Dynamic programming algorithms for the optimal cutting of equal rectangles

  • Cui Y
  • 2


    Mendeley users who have this article in their library.
  • 20


    Citations of this article.


This paper presents dynamic programming algorithms for generating optimal guillotine-cutting patterns of equal rectangles. The algorithms are applicable for solving the unconstrained problem where the blank demand is unconstrained, the constrained problem where the demand is exact, the unconstrained problem with blade length constraint, and the constrained problem with blade length constraint. The algorithms are able to generate the simplest optimal patterns to simplify the cutting process. When the sheet length is longer than the blade length of the guillotine shear used, the dynamic programming algorithm is applied to generate optimal layouts on segments of lengths no longer than the blade length, and the knapsack algorithm is employed to find the optimal layout of the segments on the sheet. The computational results indicate that the algorithms presented are more efficient than the branch-and-bound algorithms, which are the best algorithms so far that can guarantee the simplest patterns. © 2005 Elsevier Inc. All rights reserved.

Author-supplied keywords

  • CAD
  • Cutting stock problem
  • Metal sheet
  • Optimization
  • Two-dimensional cutting

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in

Find this document


  • Yaodong Cui

Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free