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The Bin Packing Problem with Precedence Constraints

Author

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  • Mauro Dell'Amico

    (DISMI, University of Modena and Reggio Emilia, 42122 Reggio Emilia, Italy)

  • José Carlos Díaz Díaz

    (DISMI, University of Modena and Reggio Emilia, 42122 Reggio Emilia, Italy)

  • Manuel Iori

    (DISMI, University of Modena and Reggio Emilia, 42122 Reggio Emilia, Italy)

Abstract

Given a set of identical capacitated bins, a set of weighted items, and a set of precedences among such items, we are interested in determining the minimum number of bins that can accommodate all items and can be ordered in such a way that all precedences are satisfied. The problem, denoted as the bin packing problem with precedence constraints (BPP-P), has a very intriguing combinatorial structure and models many assembly and scheduling issues.According to our knowledge, the BPP-P has received little attention in the literature, and in this paper we address it for the first time with exact solution methods. In particular, we develop reduction criteria, a large set of lower bounds, a variable neighborhood search upper bounding technique, and a branch-and-bound algorithm. We show the effectiveness of the proposed algorithms by means of extensive computational tests on benchmark instances and comparison with standard integer linear programming techniques.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:60:y:2012:i:6:p:1491-1504
    DOI: 10.1287/opre.1120.1109
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    References listed on IDEAS

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    Cited by:

    1. Orlando Rivera Letelier & François Clautiaux & Ruslan Sadykov, 2022. "Bin Packing Problem with Time Lags," INFORMS Journal on Computing, INFORMS, vol. 34(4), pages 2249-2270, July.
    2. Roland Braune, 2022. "Packing-based branch-and-bound for discrete malleable task scheduling," Journal of Scheduling, Springer, vol. 25(6), pages 675-704, December.
    3. Quanming Cheng & Sen Wu & Yang Zhao, 2017. "A bin packing problem of the laundry washing buckets scheduling based on the buffer area," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 8(3), pages 1981-1988, November.
    4. Mathijs Barkel & Maxence Delorme, 2023. "Arcflow Formulations and Constraint Generation Frameworks for the Two Bar Charts Packing Problem," INFORMS Journal on Computing, INFORMS, vol. 35(2), pages 475-494, March.
    5. Schulze, Philipp & Scholl, Armin & Walter, Rico, 2024. "R-SALSA: A branch, bound, and remember algorithm for the workload smoothing problem on simple assembly lines," European Journal of Operational Research, Elsevier, vol. 312(1), pages 38-55.
    6. Saharnaz Mehrani & Carlos Cardonha & David Bergman, 2022. "Models and Algorithms for the Bin-Packing Problem with Minimum Color Fragmentation," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 1070-1085, March.

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