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Cutting and Packing Beyond and Within Mathematical Programming

In: Business Optimization Using Mathematical Programming

Author

Listed:
  • Josef Kallrath

    (University of Florida)

Abstract

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.

Suggested Citation

  • Josef Kallrath, 2021. "Cutting and Packing Beyond and Within Mathematical Programming," International Series in Operations Research & Management Science, in: Business Optimization Using Mathematical Programming, edition 2, chapter 0, pages 495-526, Springer.
    • Handle: RePEc:spr:isochp:978-3-030-73237-0_15
    DOI: 10.1007/978-3-030-73237-0_15
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