Exact algorithms in bar nesting: How to cut general items from linear stocks so that wastage is minimised

This paper proposes exact, polynomial-time algorithms that solve the problem of cutting items with angled sides from a single linear stock so that wastage is minimised. In industry, this problem is called “bar nesting”. Here we give an algorithmic framework that solves several important variants of...

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Bibliographic Details
Published inComputers & industrial engineering Vol. 200; p. 110838
Main Authors Lewis, Rhyd, Bonnet, Louis
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.02.2025
Elsevier
Subjects
Bar nesting
Bin packing
Computer Science
Graph theory
Manufacturing and logistics
Mechanical engineering
Mechanics
Operations Research
Physics
Stock cutting
Bin packing
Graph theory
Stock cutting
Manufacturing and logistics
Bar nesting
Online AccessGet full text
ISSN0360-8352
1879-0550
DOI10.1016/j.cie.2024.110838

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Summary:This paper proposes exact, polynomial-time algorithms that solve the problem of cutting items with angled sides from a single linear stock so that wastage is minimised. In industry, this problem is called “bar nesting”. Here we give an algorithmic framework that solves several important variants of the problem, including cutting items from stocks with asymmetric cross-sections, cutting items whose sides occur on different planes, and the minimum score separation problem. •Exact, polynomial-time algorithms are given for single-stock bar nesting problems.•Several industry-related problem variants are considered.•Correctness proofs and source code are provided.
ISSN:0360-8352
1879-0550
DOI:10.1016/j.cie.2024.110838