Near-optimal solutions to one-dimensional cutting stock problems

https://doi.org/10.1016/0305-0548(86)90077-8Get rights and content

Abstract

This paper describes a set of heuristic procedures for efficiently generating good solutions to one-dimensional cutting stock problems in which (i) there are multiple stock lengths with constraints on their availability, (ii) it is desirable to cut the trim into as few pieces as possible and (iii) it is difficult because of the problem's structure, to round fractional, LP solutions to good feasible cutting plans. The point of departure for the procedures is the column generation technique of Gilmore and Gomory. The computational experience reported here suggests that the heuristics are both effective and efficient.

References (3)

  • P.C. Gilmore et al.

    A linear programming approach to cutting stock problems

    Opns Res.

    (1961)
There are more references available in the full text version of this article.

Cited by (37)

  • Integrated optimization of rebar detailing design and installation planning for waste reduction and productivity improvement

    2019, Automation in Construction
    Citation Excerpt :

    For the heuristic approach, Haessler [25] developed a heuristic procedure that could potentially control trim losses. Roodman [26] introduced a set of heuristic procedures for efficiently generating good solutions to one-dimensional cutting stock problems in which there were multiple stock lengths available. Gradišar et al. [27] proposed another Sequential Heuristic Procedure (SHP) to solve CSP.

  • Bin packing and cutting stock problems: Mathematical models and exact algorithms

    2016, European Journal of Operational Research
    Citation Excerpt :

    The generation of all possible patterns followed by the direct solution of (24)–(26) at integrality is the most obvious option, but it can only be adopted for instances of small size, or characterized by a special structure (see, e.g., Goulimis, 1990). Other, non exact, methods simply use rounding heuristics (like, e.g., Haessler & Sweeney, 1991; Roodman, 1986; Holthaus, 2002), but their efficiency strongly depends on the instances at hand. When these methods fail in producing an optimal integer solution, one can embed the column generation lower bound LLP into an enumeration tree, thus obtaining a branch-and-price algorithm.

  • An investigation into two bin packing problems with ordering and orientation implications

    2011, European Journal of Operational Research
    Citation Excerpt :

    For instance, we could investigate whether commercial solvers (such as Xpress and CPLEX) perform better with other integer programming formulations of the underlying TSP (see, for example, (Padberg and Sung, 1991)), or we could simply create new techniques that exploit the very specific structures of the sub-problems. It would also be interesting to see how other existing methods for the SCP and BPP might be adapted to these problems, including metaheuristic approaches (Falkenauer, 1998; Leung et al., 1997; Levine and Ducatelle, 2003) and others (Haessler and Sweeny, 1991; Roodman, 1986). One further aspect of the TCP is the question of how it might be classified according to accepted taxonomies of packing and cutting problems.

View all citing articles on Scopus

Gary Roodman is an Associate Professor of Management at The State University of New York at Binghamton and Senior Staff Associate with Computer Software Consultants, Inc. He earned a B.S.B.A. from Washington University in St Louis and M.B.A. and D.B.A. degrees from Indiana University. His principal research and consulting interest is in the design of decision support systems, particularly for the production planning process. His papers have appeared in Management Science, AIIE Transactions, Operations Research and elsewhere.

View full text