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Bounds for Non-IRUP Instances of Cutting Stock Problem with Minimal Capacity

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Mathematical Optimization Theory and Operations Research (MOTOR 2019)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1090))

Abstract

We consider the well-known cutting stock problem (CSP). An instance of CSP possesses IRUP (the integer round up property) if difference (the gap) between its optimal function value and optimal value of its continuous relaxation is less than 1. If the gap is 1 or greater, then an instance is non-IRUP. Constructing non-IRUP instances is very hard and a question about how large the gap can be is an open theoretical problem. Aim of our research is to find non-IRUP instances with minimal capacity. We have found a non-IRUP instance with integer sizes of items having capacity \(L=16\), while a previously known instance of such kind had capacity \(L = 18\). We prove that all instances with capacity \(L \le 10\) have IRUP.

Supported by RFBR, project 19-07-00895.

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Acknowledgements

The authors would like to thank the anonymous referees for valuable remarks.

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Authors and Affiliations

  1. Ufa State Aviation Technical University, Karl Marx str. 12, 450008, Ufa, Russia

    Artem V. Ripatti & Vadim M. Kartak

Authors
  1. Artem V. Ripatti
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  2. Vadim M. Kartak
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Correspondence to Artem V. Ripatti .

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Editors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Igor Bykadorov

  2. University of Greenwich, London, UK

    Vitaly Strusevich

  3. University of Aveiro, Aveiro, Portugal

    Tatiana Tchemisova

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Ripatti, A.V., Kartak, V.M. (2019). Bounds for Non-IRUP Instances of Cutting Stock Problem with Minimal Capacity. In: Bykadorov, I., Strusevich, V., Tchemisova, T. (eds) Mathematical Optimization Theory and Operations Research. MOTOR 2019. Communications in Computer and Information Science, vol 1090. Springer, Cham. https://doi.org/10.1007/978-3-030-33394-2_7

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  • DOI: https://doi.org/10.1007/978-3-030-33394-2_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-33393-5

  • Online ISBN: 978-3-030-33394-2

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