Exact Algorithms for Large-Scale Unconstrained Two and Three Staged Cutting Problems
Computational Optimization and Applications
A tabu search algorithm for large-scale guillotine (un)constrained two-dimensional cutting problems
Computers and Operations Research
Generating optimal two-section cutting patterns for rectangular blanks
Computers and Operations Research
A best-first branch and bound algorithm for unconstrained two-dimensional cutting problems
Operations Research Letters
T-shape homogenous block patterns for the two-dimensional cutting problem
Journal of Global Optimization
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This paper presents an algorithm for the unconstrained two-dimensional cutting problem of rectangular pieces. It proposes the two-stage general block pattern that can be cut into general blocks in two stages, with another two or more stages being required to cut the blocks into pieces. Firstly vertical cuts divide the stock sheet into segments, and then horizontal cuts divide the segments into general blocks. A general block contains general strips, and each cut on the block produces just one strip. The directions of two strips cut successively from a block are either parallel or perpendicular to each other. The algorithm uses a dynamic programming recursion to determine the strip layout on each block, solves knapsack problems to obtain the block layout on each segment and the segment layout on the sheet. The computational results indicate that the algorithm is highly efficient in improving material usage, and the computation time is reasonable.