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Exact solution of bin‐packing problems using column generation and branch‐and‐bound

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  • J.M. Valério de Carvalho

Abstract

We explore an arc flow formulation with side constraints for the one‐dimensionalbin‐packing problem. The model has a set of flow conservation constraints and a set ofconstraints that force the appropriate number of items to be included in the packing. Themodel is tightened by fixing some variables at zero level, to reduce the symmetry of thesolution space, and by introducing valid inequalities. The model is solved exactly using abranch‐and‐price procedure that combines deferred variable generation and branch‐and‐bound.At each iteration, the subproblem generates a set of columns, which altogether correspondto an attractive valid packing for a single bin. We describe this subproblem, and theway it is modified in the branch‐and‐bound phase, after the branching constraints are addedto the model. We report the computational times obtained in the solution of the bin‐packingproblems from the OR‐Library test data sets. The linear relaxation of this model provides astrong lower bound for the bin‐packing problem and leads to tractable branch‐and‐boundtrees for the instances under consideration. Copyright Kluwer Academic Publishers 1999

Suggested Citation

  • J.M. Valério de Carvalho, 1999. "Exact solution of bin‐packing problems using column generation and branch‐and‐bound," Annals of Operations Research, Springer, vol. 86(0), pages 629-659, January.
    • Handle: RePEc:spr:annopr:v:86:y:1999:i:0:p:629-659:10.1023/a:1018952112615
    DOI: 10.1023/A:1018952112615
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    Cited by:

    1. K L Poh & K W Choo & C G Wong, 2005. "A heuristic approach to the multi-period multi-commodity transportation problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(6), pages 708-718, June.
    2. Chung‐Lun Li & Zhi‐Long Chen, 2006. "Bin‐packing problem with concave costs of bin utilization," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(4), pages 298-308, June.
    3. Ekici, Ali, 2023. "A large neighborhood search algorithm and lower bounds for the variable-Sized bin packing problem with conflicts," European Journal of Operational Research, Elsevier, vol. 308(3), pages 1007-1020.
    4. Arbib, Claudio & Marinelli, Fabrizio, 2017. "Maximum lateness minimization in one-dimensional bin packing," Omega, Elsevier, vol. 68(C), pages 76-84.
    5. Elhedhli, Samir, 2005. "Ranking lower bounds for the bin-packing problem," European Journal of Operational Research, Elsevier, vol. 160(1), pages 34-46, January.
    6. Irawan, Chandra Ade & Song, Xiang & Jones, Dylan & Akbari, Negar, 2017. "Layout optimisation for an installation port of an offshore wind farm," European Journal of Operational Research, Elsevier, vol. 259(1), pages 67-83.

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