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A residual recombination heuristic for one-dimensional cutting stock problems

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Abstract

Cutting stock problems arise in manufacturing industries where large objects need to be cut into smaller pieces. The cutting process usually results in a waste of material; thus, mathematical optimization models are used to reduce losses and take economic gains. This paper introduces a new heuristic procedure, called the Residual Recombination Heuristic (RRH), to the one-dimensional cutting stock problem. The well-known column generation technique typically produces relaxed solutions with non-integer entries, which, in this approach, we associate with a set of residual cutting patterns. The central aspect of this contribution involves recombining these residual cutting patterns in different ways; therefore, generating new integer feasible cutting patterns. Experimental studies and statistical analyses were conducted based on different instances from the literature. We analyze heuristic performance by measuring the waste of material, the number of instances solved to optimality, and by comparing it with other heuristics in the literature. The computational time suggests the suitability of the heuristic for solving real-world problems.

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Authors and Affiliations

  1. School of Applied Sciences, University of Campinas, R. Pedro Zaccaria, 1300, Limeira, São Paulo, 13484-350, Brazil

    B. S. C. Campello, C. T. L. S. Ghidini, A. O. C. Ayres & W. A. Oliveira

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  1. B. S. C. Campello
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  2. C. T. L. S. Ghidini
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  3. A. O. C. Ayres
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  4. W. A. Oliveira
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Correspondence to B. S. C. Campello.

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B. S. C. Campello is grateful to CAPES (master’s program scholarships, Grant 01P-3717/2017). C. T. L. S. Ghidini wishes to thank FAPESP (Grant 2015/02184-7) and FAEPEX-Unicamp (Grant 519.292-262/15). A. O. C. Ayres is grateful to FAEPEX-Unicamp (master’s program scholarships, Grants 1123/15 and 519.292-262/15).

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Campello, B.S.C., Ghidini, C.T.L.S., Ayres, A.O.C. et al. A residual recombination heuristic for one-dimensional cutting stock problems. TOP 30, 194–220 (2022). https://doi.org/10.1007/s11750-021-00611-3

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  • DOI: https://doi.org/10.1007/s11750-021-00611-3

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