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A Tree-Based Heuristic for the One-Dimensional Cutting Stock Problem Optimization Using Leftovers.

Glaucia Maria Bressan1, Matheus Henrique Pimenta-Zanon2, Fabio Sakuray3

  • 1Mathematics Department, Universidade Tecnológica Federal do Paraná (UTFPR), Alberto Carazzai, 1640, Cornélio Procópio 86300-000, PR, Brazil.

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Summary
This summary is machine-generated.

This study introduces a new tree-based heuristic for the one-dimensional cutting stock problem. The method effectively minimizes cut bars and processing time, increasing usable leftovers for industrial applications.

Keywords:
cutting problemsheuristic proceduresoptimizationusable leftovers

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Area of Science:

  • Operations Research
  • Industrial Engineering
  • Applied Mathematics

Background:

  • Cutting stock problems involve optimizing the use of raw materials to meet demand for specific item sizes.
  • Traditional methods can lead to significant material waste (losses) or underutilized remnants (leftovers).
  • Minimizing waste and cost is crucial for efficiency in industrial manufacturing processes.

Purpose of the Study:

  • To develop and evaluate a novel tree-based heuristic algorithm for the one-dimensional cutting stock problem.
  • To minimize the total number of cut bars required to satisfy item demand.
  • To improve material utilization by maximizing leftovers and reducing losses.

Main Methods:

  • A tree-based heuristic algorithm was designed to optimize cutting patterns.
  • The algorithm was applied to the one-dimensional cutting stock problem with a single bar type and unlimited stock.
  • Simulation results were compared against the established RGRL1 algorithm and theoretical limiting values.

Main Results:

  • The proposed heuristic significantly reduces the number of bars needed compared to existing methods.
  • Processing time for the cutting stock problem was decreased.
  • The heuristic generates larger quantities of usable leftovers by effectively grouping material losses.

Conclusions:

  • The developed tree-based heuristic offers an efficient solution for the one-dimensional cutting stock problem.
  • It leads to substantial reductions in raw material consumption and manufacturing costs.
  • The method enhances industrial process efficiency through better material management and waste reduction.