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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.
List of contents
Modeling.- Knapsack Problems.- One-Dimensional Bin Packing.- One-Dimensional Cutting Stock.- Orthogonal Packing Feasibility, Two-Dimensional Knapsack Problems.- Optimal Guillotine Cutting.- Packing Rectangles into a Strip.- Two-Dimensional Bin Packing.- Quality Restrictions.- Pallet Loading.- Container Loading.- Packing of Polygonal Pieces.- Circle and Sphere Packing.
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.
Summary
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
Additional text
“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)
Report
"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)
