Knapsack problems: algorithms and computer implementations
Knapsack problems: algorithms and computer implementations
Computers and Operations Research
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
A New Exact Algorithm for General Orthogonal D-Dimensional Knapsack Problems
ESA '97 Proceedings of the 5th Annual European Symposium on Algorithms
On rectangle packing: maximizing benefits
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
An Exact Algorithm for Constrained Two-Dimensional Two-Staged Cutting Problems
Operations Research
A Tale of Two Dimensional Bin Packing
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
INFORMS Journal on Computing
A recursive algorithm for constrained two-dimensional cutting problems
Computational Optimization and Applications
An Exact Algorithm for Higher-Dimensional Orthogonal Packing
Operations Research
Arc-flow model for the two-dimensional guillotine cutting stock problem
Computers and Operations Research
A new graph-theoretical model for k-dimensional guillotine-cutting problems
WEA'08 Proceedings of the 7th international conference on Experimental algorithms
On the two-dimensional Knapsack Problem
Operations Research Letters
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The two-dimensional knapsack problem requires to pack a maximum profit subset of ''small'' rectangular items into a unique ''large'' rectangular sheet. Packing must be orthogonal without rotation, i.e., all the rectangle heights must be parallel in the packing, and parallel to the height of the sheet. In addition, we require that each item can be unloaded from the sheet in stages, i.e., by unloading simultaneously all items packed at the same either y or x coordinate. This corresponds to use guillotine cuts in the associated cutting problem. In this paper we present a recursive exact procedure that, given a set of items and a unique sheet, constructs the set of associated guillotine packings. Such a procedure is then embedded into two exact algorithms for solving the guillotine two-dimensional knapsack problem. The algorithms are computationally evaluated on well-known benchmark instances from the literature. The C++ source code of the recursive procedure is available upon request from the authors.