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A branch-and-price algorithm for the two-dimensional vector packing problem with piecewise linear cost function

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  • Hu, Qian
  • Zhu, Wenbin
  • Qin, Hu
  • Lim, Andrew

Abstract

The two-dimensional vector packing problem with piecewise linear cost function (2DVPP-PLC) models a practical packing problem faced by many companies that use courier services. We propose a branch-and-price algorithm to solve the 2DVPP-PLC exactly. The column generation procedure is a key component that affects the performance of a branch-and-price algorithm. The pricing problem exhibits an interesting structure that allows us to decompose it into subproblems that form a lattice. We explore dominance relations on the lattice and design an efficient algorithm for the pricing problem. Experimental results show that our branch-and-price algorithm is capable of solving 2DVPP-PLC test instances effectively.

Suggested Citation

  • Hu, Qian & Zhu, Wenbin & Qin, Hu & Lim, Andrew, 2017. "A branch-and-price algorithm for the two-dimensional vector packing problem with piecewise linear cost function," European Journal of Operational Research, Elsevier, vol. 260(1), pages 70-80.
    • Handle: RePEc:eee:ejores:v:260:y:2017:i:1:p:70-80
    DOI: 10.1016/j.ejor.2016.12.021
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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. Zhen, Lu & Wang, Kai & Wang, Shuaian & Qu, Xiaobo, 2018. "Tug scheduling for hinterland barge transport: A branch-and-price approach," European Journal of Operational Research, Elsevier, vol. 265(1), pages 119-132.
    3. Katrin Heßler & Timo Gschwind & Stefan Irnich, 2017. "Stabilized Branch-and-Price Algorithms for Vector Packing Problems," Working Papers 1713, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    4. 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.
    5. Heßler, Katrin & Gschwind, Timo & Irnich, Stefan, 2018. "Stabilized branch-and-price algorithms for vector packing problems," European Journal of Operational Research, Elsevier, vol. 271(2), pages 401-419.

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