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A branch-and-price algorithm for the two-dimensional vector packing problem

Author

Listed:
  • Wei, Lijun
  • Lai, Minghui
  • Lim, Andrew
  • Hu, Qian

Abstract

The two-dimensional vector packing problem is a well-known generalization of the classical bin packing problem. It considers two attributes for each item and bin. Two capacity constraints must be satisfied in a feasible packing solution for each bin. The objective is to minimize the number of bins used. To compute optimal solutions for the problem, we propose a new branch-and-price algorithm. A goal cut that sets a lower bound to the objective is used. It is effective in speeding up column generation by reducing the number of iterations. To efficiently solve the pricing problem, we develop a branch-and-bound method with dynamic programming, which first eliminates conflicts between two items through branching, and then solves the two-constraint knapsack problem at leaf nodes through dynamic programming. Extensive computational experiments were conducted based on 400 test instances from existing literature. Our algorithm significantly outperformed the existing branch-and-price algorithms. Most of the test instances were solved within just a few seconds.

Suggested Citation

  • Wei, Lijun & Lai, Minghui & Lim, Andrew & Hu, Qian, 2020. "A branch-and-price algorithm for the two-dimensional vector packing problem," European Journal of Operational Research, Elsevier, vol. 281(1), pages 25-35.
    • Handle: RePEc:eee:ejores:v:281:y:2020:i:1:p:25-35
    DOI: 10.1016/j.ejor.2019.08.024
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    Cited by:

    1. Haouari, Mohamed & Mhiri, Mariem, 2024. "Lower and upper bounding procedures for the bin packing problem with concave loading cost," European Journal of Operational Research, Elsevier, vol. 312(1), pages 56-69.
    2. Wang, Ting & Hu, Qian & Lim, Andrew, 2022. "An exact algorithm for two-dimensional vector packing problem with volumetric weight and general costs," European Journal of Operational Research, Elsevier, vol. 300(1), pages 20-34.
    3. Artur Pessoa & Ruslan Sadykov & Eduardo Uchoa, 2021. "Solving Bin Packing Problems Using VRPSolver Models," SN Operations Research Forum, Springer, vol. 2(2), pages 1-25, June.
    4. Katrin Heßler & Stefan Irnich & Tobias Kreiter & Ulrich Pferschy, 2020. "Lexicographic Bin-Packing Optimization for Loading Trucks in a Direct-Shipping System," Working Papers 2009, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.

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