008. "Robust portfolio modeling with incomplete cost information and project interdependencies," European Journal of Operational Research, Elsevier, vol. 190(3), pages 679-695, November.
    4. Lin, Feng-Tse, 2008. "Solving the knapsack problem with imprecise weight coefficients using genetic algorithms," European Journal of Operational Research, Elsevier, vol. 185(1), pages 133-145, February.
    5. Liesio, Juuso & Mild, Pekka & Salo, Ahti, 2007. "Preference programming for robust portfolio modeling and project selection," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1488-1505, September.
    6. Julie Stal-Le Cardinal & Vincent Mousseau & Jun Zheng, 2011. "An Application of Constrained Multicriteria Sorting to Student Selection," International Series in Operations Research & Management Science, in: Ahti Salo & Jeffrey Keisler & Alec Morton (ed.), Portfolio Decision Analysis, chapter 0, pages 213-240, Springer.
    7. Lin, Feng-Tse & Yao, Jing-Shing, 2001. "Using fuzzy numbers in knapsack problems," European Journal of Operational Research, Elsevier, vol. 135(1), pages 158-176, November.
    8. Lahdelma, Risto & Miettinen, Kaisa & Salminen, Pekka, 2003. "Ordinal criteria in stochastic multicriteria acceptability analysis (SMAA)," European Journal of Operational Research, Elsevier, vol. 147(1), pages 117-127, May.
    9. Wang, Jue & Xu, Wei & Ma, Jian & Wang, Shouyang, 2013. "A vague set based decision support approach for evaluating research funding programs," European Journal of Operational Research, Elsevier, vol. 230(3), pages 656-665.
    10. Kasperski, Adam & Zielinski, Pawel, 2010. "Minmax regret approach and optimality evaluation in combinatorial optimization problems with interval and fuzzy weights," European Journal of Operational Research, Elsevier, vol. 200(3), pages 680-687, February.
    11. Barbati, Maria & Greco, Salvatore & Kadziński, Miłosz & Słowiński, Roman, 2018. "Optimization of multiple satisfaction levels in portfolio decision analysis," Omega, Elsevier, vol. 78(C), pages 192-204.
    12. Ralph L. Keeney & Timothy L. McDaniels, 1999. "Identifying and Structuring Values to Guide Integrated Resource Planning at BC Gas," Operations Research, INFORMS, vol. 47(5), pages 651-662, October.
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    Cited by:

    1. Beliakov, Gleb, 2022. "Knapsack problems with dependencies through non-additive measures and Choquet integral," European Journal of Operational Research, Elsevier, vol. 301(1), pages 277-286.

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