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Journal ArticleDOI

An instance of the cutting stock problem for which the rounding property does not hold

Odile Marcotte
- 01 Feb 1986 - 
- Vol. 4, Iss: 5, pp 239-243
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TLDR
In this article, it was shown that it is NP-hard to decide whether the rounding holds or not for an instance of the cutting stock problem for which the rounding property does not hold.
About: 
This article is published in Operations Research Letters.The article was published on 1986-02-01. It has received 55 citations till now. The article focuses on the topics: Rounding & Cutting stock problem.

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Citations
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Journal ArticleDOI

Exact solution of bin‐packing problems using column generation and branch‐and‐bound

J. M. Valério de Carvalho
- 01 Jan 1999 - 
TL;DR: The linear relaxation of this model provides a strong lower bound for the bin‐packing problem and leads to tractable branch‐and‐bound trees for the instances under consideration.
Journal ArticleDOI

Cutting and Packing Problems: A Categorized, Application-Orientated Research Bibliography

Paul E. Sweeney, +1 more
- 01 Jul 1992 - 
TL;DR: All of the books and journal articles listed in the bibliography have been categorized according to the dimensionality of the problems studied and the solution methodologies employed.
Journal ArticleDOI

Bin Packing and Cutting Stock Problems: Mathematical Models and Exact Algorithms

Maxence Delorme, +2 more
- 16 Nov 2016 - 
TL;DR: The most important mathematical models and algorithms developed for the exact solution of the one-dimensional bin packing and cutting stock problems are reviewed and the performance of the main available software tools are evaluated.
Journal ArticleDOI

Solving binary cutting stock problems by column generation and branch-and-bound

Pamela H. Vance, +3 more
- 01 May 1994 - 
TL;DR: An algorithm is presented that employs both column generation and branch-and-bound to obtain optimal integer solutions for the binary cutting stock problem and a branching rule is formulated that can be incorporated into the subproblem to allow column generation at any node in the branch- and-bound tree.
Journal ArticleDOI

Computational study of a column generation algorithm for bin packing and cutting stock problems

François Vanderbeck
- 01 Dec 1999 - 
TL;DR: The main focus of the research is to study the extend to which standard branch- and-bound enhancement features such as variable fixing, the tightening of the formulation with cutting planes, early branching, and rounding heuristics can be usefully incorporated in a branch-and-price algorithm.
References
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Johnson: Computers and Intractability-A Guide to the Theory of NP-Completeness

Michael Randolph Garey
Book

Computers and Intractability: A Guide to the Theory of NP-Completeness

Michael Randolph Garey, +1 more
TL;DR: The second edition of a quarterly column as discussed by the authors provides a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NP-Completeness,” W. H. Freeman & Co., San Francisco, 1979.
Journal ArticleDOI

The cutting stock problem and integer rounding

Odile Marcotte
- 01 Sep 1985 - 
TL;DR: It is proved that certain classes of cutting stock problems have the integer round-up property and the proof of these results relies upon the decomposition properties of certain knapsack polyhedra.
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Integer Rounding for Polymatroid and Branching Optimization Problems

S. Baum, +1 more
- 01 Dec 1981 - 
TL;DR: In this article, the integer round-down and round-up properties for certain matrices related to integral polymatroids and branchings in directed graphs were shown. And they were shown to hold for all matrices with rational entries.