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New lower bounds for bin packing problems with conflicts

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  • Khanafer, Ali
  • Clautiaux, François
  • Talbi, El-Ghazali

Abstract

The bin packing problem with conflicts (BPC) consists of minimizing the number of bins used to pack a set of items, where some items cannot be packed together in the same bin due to compatibility restrictions. The concepts of dual-feasible functions (DFF) and data-dependent dual-feasible functions (DDFF) have been used in the literature to improve the resolution of several cutting and packing problems. In this paper, we propose a general framework for deriving new DDFF as well as a new concept of generalized data-dependent dual-feasible functions (GDDFF), a conflict generalization of DDFF. The GDDFF take into account the structure of the conflict graph using the techniques of graph triangulation and tree-decomposition. Then we show how these techniques can be used in order to improve the existing lower bounds.

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  • Khanafer, Ali & Clautiaux, François & Talbi, El-Ghazali, 2010. "New lower bounds for bin packing problems with conflicts," European Journal of Operational Research, Elsevier, vol. 206(2), pages 281-288, October.
    • Handle: RePEc:eee:ejores:v:206:y:2010:i:2:p:281-288
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    References listed on IDEAS

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    Cited by:

    1. Liao, Chung-Shou & Hsu, Chia-Hong, 2013. "New lower bounds for the three-dimensional orthogonal bin packing problem," European Journal of Operational Research, Elsevier, vol. 225(2), pages 244-252.
    2. Kartak, Vadim M. & Ripatti, Artem V., 2018. "The minimum raster set problem and its application to the d-dimensional orthogonal packing problem," European Journal of Operational Research, Elsevier, vol. 271(1), pages 33-39.
    3. Bayliss, Christopher & Currie, Christine S.M. & Bennell, Julia A. & Martinez-Sykora, Antonio, 2021. "Queue-constrained packing: A vehicle ferry case study," European Journal of Operational Research, Elsevier, vol. 289(2), pages 727-741.
    4. Renatha Capua & Yuri Frota & Luiz Satoru Ochi & Thibaut Vidal, 2018. "A study on exponential-size neighborhoods for the bin packing problem with conflicts," Journal of Heuristics, Springer, vol. 24(4), pages 667-695, August.
    5. Ekici, Ali, 2023. "A large neighborhood search algorithm and lower bounds for the variable-Sized bin packing problem with conflicts," European Journal of Operational Research, Elsevier, vol. 308(3), pages 1007-1020.
    6. Stefan Schwerdfeger & Nils Boysen & Dirk Briskorn, 2018. "Just-in-time logistics for far-distant suppliers: scheduling truck departures from an intermediate cross-docking terminal," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(1), pages 1-21, January.
    7. Mauro Dell'Amico & José Carlos Díaz Díaz & Manuel Iori, 2012. "The Bin Packing Problem with Precedence Constraints," Operations Research, INFORMS, vol. 60(6), pages 1491-1504, December.

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