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A branch-and-price algorithm for the variable size bin packing problem with minimum filling constraint

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  • Andrea Bettinelli
  • Alberto Ceselli
  • Giovanni Righini

Abstract

In this paper we consider a variation of the bin packing problem in which bins of different types have different costs and capacities. Furthermore, each bin has to be filled at least to a certain level, which depends on its type. We present a set partitioning formulation and an exact optimization algorithm which exploits column generation and specialized heuristics. We compare our algorithm with the general purpose solver ILOG CPLEX, running on two compact ILP formulations and we report on experimental results on instances we have generated from data-sets for the variable size bin packing problem. Copyright Springer Science+Business Media, LLC 2010

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  • Andrea Bettinelli & Alberto Ceselli & Giovanni Righini, 2010. "A branch-and-price algorithm for the variable size bin packing problem with minimum filling constraint," Annals of Operations Research, Springer, vol. 179(1), pages 221-241, September.
    • Handle: RePEc:spr:annopr:v:179:y:2010:i:1:p:221-241:10.1007/s10479-008-0452-9
    DOI: 10.1007/s10479-008-0452-9
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    References listed on IDEAS

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    Cited by:

    1. Mauro Baldi & Teodor Crainic & Guido Perboli & Roberto Tadei, 2014. "Branch-and-price and beam search algorithms for the Variable Cost and Size Bin Packing Problem with optional items," Annals of Operations Research, Springer, vol. 222(1), pages 125-141, November.
    2. Yulle G. F. Borges & Vinícius L. Lima & Flávio K. Miyazawa & Lehilton L. C. Pedrosa & Thiago A. Queiroz & Rafael C. S. Schouery, 2024. "Algorithms for the bin packing problem with scenarios," Journal of Combinatorial Optimization, Springer, vol. 48(4), pages 1-28, November.
    3. 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.
    4. S. Basso & A. Ceselli & A. Tettamanzi, 2020. "Random sampling and machine learning to understand good decompositions," Annals of Operations Research, Springer, vol. 284(2), pages 501-526, January.
    5. Perboli, Guido & Brotcorne, Luce & Bruni, Maria Elena & Rosano, Mariangela, 2021. "A new model for Last-Mile Delivery and Satellite Depots management: The impact of the on-demand economy," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 145(C).
    6. Paul A Chircop & Timothy J Surendonk, 2019. "Constraint programming heuristics and software tools for amphibious embarkation planning," The Journal of Defense Modeling and Simulation, , vol. 16(3), pages 233-254, July.
    7. Zhou Xu, 2013. "The knapsack problem with a minimum filling constraint," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(1), pages 56-63, February.

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