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The two-dimensional vector packing problem with general costs

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  • Hu, Qian
  • Wei, Lijun
  • Lim, Andrew

Abstract

The two-dimensional vector packing problem with general costs (2DVPP-GC) arises in logistics where shipping items of different weight and volume are packed into cartons before being transported by a courier company. In practice, the delivery cost of a carton of items is usually retrieved from a cost table. The costs may not preserve any known mathematical function since it could specify arbitrary price at any possible weight. Such a general pricing scheme meets a majority of real-world bin packing applications, where the price of delivery service is determined by many complicated and correlated factors. Compared to the classical bin packing problem and its variants, the 2DVPP-GC is more complex and challenging. To solve the 2DVPP-GC with minimizing the total cost, we propose a memetic algorithm to compute solutions of high quality. Fitness functions and improved operators are proposed to achieve effectiveness. Computational experiments on a variety of test instances show that the algorithm is competent to solve the 2DVPP-GC. In particular, optimal solutions are found in a second for all the test instances that have a known optimal solution.

Suggested Citation

  • Hu, Qian & Wei, Lijun & Lim, Andrew, 2018. "The two-dimensional vector packing problem with general costs," Omega, Elsevier, vol. 74(C), pages 59-69.
    • Handle: RePEc:eee:jomega:v:74:y:2018:i:c:p:59-69
    DOI: 10.1016/j.omega.2017.01.006
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    1. Wascher, Gerhard & Hau[ss]ner, Heike & Schumann, Holger, 2007. "An improved typology of cutting and packing problems," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1109-1130, December.
    2. Wei, Lijun & Zhu, Wenbin & Lim, Andrew, 2015. "A goal-driven prototype column generation strategy for the multiple container loading cost minimization problem," European Journal of Operational Research, Elsevier, vol. 241(1), pages 39-49.
    3. Hu, Qian & Lim, Andrew & Zhu, Wenbin, 2015. "The two-dimensional vector packing problem with piecewise linear cost function," Omega, Elsevier, vol. 50(C), pages 43-53.
    4. Fleszar, Krzysztof & Charalambous, Christoforos, 2011. "Average-weight-controlled bin-oriented heuristics for the one-dimensional bin-packing problem," European Journal of Operational Research, Elsevier, vol. 210(2), pages 176-184, April.
    5. Lim, A. & Rodrigues, B. & Wang, Y., 2003. "A multi-faced buildup algorithm for three-dimensional packing problems," Omega, Elsevier, vol. 31(6), pages 471-481, December.
    6. Shoshana Anily & Julien Bramel & David Simchi-Levi, 1994. "Worst-Case Analysis of Heuristics for the Bin Packing Problem with General Cost Structures," Operations Research, INFORMS, vol. 42(2), pages 287-298, April.
    7. Leung, Joseph Y.-T. & Li, Chung-Lun, 2008. "An asymptotic approximation scheme for the concave cost bin packing problem," European Journal of Operational Research, Elsevier, vol. 191(2), pages 582-586, December.
    8. Dyckhoff, Harald, 1990. "A typology of cutting and packing problems," European Journal of Operational Research, Elsevier, vol. 44(2), pages 145-159, January.
    9. Che, Chan Hou & Huang, Weili & Lim, Andrew & Zhu, Wenbin, 2011. "The multiple container loading cost minimization problem," European Journal of Operational Research, Elsevier, vol. 214(3), pages 501-511, November.
    10. Kang, Jangha & Park, Sungsoo, 2003. "Algorithms for the variable sized bin packing problem," European Journal of Operational Research, Elsevier, vol. 147(2), pages 365-372, June.
    11. Silvano Martello & David Pisinger & Daniele Vigo, 2000. "The Three-Dimensional Bin Packing Problem," Operations Research, INFORMS, vol. 48(2), pages 256-267, April.
    12. Silvano Martello & Daniele Vigo, 1998. "Exact Solution of the Two-Dimensional Finite Bin Packing Problem," Management Science, INFORMS, vol. 44(3), pages 388-399, March.
    13. Martinez-Sykora, Antonio & Alvarez-Valdes, Ramon & Bennell, Julia & Tamarit, Jose Manuel, 2015. "Constructive procedures to solve 2-dimensional bin packing problems with irregular pieces and guillotine cuts," Omega, Elsevier, vol. 52(C), pages 15-32.
    14. David Pisinger & Mikkel Sigurd, 2007. "Using Decomposition Techniques and Constraint Programming for Solving the Two-Dimensional Bin-Packing Problem," INFORMS Journal on Computing, INFORMS, vol. 19(1), pages 36-51, February.
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    Cited by:

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    2. Otto, Alena & Li, Xiyu, 2020. "Product sequencing in multiple-piece-flow assembly lines," Omega, Elsevier, vol. 91(C).

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