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Cutting and Packing Beyond and Within Mathematical Programming

2021; Springer Science+Business Media; Linguagem: Inglês

10.1007/978-3-030-73237-0_15

2214-7934

Josef Kallrath,

Computational Geometry and Mesh Generation

This chapter, based on material provided and written by Prof. Dr. Yuriy Stoyan & Prof. Dr. Tatiana Romanova ( The National Academy of Sciences of Ukraine, Institute of Mechanical Engineering Problems, Department of Mathematical Modeling and Optimal Design, Kharkiv, Ukraine & Kharkiv National University of Radioelectronics, Department of Applied Mathematics.), is devoted to the phi-function technique used for mathematical modeling of cutting and packing (C&P) problems. Phi-functions are constructed here for some 2D and 3D geometric objects. Phi-functions can be described by quite simple formulas. A general solution strategy using phi-functions is outlined. Conceptually, the Phi-function approach exploits NLP and MINLP and can be understood as cutting and packing beyond and within Mathematical Programming. It also exploits polylithic modeling and solution techniques.