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A general heuristic for two-dimensional nesting problems with limited-size containers

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  • Leandro R. Mundim
  • Marina Andretta
  • Maria Antónia Carravilla
  • José Fernando Oliveira

Abstract

Cutting raw-material into smaller parts is a fundamental phase of many production processes. These operations originate raw-material waste that can be minimised. These problems have a strong economic and ecological impact and their proper solving is essential to many sectors of the economy, such as the textile, footwear, automotive and shipbuilding industries, to mention only a few. Two-dimensional (2D) nesting problems, in particular, deal with the cutting of irregularly shaped pieces from a set of larger containers, so that either the waste is minimised or the value of the pieces actually cut from the containers is maximised. Despite the real-world practical relevance of these problems, very few approaches have been proposed capable of dealing with concrete characteristics that arise in practice. In this paper, we propose a new general heuristic (H4NP) for all 2D nesting problems with limited-size containers: the Placement problem, the Knapsack problem, the Cutting Stock problem, and the Bin Packing problem. Extensive computational experiments were run on a total of 1100 instances. H4NP obtained equal or better solutions for 73% of the instances for which there were previous results against which to compare, and new benchmarks are proposed.

Suggested Citation

  • Leandro R. Mundim & Marina Andretta & Maria Antónia Carravilla & José Fernando Oliveira, 2018. "A general heuristic for two-dimensional nesting problems with limited-size containers," International Journal of Production Research, Taylor & Francis Journals, vol. 56(1-2), pages 709-732, January.
    • Handle: RePEc:taf:tprsxx:v:56:y:2018:i:1-2:p:709-732
    DOI: 10.1080/00207543.2017.1394598
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    Cited by:

    1. Gahm, Christian & Uzunoglu, Aykut & Wahl, Stefan & Ganschinietz, Chantal & Tuma, Axel, 2022. "Applying machine learning for the anticipation of complex nesting solutions in hierarchical production planning," European Journal of Operational Research, Elsevier, vol. 296(3), pages 819-836.
    2. Igor Kierkosz & Maciej Łuczak, 2019. "A one-pass heuristic for nesting problems," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 29(1), pages 37-60.

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