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An Optimization Algorithm for the Ordered Open-End Bin-Packing Problem

Author

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  • Alberto Ceselli

    (Dipartimento di Tecnologie dell'Informazione, Università degli Studi di Milano, 26013 Crema, Italy)

  • Giovanni Righini

    (Dipartimento di Tecnologie dell'Informazione, Università degli Studi di Milano, 26013 Crema, Italy)

Abstract

The ordered open-end bin-packing problem is a variant of the bin-packing problem in which the items to be packed are sorted in a given order and the capacity of each bin can be exceeded by the last item packed into the bin. We present a branch-and-price algorithm for its exact optimization. The pricing subproblem is a special variant of the binary knapsack problem, in which the items are ordered and the last one does not consume capacity. We present a specialized optimization algorithm for this subproblem. The speed of the column generation algorithm is improved by subgradient optimization steps, allowing for multiple pricing and variable fixing. Computational results are presented on instances of different sizes and items with different correlations between their size and their position in the given order.

Suggested Citation

  • Alberto Ceselli & Giovanni Righini, 2008. "An Optimization Algorithm for the Ordered Open-End Bin-Packing Problem," Operations Research, INFORMS, vol. 56(2), pages 425-436, April.
    • Handle: RePEc:inm:oropre:v:56:y:2008:i:2:p:425-436
    DOI: 10.1287/opre.1070.0415
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    References listed on IDEAS

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    1. Egon Balas & Eitan Zemel, 1980. "An Algorithm for Large Zero-One Knapsack Problems," Operations Research, INFORMS, vol. 28(5), pages 1130-1154, October.
    2. Lodi, Andrea & Martello, Silvano & Monaci, Michele, 2002. "Two-dimensional packing problems: A survey," European Journal of Operational Research, Elsevier, vol. 141(2), pages 241-252, September.
    3. Jian Yang & Joseph Y.-T. Leung, 2003. "The Ordered Open-End Bin-Packing Problem," Operations Research, INFORMS, vol. 51(5), pages 759-770, October.
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    Cited by:

    1. Lixin Tang & Gongshu Wang & Zhi-Long Chen, 2014. "Integrated Charge Batching and Casting Width Selection at Baosteel," Operations Research, INFORMS, vol. 62(4), pages 772-787, August.
    2. Maxence Delorme & Manuel Iori, 2020. "Enhanced Pseudo-polynomial Formulations for Bin Packing and Cutting Stock Problems," INFORMS Journal on Computing, INFORMS, vol. 32(1), pages 101-119, January.
    3. Menezes, Gustavo Campos & Mateus, Geraldo Robson & Ravetti, Martín Gómez, 2017. "A branch and price algorithm to solve the integrated production planning and scheduling in bulk ports," European Journal of Operational Research, Elsevier, vol. 258(3), pages 926-937.
    4. Soto Cardona, Osman Camilo & Mejía Argueta, Christopher & Sarmiento, Alfonso Tullio, 2015. "A cost-efficient method to optimize package size in emerging marketsAuthor-Name: Gámez Albán, Harol Mauricio," European Journal of Operational Research, Elsevier, vol. 241(3), pages 917-926.
    5. Delle Donne, Diego & Alfandari, Laurent & Archetti, Claudia & Ljubić, Ivana, 2023. "Freight-on-Transit for urban last-mile deliveries: A strategic planning approach," Transportation Research Part B: Methodological, Elsevier, vol. 169(C), pages 53-81.
    6. 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.
    7. 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.

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