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Cutting stock problems with nondeterministic item lengths: a new approach to server consolidation

Author

Listed:
  • John Martinovic

    (Technische Universität Dresden)

  • Markus Hähnel

    (Technische Universität Dresden)

  • Guntram Scheithauer

    (Technische Universität Dresden)

  • Waltenegus Dargie

    (Technische Universität Dresden)

  • Andreas Fischer

    (Technische Universität Dresden)

Abstract

Based on an application in the field of server consolidation, we consider the one-dimensional cutting stock problem with nondeterministic item lengths. After a short introduction to the general topic we investigate the case of normally distributed item lengths in more detail. Within this framework, we present two lower bounds as well as two heuristics to obtain upper bounds, where the latter are either based on a related (ordinary) cutting stock problem or an adaptation of the first fit decreasing heuristic to the given stochastical context. For these approximation techniques, dominance relations are discussed, and theoretical performance results are stated. As a main contribution, we develop a characterization of feasible patterns by means of one linear and one quadratic inequality. Based on this, we derive two exact modeling approaches for the nondeterministic cutting stock problem, and provide results of numerical simulations.

Suggested Citation

  • John Martinovic & Markus Hähnel & Guntram Scheithauer & Waltenegus Dargie & Andreas Fischer, 2019. "Cutting stock problems with nondeterministic item lengths: a new approach to server consolidation," 4OR, Springer, vol. 17(2), pages 173-200, June.
    • Handle: RePEc:spr:aqjoor:v:17:y:2019:i:2:d:10.1007_s10288-018-0384-4
    DOI: 10.1007/s10288-018-0384-4
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    References listed on IDEAS

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    1. Valerio de Carvalho, J. M., 2002. "LP models for bin packing and cutting stock problems," European Journal of Operational Research, Elsevier, vol. 141(2), pages 253-273, September.
    2. Belov, G. & Scheithauer, G., 2006. "A branch-and-cut-and-price algorithm for one-dimensional stock cutting and two-dimensional two-stage cutting," European Journal of Operational Research, Elsevier, vol. 171(1), pages 85-106, May.
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    6. Guntram Scheithauer, 2018. "One-Dimensional Cutting Stock," International Series in Operations Research & Management Science, in: Introduction to Cutting and Packing Optimization, chapter 0, pages 73-122, Springer.
    7. Martinovic, J. & Scheithauer, G. & Valério de Carvalho, J.M., 2018. "A comparative study of the arcflow model and the one-cut model for one-dimensional cutting stock problems," European Journal of Operational Research, Elsevier, vol. 266(2), pages 458-471.
    8. Delorme, Maxence & Iori, Manuel & Martello, Silvano, 2016. "Bin packing and cutting stock problems: Mathematical models and exact algorithms," European Journal of Operational Research, Elsevier, vol. 255(1), pages 1-20.
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    Cited by:

    1. John Martinovic & Markus Hähnel & Guntram Scheithauer & Waltenegus Dargie, 2022. "An introduction to stochastic bin packing-based server consolidation with conflicts," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(2), pages 296-331, July.

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