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An Improved Upper Bound for the Gap of Skiving Stock Instances of the Divisible Case

In: Operations Research Proceedings 2017

Author

Listed:
  • John Martinovic

    (Institut für Numerische Mathematik, Technische Universität Dresden)

  • Guntram Scheithauer

    (Institut für Numerische Mathematik, Technische Universität Dresden)

Abstract

The 1D skiving stock problem (SSP) is a combinatorial optimization problem being of high relevance whenever an efficient utilization of given resources is intended. In the classical formulation, (small) items shall be used to build as many large objects (specified by some required length) as possible. Due to the NP-hardness of the SSP, the performance of the LP relaxation (measured by the additive gap of the related optimal values) and/or heuristics are of scientific interest. In this paper, theoretical properties of the best fit decreasing heuristic (for the SSP) are investigated and shown to provide a new and improved upper bound for the gap of the so-called divisible case.

Suggested Citation

  • John Martinovic & Guntram Scheithauer, 2018. "An Improved Upper Bound for the Gap of Skiving Stock Instances of the Divisible Case," Operations Research Proceedings, in: Natalia Kliewer & Jan Fabian Ehmke & Ralf Borndörfer (ed.), Operations Research Proceedings 2017, pages 179-184, Springer.
  • Handle: RePEc:spr:oprchp:978-3-319-89920-6_25
    DOI: 10.1007/978-3-319-89920-6_25
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