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A heuristic for the Minimum Score Separation Problem, a combinatorial problem associated with the cutting stock problem

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  • Kai Helge Becker

    (Queensland University of Technology (QUT), Brisbane, Australia)

  • Gautam Appa

    (London School of Economics and Political Science, London, UK)

Abstract

The Minimum Score Separation Problem (MSSP) is a combinatorial problem that was introduced in JORS 55 as an open problem in the paper industry arising in conjunction with the cutting stock problem. During the process of producing boxes, flat papers are prepared for folding by being scored with knives. The problem is to determine whether and how a given production pattern of boxes can be arranged such that a certain minimum distance between the knives can be kept. Introducing the concept of matching-based alternating Hamiltonian paths, this paper models the MSSP as the problem of finding an alternating Hamiltonian path on a graph that is the union of a matching and a type of graph known as a ‘threshold graph’. On this basis, we find a heuristic that can quickly recognize a large percentage of feasible and infeasible instances of the MSSP. Detailed computational experiments demonstrate the efficiency of our approach.

Suggested Citation

  • Kai Helge Becker & Gautam Appa, 2015. "A heuristic for the Minimum Score Separation Problem, a combinatorial problem associated with the cutting stock problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(8), pages 1297-1311, August.
    • Handle: RePEc:pal:jorsoc:v:66:y:2015:i:8:p:1297-1311
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    Citations

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    Cited by:

    1. Yaodong Cui & Xiang Song & Yan Chen & Yi-Ping Cui, 2017. "New model and heuristic solution approach for one-dimensional cutting stock problem with usable leftovers," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(3), pages 269-280, March.
    2. Hawa, Asyl L. & Lewis, Rhyd & Thompson, Jonathan M., 2022. "Exact and approximate methods for the score-constrained packing problem," European Journal of Operational Research, Elsevier, vol. 302(3), pages 847-859.

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