This paper discusses some of the basic formulation issues and solution procedures for solving one-and two-dimensional cutting stock problems. Linear programming, sequential heuristic and hybrid solution procedures are described. For two-dimensional cutting stock problems with rectangular shapes, we also propose an approach for solving large problems with limits on the number of times an ordered size may appear in a pattern.

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This paper presents a procedure for solving one-dimensional cutting stock problems when both the master rolls and customer orders have multiple quality gradations. The procedure described here is a two-stage sequential heuristic. An innovative shadow price-based procedure is first used to select slitting patterns for master rolls with variable quality characteristics. Then a residual problem for the available first-quality (' perfect') master rolls is solved with a linear programming model. An important characteristic of this approach is its robustness. The procedure can deal effectively with problems of varying size and complexity and can also easily be adapted to changing circumstances with respect to production quality and demand.