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New cases of the cutting stock problem having MIRUP

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Abstract.

The modified integer round-up property (MIRUP) for a linear integer minimization problem means that the optimal value of this problem is not greater than the optimal value of the corresponding LP relaxation rounded up plus one. In earlier papers the MIRUP was shown to hold for the so-called divisible case and some other subproblems of the one-dimensional cutting stock problem. In this paper we extend the results by using special transformations, proving the existence of non-elementary patterns in the solution, and using more detailed greedy techniques.

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Authors and Affiliations

  1. Institute of Numerical Mathematics, Dresden University of Technology, Mommsenstr. 13, D-01062 Dresden, Germany (e-mail: Christoph.Nitsche@sz-online.de; scheit@math.tu-dresden.de; terno@math.tu-dresden.de), , , , , , DE

    Christoph Nitsche, Guntram Scheithauer & Johannes Terno

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  1. Christoph Nitsche
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  2. Guntram Scheithauer
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  3. Johannes Terno
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Received October 1996/Revised version July 1997

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Nitsche, C., Scheithauer, G. & Terno, J. New cases of the cutting stock problem having MIRUP. Mathematical Methods of OR 48, 105–115 (1998). https://doi.org/10.1007/PL00020909

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  • DOI: https://doi.org/10.1007/PL00020909

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