Computers and Operations Research
Optimal orthogonal tiling of 2-D iterations
Journal of Parallel and Distributed Computing
The cutting stock problem in a hardboard industry: a case study
Computers and Operations Research
Discrete Optimization Algorithms with Pascal Programs
Discrete Optimization Algorithms with Pascal Programs
Recent advances on two-dimensional bin packing problems
Discrete Applied Mathematics
Generating optimal two-section cutting patterns for rectangular blanks
Computers and Operations Research
Two-stage general block patterns for the two-dimensional cutting problem
Computers and Operations Research
INFORMS Journal on Computing
Heuristic and exact algorithms for generating homogenous constrained three-staged cutting patterns
Computers and Operations Research
T-shape homogenous block patterns for the two-dimensional cutting problem
Journal of Global Optimization
A recursive algorithm for constrained two-dimensional cutting problems
Computational Optimization and Applications
Generating optimal two-section cutting patterns for rectangular blanks
Computers and Operations Research
Exact algorithms for the two-dimensional guillotine knapsack
Computers and Operations Research
A parallel algorithm for constrained two-staged two-dimensional cutting problems
Computers and Industrial Engineering
A parallel algorithm for two-staged two-dimensional fixed-orientation cutting problems
Computational Optimization and Applications
Simple block patterns for the two-dimensional cutting problem
Mathematical and Computer Modelling: An International Journal
A recursive branch-and-bound algorithm for constrained homogenous T-shape cutting patterns
Mathematical and Computer Modelling: An International Journal
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In this paper we propose two exact algorithms for solving both two-staged and three staged unconstrained (un)weighted cutting problems. The two-staged problem is solved by applying a dynamic programming procedure originally developed by Gilmore and Gomory [Gilmore and Gomory, Operations Research, vol. 13, pp. 94–119, 1965]. The three-staged problem is solved by using a top-down approach combined with a dynamic programming procedure. The performance of the exact algorithms are evaluated on some problem instances of the literature and other hard randomly-generated problem instances (a total of 53 problem instances). A parallel implementation is an important feature of the algorithm used for solving the three-staged version.