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Cardinality constrained bin‐packing problems

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  • H. Kellerer
  • U. Pferschy

Abstract

We are concerned with a variant of the classical one‐dimensionalbin‐packing problem. n items have to be packed into unit‐capacity bins such that the total number of used bins isminimized with the additional constraint that at most k items can beassigned to one bin. In 1975, Krause et al. analyzed several approximation algorithms forthis problem and showed that they all have an asymptotic worst‐case performance ratioof 2. No better algorithms have been found so far. We present a new heuristic with anasymptotic worst-case bound of 3/2 and O(n log 2 n)running time. Copyright Kluwer Academic Publishers 1999

Suggested Citation

  • H. Kellerer & U. Pferschy, 1999. "Cardinality constrained bin‐packing problems," Annals of Operations Research, Springer, vol. 92(0), pages 335-348, January.
    • Handle: RePEc:spr:annopr:v:92:y:1999:i:0:p:335-348:10.1023/a:1018947117526
    DOI: 10.1023/A:1018947117526
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    Cited by:

    1. Hiroshi Fujiwara & Koji Kobayashi, 2015. "Improved lower bounds for the online bin packing problem with cardinality constraints," Journal of Combinatorial Optimization, Springer, vol. 29(1), pages 67-87, January.
    2. Borja Ena & Alberto Gomez & Borja Ponte & Paolo Priore & Diego Diaz, 2022. "Homogeneous grouping of non-prime steel products for online auctions: a case study," Annals of Operations Research, Springer, vol. 315(1), pages 591-621, August.
    3. Marc Peeters & Zeger Degraeve, 2004. "The Co-Printing Problem: A Packing Problem with a Color Constraint," Operations Research, INFORMS, vol. 52(4), pages 623-638, August.
    4. Jaykrishnan, G. & Levin, Asaf, 2024. "Scheduling with cardinality dependent unavailability periods," European Journal of Operational Research, Elsevier, vol. 316(2), pages 443-458.
    5. Burke, E.K. & Landa Silva, J.D., 2006. "The influence of the fitness evaluation method on the performance of multiobjective search algorithms," European Journal of Operational Research, Elsevier, vol. 169(3), pages 875-897, March.

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