One-dimensional cutting stock problem to minimize the number of different patterns

Umetani, Shunji; Yagiura, Mutsunori; Ibaraki, Toshihide

doi:10.1016/s0377-2217(02)00239-4

Cited by 85 publications

(52 citation statements)

References 14 publications

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“…The neighbourhood of the local search is given by a subset of cutting patterns which have prospect of improving the current solution. As shown in the experimental study reported in Umetani et al (2003), the performance of ILS-APG is comparable to SHP and KOMBI algorithms.…”

Section: Literature Reviewmentioning

confidence: 56%

“…In Valério de Carvalho (2002) several formulations of the one-dimensional cutting stock are reviewed, and its particular case called the binpacking problem, and the relations between their relaxations are analysed. As is pointed in Umetani et al (2003), this problem is often formulated as an integer programming (IP) problem, and its linear programming (LP) relaxation is exploited in many heuristic algorithms; e.g. first solve the LP and then modify the LP solution to an integer solution heuristically.…”

Section: Literature Reviewmentioning

confidence: 99%

“…Although the three types commented above are the most classic approaches to setup minimization, there are others, for example, the iterated local search algorithm with adaptive pattern generation proposed in Umetani et al (2003) called ILS-APG. The main components of this algorithm are a procedure to build up an initial solution and a local search method.…”

Section: Literature Reviewmentioning

confidence: 99%

See 2 more Smart Citations

An effective solution for a real cutting stock problem in manufacturing plastic rolls

et al. 2008

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We confront a practical cutting stock problem from a production plant of plastic rolls. The problem is a variant of the well-known one dimensional cutting stock, with particular constraints and optimization criteria defined by the experts of the company. We start by giving a problem formulation in which optimization criteria have been considered in linear hierarchy according to expert preferences, and then propose a heuristic solution based on a GRASP algorithm. The generation phase of this algorithm solves a simplified version which is rather similar to the conventional one dimensional cutting stock. To do that, we propose a Sequential Heuristic Randomized Procedure (SHRP). Then in the repairing phase, the solution of the simplified problem is transformed into a solution to the real problem. For experimental study we have chosen a set of problem instances of com-mon use to compare SHRP with another recent approach. Also, we show by means of examples, how our approach works over instances taken from the real production process.

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Section: Literature Reviewmentioning

confidence: 56%

Section: Literature Reviewmentioning

confidence: 99%

Section: Literature Reviewmentioning

confidence: 99%

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An effective solution for a real cutting stock problem in manufacturing plastic rolls

et al. 2008

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“…They do not report any systematic numerical experiments, but -in order to demonstrate the trade-off between input and trim loss, and to exemplify their approach -they give the objective function values of the solutions they have obtained for four problem instances. Umetani et al (2003aUmetani et al ( , 2003b) also mention that their algorithms, ILS and ILS-APG, may be applied iteratively for different values of max(s), and they claim (Umetani et al, 2003a, p. 1094) that their numerical experiments have generated reasonable trade-off curves. The solutions provided are non-dominated ones.…”

Section: Approaches For the Generation Of Trade-off Curvesmentioning

confidence: 99%

Extensions of cutting problems: setups

Henn¹,

Wäscher²

2013

Pesqui. Oper.

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ABSTRACT. Even though the body of literature in the area of cutting and packing is growing rapidly, research seems to focus on standard problems in the first place, while practical aspects are less frequently dealt with. This is particularly true for setup processes which arise in industrial cutting processes whenever a new cutting pattern is started (i.e. a pattern is different from its predecessor) and the cutting equipment has to be prepared in order to meet the technological requirements of the new pattern. Setups involve the consumption of resources and the loss of production time capacity. Therefore, consequences of this kind must explicitly be taken into account for the planning and control of industrial cutting processes. This results in extensions to traditional models which will be reviewed here. We show how setups can be represented in such models, and we report on the algorithms which have been suggested for the determination of solutions of the respective models. We discuss the value of these approaches and finally point out potential directions of future research.

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“…These methods (not including ANLCP) were also used as basis of comparison by Umetami et al [19] with the heuristic APG. We run CUTGEN1 with the same seed (i.e.,1994) and parameters defined in [7] and [19] The methods NANLCP and ANLCP and the heuristic SHP were implemented by the authors in Fortran, running under g77 for Linux, in a Athlon XP 1800Mhz, 512MB of RAM. The results for KOMBI234 were obtained from an implementation in MODULA-2 in MSDOS operating system with a IBM 486/66.…”

Section: Computational Experimentsmentioning

confidence: 99%

Nonlinear cutting stock problem model to minimize the number of different patterns and objects

Moretti¹,

Neto²

2008

Mat. apl. comput.

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Abstract. In this article we solve a nonlinear cutting stock problem which represents a cutting stock problem that considers the minimization of, both, the number of objects used and setup.We use a linearization of the nonlinear objective function to make possible the generation of good columns with the Gilmore and Gomory procedure. Each time a new column is added to the problem, we solve the original nonlinear problem by an Augmented Lagrangian method.This process is repeated until no more profitable columns is generated by Gilmore and Gomory technique. Finally, we apply a simple heuristic to obtain an integral solution for the original nonlinear integer problem.Mathematical subject classification: 65K05.

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One-dimensional cutting stock problem to minimize the number of different patterns

Cited by 85 publications

References 14 publications

An effective solution for a real cutting stock problem in manufacturing plastic rolls

An effective solution for a real cutting stock problem in manufacturing plastic rolls

Extensions of cutting problems: setups

Nonlinear cutting stock problem model to minimize the number of different patterns and objects

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