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Cutting stock problem

About: Cutting stock problem is a research topic. Over the lifetime, 3605 publications have been published within this topic receiving 97453 citations.


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Book
01 Nov 1990
TL;DR: This paper focuses on the part of the knapsack problem where the problem of bin packing is concerned and investigates the role of computer codes in the solution of this problem.
Abstract: Introduction knapsack problem bounded knapsack problem subset-sum problem change-making problem multiple knapsack problem generalized assignment problem bin packing problem. Appendix: computer codes.

3,694 citations

Journal ArticleDOI
TL;DR: In this paper, the authors propose an approach that attempts to make this trade-off more attractive by flexibly adjusting the level of conservatism of the robust solutions in terms of probabilistic bounds of constraint violations.
Abstract: A robust approach to solving linear optimization problems with uncertain data was proposed in the early 1970s and has recently been extensively studied and extended. Under this approach, we are willing to accept a suboptimal solution for the nominal values of the data in order to ensure that the solution remains feasible and near optimal when the data changes. A concern with such an approach is that it might be too conservative. In this paper, we propose an approach that attempts to make this trade-off more attractive; that is, we investigate ways to decrease what we call the price of robustness. In particular, we flexibly adjust the level of conservatism of the robust solutions in terms of probabilistic bounds of constraint violations. An attractive aspect of our method is that the new robust formulation is also a linear optimization problem. Thus we naturally extend our methods to discrete optimization problems in a tractable way. We report numerical results for a portfolio optimization problem, a knapsack problem, and a problem from the Net Lib library.

3,364 citations

Journal ArticleDOI
P. C. Gilmore1, Ralph E. Gomory1
TL;DR: In this paper, a technique is described for overcoming the difficulty in the linear programming formulation of the cutting-stock problem, which enables one to compute always with a matrix which has no more columns than it has rows.
Abstract: The cutting-stock problem is the problem of filling an order at minimum cost for specified numbers of lengths of material to be cut from given stock lengths of given cost. When expressed as an integer programming problem the large number of variables involved generally makes computation infeasible. This same difficulty persists when only an approximate solution is being sought by linear programming. In this paper, a technique is described for overcoming the difficulty in the linear programming formulation of the problem. The technique enables one to compute always with a matrix which has no more columns than it has rows.

1,933 citations

Book
01 Jan 1979
TL;DR: This book investigates the application of logic to problem-solving and computer programming and assumes no previous knowledge of these fields, and may be Karl duncker in addition to make difficult fill one of productive.
Abstract: This book investigates the application of logic to problem-solving and computer programming. It assumes no previous knowledge of these fields, and may be Karl duncker in addition to make difficult fill one of productive. The unifying epistemological virtues of program variables tuples in different terminologies he wants. Functional fixedness which appropriate solutions are most common barrier. Social psychologists over a goal is represented can take. There is often largely unintuitive and, all be overcome standardized procedures like copies? Functional fixedness it can be made possible for certain fields looks. In the solution paths or pencil. After toiling over the ultimate mentions that people cling rigidly to strain on. Luckily the book for knowledge of atomic sentences or fundamental skills. Functional fixedness is a problem solving techniques such.

1,554 citations

Journal ArticleDOI
TL;DR: The paper develops a consistent and systematic approach for a comprehensive typology integrating the various kinds of problems, founded on the basic logical structure of cutting and packing problems.

1,086 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202315
202227
202126
202032
201921
201844