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Large proper gaps in bin packing and dual bin packing problems

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  • Vadim M. Kartak

    (Bashkir State Pedagogical University named after M. Akmullah
    Ufa State Aviation Technical University)

  • Artem V. Ripatti

    (Bashkir State Pedagogical University named after M. Akmullah
    Ufa State Aviation Technical University)

Abstract

We consider the one-dimensional skiving stock problem, also known as the dual bin packing problem, with the aim of maximizing the best known dual and proper dual gaps. We apply the methods of computational search of large gaps initially developed for the one-dimensional cutting stock problem, which is related to the bin packing problem. The best known dual gap is raised from 1.0476 to 1.1795. The proper dual gap is improved to 1.1319. We also apply a number of new heuristics developed for the skiving stock problem back to the cutting stock problem, raising the largest known proper gap from 1.0625 to 1.1.

Suggested Citation

  • Vadim M. Kartak & Artem V. Ripatti, 2019. "Large proper gaps in bin packing and dual bin packing problems," Journal of Global Optimization, Springer, vol. 74(3), pages 467-476, July.
    • Handle: RePEc:spr:jglopt:v:74:y:2019:i:3:d:10.1007_s10898-018-0696-0
    DOI: 10.1007/s10898-018-0696-0
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    References listed on IDEAS

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    1. P. C. Gilmore & R. E. Gomory, 1961. "A Linear Programming Approach to the Cutting-Stock Problem," Operations Research, INFORMS, vol. 9(6), pages 849-859, December.
    2. John Martinovic & Guntram Scheithauer, 2016. "The proper relaxation and the proper gap of the skiving stock problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 84(3), pages 527-548, December.
    3. Vijayakumar, Bharathwaj & Parikh, Pratik J. & Scott, Rosalyn & Barnes, April & Gallimore, Jennie, 2013. "A dual bin-packing approach to scheduling surgical cases at a publicly-funded hospital," European Journal of Operational Research, Elsevier, vol. 224(3), pages 583-591.
    4. Csirik, J. & Frenk, J.B.G. & Galambos, G. & Rinnooy Kan, A.H.G., 1991. "Probabilistic analysis of algorithms for dual bin packing problems," Econometric Institute Research Papers 11733, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    5. Scheithauer, Guntram & Terno, Johannes, 1995. "The modified integer round-up property of the one-dimensional cutting stock problem," European Journal of Operational Research, Elsevier, vol. 84(3), pages 562-571, August.
    6. Nitsche, Christoph & Scheithauer, Guntram & Terno, Johannes, 1999. "Tighter relaxations for the cutting stock problem," European Journal of Operational Research, Elsevier, vol. 112(3), pages 654-663, February.
    7. Peeters, Marc & Degraeve, Zeger, 2006. "Branch-and-price algorithms for the dual bin packing and maximum cardinality bin packing problem," European Journal of Operational Research, Elsevier, vol. 170(2), pages 416-439, April.
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    Cited by:

    1. John Martinovic, 2022. "A note on the integrality gap of cutting and skiving stock instances," 4OR, Springer, vol. 20(1), pages 85-104, March.

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