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The robust machine availability problem – bin packing under uncertainty

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  • Guopeng Song
  • Daniel Kowalczyk
  • Roel Leus

Abstract

We define and solve the robust machine availability problem in a parallel machine environment, which aims to minimize the number of identical machines required while completing all the jobs before a given deadline. The deterministic version of this problem essentially coincides with the bin packing problem. Our formulation preserves a user-defined robustness level regarding possible deviations in the job durations. For better computational performance, a branch-and-price procedure is proposed based on a set covering reformulation. We use zero-suppressed binary decision diagrams for solving the pricing problem, which enable us to manage the difficulty entailed by the robustness considerations as well as by extra constraints imposed by branching decisions. Computational results are reported that show the effectiveness of a pricing solver with zero-suppressed binary decision diagrams compared with a mixed integer programming solver.

Suggested Citation

  • Guopeng Song & Daniel Kowalczyk & Roel Leus, 2018. "The robust machine availability problem – bin packing under uncertainty," IISE Transactions, Taylor & Francis Journals, vol. 50(11), pages 997-1012, November.
    • Handle: RePEc:taf:uiiexx:v:50:y:2018:i:11:p:997-1012
    DOI: 10.1080/24725854.2018.1468122
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    Citations

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    Cited by:

    1. Artur Alves Pessoa & Michael Poss & Ruslan Sadykov & François Vanderbeck, 2021. "Branch-Cut-and-Price for the Robust Capacitated Vehicle Routing Problem with Knapsack Uncertainty," Operations Research, INFORMS, vol. 69(3), pages 739-754, May.
    2. Novak, Antonin & Sucha, Premysl & Novotny, Matej & Stec, Richard & Hanzalek, Zdenek, 2022. "Scheduling jobs with normally distributed processing times on parallel machines," European Journal of Operational Research, Elsevier, vol. 297(2), pages 422-441.
    3. Yanıkoğlu, İhsan & Yavuz, Tonguc, 2022. "Branch-and-price approach for robust parallel machine scheduling with sequence-dependent setup times," European Journal of Operational Research, Elsevier, vol. 301(3), pages 875-895.
    4. Shanshan Wang & Jinlin Li & Sanjay Mehrotra, 2021. "Chance-Constrained Multiple Bin Packing Problem with an Application to Operating Room Planning," INFORMS Journal on Computing, INFORMS, vol. 33(4), pages 1661-1677, October.

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