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New cases of the cutting stock problem having MIRUP

Author

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  • Christoph Nitsche
  • Guntram Scheithauer
  • Johannes Terno

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. Copyright Springer-Verlag Berlin Heidelberg 1998

Suggested Citation

  • Christoph Nitsche & Guntram Scheithauer & Johannes Terno, 1998. "New cases of the cutting stock problem having MIRUP," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 48(1), pages 105-115, September.
    • Handle: RePEc:spr:mathme:v:48:y:1998:i:1:p:105-115
    DOI: 10.1007/PL00020909
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    Cited by:

    1. Wagenaar, J.C. & Fragkos, I. & Faro, W.L.C., 2023. "Transportation asset acquisition under a newsvendor model with cutting-stock restrictions: Approximation and decomposition algorithms," Other publications TiSEM 97eddbd0-6e34-489c-b27d-9, Tilburg University, School of Economics and Management.
    2. Filippi, Carlo, 2007. "On the bin packing problem with a fixed number of object weights," European Journal of Operational Research, Elsevier, vol. 181(1), pages 117-126, August.

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