Knapsack problems: algorithms and computer implementations
Knapsack problems: algorithms and computer implementations
Software—Practice & Experience - Special issue on discrete algorithm engineering
A combined approach to the solution to the general one-dimensional cutting stock problem
Computers and Operations Research
Variable-sized object packing and its applications to instruction cache design
Computers and Electrical Engineering
0-1 reformulations of the multicommodity capacitated network design problem
Discrete Applied Mathematics
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The multistage cutting stock problem (CSP) generalizes the one-dimensional CSP when a lengthwise cutting process is distributed over two or more successive stages. At every stage of the cutting process incoming rolls are slit into smaller rolls by width. The problem is to minimize total trim loss occurring at all stages of technological process meeting customer demands for finished rolls. We propose a row and column generation technique for solving the multistage one-dimensional CSP. The technique is a generalization of the column generation method suggested by Gilmore and Gomory for solving a classic CSP. The procedure generates only those intermediate rolls (rows) and cutting patterns (columns) that are needed. An auxiliary problem embedded into the frame of the revised simplex algorithm is a non-linear knapsack problem that can be solved efficiently. Computational results prove the overall method is a valuable addition to the tool set for modeling and solving the multistage CSP.