The Three-Dimensional Bin Packing Problem
Operations Research
Recent advances on two-dimensional bin packing problems
Discrete Applied Mathematics
A squeaky wheel optimisation methodology for two-dimensional strip packing
Computers and Operations Research
A genetic programming hyper-heuristic approach for evolving 2-D strip packing heuristics
IEEE Transactions on Evolutionary Computation
Exact algorithms for the two-dimensional guillotine knapsack
Computers and Operations Research
LP bounds in various constraint programming approaches for orthogonal packing
Computers and Operations Research
Automating the packing heuristic design process with genetic programming
Evolutionary Computation
Theoretical investigation of aggregation in pseudo-polynomial network-flow models
ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
New Hybrid Discrete PSO for Solving Non Convex Trim Loss Problem
International Journal of Applied Evolutionary Computation
Expert Systems with Applications: An International Journal
Models for the two-dimensional two-stage cutting stock problem with multiple stock size
Computers and Operations Research
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We describe an exact model for the two-dimensional cutting stock problem with two stages and the guillotine constraint. It is an integer linear programming (ILP) arc-flow model, formulated as a minimum flow problem, which is an extension of a model proposed by Valerio de Carvalho for the one dimensional case. In this paper, we explore the behavior of this model when it is solved with a commercial software, explicitly considering all its variables and constraints. We also derive a new family of cutting planes and a new lower bound, and consider some variants of the original problem. The model was tested on a set of real instances from the wood industry, with very good results. Furthermore the lower bounds provided by the linear programming relaxation of the model compare favorably with the lower bounds provided by models based on assignment variables.