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A New Branch-and-Price-and-Cut Algorithm for One-Dimensional Bin-Packing Problems

Author

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  • Lijun Wei

    (Key Laboratory of Computer Integrated Manufacturing System, School of Electromechanical Engineering, Guangdong University of Technology, 510006 Guangzhou, People's Republic of China)

  • Zhixing Luo,

    (School of Management and Engineering, Nanjing University, 210093 Nanjing, People’s Republic of China;)

  • Roberto Baldacci

    (Department of Industrial Systems Engineering and Management, National University of Singapore, Singapore 119077)

  • Andrew Lim

    (Department of Electrical, Electronic, and Information Engineering "Guglielmo Marconi," University of Bologna, 47521 Cesena, Italy)

Abstract

In this paper, a new branch-and-price-and-cut algorithm is proposed to solve the one-dimensional bin-packing problem (1D-BPP). The 1D-BPP is one of the most fundamental problems in combinatorial optimization and has been extensively studied for decades. Recently, a set of new 500 test instances were proposed for the 1D-BPP, and the best exact algorithm proposed in the literature can optimally solve 167 of these new instances, with a time limit of 1 hour imposed on each execution of the algorithm. The exact algorithm proposed in this paper is based on the classical set-partitioning model for the 1DBPPs and the subset row inequalities. We describe an ad hoc label-setting algorithm to solve the pricing problem, dominance, and fathoming rules to speed up its computation and a new primal heuristic. The exact algorithm can easily handle some practical constraints, such as the incompatibility between the items, and therefore, we also apply it to solve the one-dimensional bin-packing problem with conflicts (1D-BPPC). The proposed method is tested on a large family of 1D-BPP and 1D-BPPC classes of instances. For the 1D-BPP, the proposed method can optimally solve 237 instances of the new set of difficult instances; the largest instance involves 1,003 items and bins of capacity 80,000. For the 1D-BPPC, the experiments show that the method is highly competitive with state-of-the-art methods and that it successfully closed several open 1D-BPPC instances.

Suggested Citation

  • Lijun Wei & Zhixing Luo, & Roberto Baldacci & Andrew Lim, 2020. "A New Branch-and-Price-and-Cut Algorithm for One-Dimensional Bin-Packing Problems," INFORMS Journal on Computing, INFORMS, vol. 32(2), pages 428-443, April.
    • Handle: RePEc:inm:orijoc:v:32:y:2020:i:2:p:428-443
    DOI: 10.1287/ijoc.2018.0867
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    References listed on IDEAS

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