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Introduction to Cutting and Packing Optimization

Problems, Modeling Approaches, Solution Methods

  • Textbook
  • © 2018

Overview

Authors:
  1. Guntram Scheithauer

    1. Institute for Numerical Mathematics, TU Dresden, Dresden, Germany

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  • Introduces the fundamental knowledge for dealing with cutting and packing problems
  • Presents novel modeling and solution approaches for the first time
  • Includes numerous exercises and solutions to deepen the acquired knowledge

Part of the book series: International Series in Operations Research & Management Science (ISOR, volume 263)

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xxiv
    Download chapter PDF

  2. Modeling

    • Guntram Scheithauer
    Pages 1-18

  3. Knapsack Problems

    • Guntram Scheithauer
    Pages 19-45

  4. One-Dimensional Bin Packing

    • Guntram Scheithauer
    Pages 47-72

  5. One-Dimensional Cutting Stock

    • Guntram Scheithauer
    Pages 73-122

  6. Orthogonal Packing Feasibility, Two-Dimensional Knapsack Problems

    • Guntram Scheithauer
    Pages 123-156

  7. Optimal Guillotine Cutting

    • Guntram Scheithauer
    Pages 157-181

  8. Packing Rectangles into a Strip

    • Guntram Scheithauer
    Pages 183-226

  9. Two-Dimensional Bin Packing

    • Guntram Scheithauer
    Pages 227-244

  10. Quality Restrictions

    • Guntram Scheithauer
    Pages 245-278

  11. Pallet Loading

    • Guntram Scheithauer
    Pages 279-316

  12. Container Loading

    • Guntram Scheithauer
    Pages 317-344

  13. Packing of Polygonal Pieces

    • Guntram Scheithauer
    Pages 345-383

  14. Circle and Sphere Packing

    • Guntram Scheithauer
    Pages 385-405

  15. Back Matter

    Pages 407-410
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Keywords

About this book

This book provides a comprehensive overview of the most important and frequently considered optimization problems concerning cutting and packing. Based on appropriate modeling approaches for the problems considered, it offers an introduction to the related solution methods. It also addresses aspects like performance results for heuristic algorithms and bounds of the optimal value, as well as the packability of a given set of objects within a predefined container. The problems discussed arise in a wide variety of different fields of application and research, and as such, the fundamental knowledge presented in this book make it a valuable resource for students, practitioners, and researchers who are interested in dealing with such tasks. 

Reviews

“The authors provide a comprehensive textbook about the cutting and packing problems. … The book is a good choice for students of mathematics, IT or engineering, researchers in the area of optimization as well as the pre-conditions dealing with problems of this kind.” (Marcin Anholcer, zbMATH 1391.90002, 2018)



“The book delves into details and it provides a comprehensive treatment of appropriate modelling approaches and solution methods of the problem types presented. The strategy of first addressing simple problems and then building up to the more complex ones is an effective teaching and learning strategy. This makes the book a valuable source of fundamental knowledge and latest research results for students, practitioners, and researchers who find themselves facing cutting and packing challenges.” (Hans W. Ittmann, IFORS News, Vol. 11 (4), December, 2017)

Authors and Affiliations

  • Institute for Numerical Mathematics, TU Dresden, Dresden, Germany

    Guntram Scheithauer

About the author

Guntram Scheithauer was born in Bischofswerda, Saxony, Germany in 1954. He studied Mathematics at Technische Universität Dresden from 1974 to 1979, with a focus on Numerical Mathematics and Optimization. He received his PhD in the area of Discrete Optimization from the same institute in 1983. Throughout his career, his work has focused on both practical and theoretical aspects of cutting and packing problems. He has been a member of staff at the TU Dresden since 1983.

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