A heuristic for the one-dimensional cutting stock problem with pattern reduction

A sequential heuristic algorithm is presented for the one-dimensional cutting stock problem in which a set of items with specified length and demand are cut from the stock rods such that the waste is minimized. The algorithm generates a cutting pattern using items of a selected subset of the unassigned items, determines the frequency (number of times) at which the pattern can be used, deletes from the set of the unassigned items those that are assigned to the current pattern, and repeats until all items have been assigned. The selected subset is determined such that the frequency of the generated pattern can be as large as possible, provided that some constraints are observed to keep reasonable trim loss, and the cutting pattern is obtained from solving a bounded knapsack problem. The computational test on 18 classes of 1800 benchmark instances indicates that the algorithm performs better than two recently published algorithms for pattern reduction.