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Mathematical models and heuristic methods for nesting problems

Mundim, Leandro Resende

Biblioteca Digital de Teses e Dissertações da USP; Universidade de São Paulo; Instituto de Ciências Matemáticas e de Computação 2017-08-18

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  • Título:
    Mathematical models and heuristic methods for nesting problems
  • Autor: Mundim, Leandro Resende
  • Orientador: Andretta, Marina; Oliveira, José Fernando da Costa
  • Assuntos: Métodos Heurísticos; Problemas De Corte E Empacotamento De Itens Irregulares; Programação Matemática; Heuristics; Irregular Cutting And Packing Problems; Mathematical Programming
  • Notas: Tese (Doutorado)
  • Descrição: Irregular cutting and packing problems, with convex and non-convex polygons, are found in many industries such as metal mechanics, textiles, of shoe making, the furniture making and others. In this thesis we study the two-dimensional version of these problems, where we want to allocate a set of items, without overlap, inside one or more containers, limited or unlimited, so as to optimize an objective function. In this document we study the knapsack problem, placement problem, strip packing problem, cutting stock problem and bin packing problem. For these problems, the heuristic methods and mathematical programming models are proposed and presented very promising results, surpassing in many cases the best results in the specialized literature. This thesis is organized as follows. In Chapter 1, we present a review of the studied problems, the value proposition for this thesis with the main contributions and ideas. In Chapter 2, we propose a metaheursitic for the strip packing problem with irregular items and circles. Then, in Chapter 3, we present a generic heuristic for the allocation of irregular items that may be weakly or strongly heterogeneous and will be allocated in a container (output maximization problems) or multiple containers (input minimization problems). In Chapter 4, we propose a solution method for the cutting stock problem with deterministic demand and stochastic demand. In Chapters 5 and 6, we present mathematical programming models for the strip packing problem. Finally, in Chapter 7, we present a conclusion and a concise direction for future works.
  • DOI: 10.11606/T.55.2017.tde-08122017-143216
  • Editor: Biblioteca Digital de Teses e Dissertações da USP; Universidade de São Paulo; Instituto de Ciências Matemáticas e de Computação
  • Data de criação/publicação: 2017-08-18
  • Formato: Adobe PDF
  • Idioma: Inglês
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