A pattern reduction procedure in a one-dimensional cutting stock problem by grouping items according to their demands

Cutting and packing problems appear in many industrial settings where larger pieces are cut into smaller ones in order to produce items or products that are required by other industries or customers, e.g., paper, steel and fiber industries. A solution for the cutting problem consists in determining a group of patterns and their frequencies, that is, the number of times that a pattern is cut to supply the demand. Cost of the production may be dependent on the pattern changes, because they might require time and people to prepare the equipment. This work introduces a heuristic method/approach that produces a solution to the one-dimensional cutting stock problem with a reduced number of different patterns in the solution. The heuristic method proposed begin separating the items in two disjointed groups, according to their demands. Patterns are generated with items of these groups and those with limited waste are accepted. A residual problem is solved with items whose demands are not satisfied and, with the solution obtained, we apply a pattern reducing procedure of the literature.