Cutting and Packing Problems

This book provides a comprehensive overview of practical cutting and packing problems, presenting practical algorithms for solving these problems from the perspective of combinatorial optimization. It also discusses the geometric properties and tools for cutting and packing problems. Problems of cutting and packing objects have been extensively studied for many years because of the numerous real-world applications—for instance, in the clothing, logistics, manufacturing, and material industries. They can be classified in three ways according to their dimensions: The one-dimensional problem is the most basic category of problems including knapsack problems, bin packing problems, and cutting stock problems. The two-dimensional geometric problems include rectangle packing problems, circle packing problems, and polygon packing problems. The three-dimensional problem is the most difficult category and has applications in container loading, cargo and warehouse management and so forth. Most of these variants are NP-hard, since they contain as a special case the knapsack problem or the bin packing problem, which are already known to be NP-hard. Therefore, heuristics and metaheuristics are essential for designing practical algorithms for these problems. In addition to practical algorithms for solving a wide variety of cutting and packing problems, the book also considers another feature of cutting and packing problems: the need to develop powerful geometric tools to handle the wide variety and complexity of shapes that need to be packed.