Introduction to Cutting and Packing Optimization

1. Front Matter

   Pages i-xxiv

   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

    PDF

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. 

• cutting problem
• packing problem
• allocation problem
• bin packing
• strip packing
• circle and sphere packing

“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)

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

  Guntram Scheithauer

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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