In the one-dimensional cutting stock problem with usable leftovers (1DCSPUL), items of the current order are cut from stock bars to minimize material cost. Here, stock bars include both standard ones bought commercially and old leftovers generated in processing previous orders, and cutting patterns often include new leftovers that are usable in processing subsequent orders. Leftovers of the same length are considered to be of the same type. The number of types of leftovers should be limited to simplify the cutting process and reduce the storage area. This paper presents an integer programming model for the 1DCSPUL with limited leftover types and describes a heuristic algorithm based on a column-generation procedure to solve it. Computational results show that the proposed approach is more effective than several published algorithms in reducing trim loss, especially when the number of types of leftovers is limited.

This paper presents a heuristic for the constrained two-dimensional cutting problem in which a guillotine divides a plate into rectangular pieces. The objective of the proposed heuristic is to maximize the pattern value (that is, the total value of the pieces produced from the plate) while observing the constraint that the number produced of a piece can not exceed the demand for that piece. The algorithm uses a simple recursion approach to consider a set of cutting patterns with specified geometric features, and uses a bound technique to discard unpromising branches. It can give solutions competitive with those of other heuristic algorithms. Its solutions to some benchmark instances are better than those currently reported in the literature.

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