An Approximation Scheme for the Two-Stage, Two-Dimensional Bin Packing Problem
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
Probabilistic subproblem selection in branch-and-bound algorithms
Journal of Computational and Applied Mathematics
A Tale of Two Dimensional Bin Packing
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Efficient Production-Distribution System Design
Management Science
Heuristic and exact algorithms for generating homogenous constrained three-staged cutting patterns
Computers and Operations Research
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Heuristic algorithm for a cutting stock problem in the steel bridge construction
Computers and Operations Research
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Computers and Industrial Engineering
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Computers and Operations Research
Probabilistic subproblem selection in branch-and-bound algorithms
Journal of Computational and Applied Mathematics
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Computers and Operations Research
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Models for the two-dimensional two-stage cutting stock problem with multiple stock size
Computers and Operations Research
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We consider the cutting of rectangular order pieces into stock pieces of specified width and length. The cutting process involves three stages of orthogonal guillotine cutting: Stock pieces are cut into sections that are cut into slits that are cut into order pieces. Restrictions imposed on the cutting process make the combinatorial structure of the problem more complex, but limit the scope of solution space. The objective of the problem is mainly to minimize waste, but our model also accounts for other issues such as aging stock pieces, urgent or optional orders, and fixed setup costs. Our solution approach involves a nested decomposition of the problem and the recursive use of the column-generation technique: We use a column-generation formulation of the problem (Gilmore and Gomory 1965) and the cutting-pattern--generation subproblem is itself solved using a column-generation algorithm. LP-based lower bounds on the minimum cost are computed and, by rounding the LP solution, a feasible solution and associated upper bound is obtained. This approach could in principle be used in a branch-and-bound search to solve the problem to optimality. We report computational results for industrial instances. The algorithm is being used in industry as a production-planning tool.