Exact and heuristic algorithms for staged cutting problems

Abstract

This paper presents exact and heuristic algorithms for unconstrained staged cutting problems. For a k-stage pattern, a group of parallel cuts at the final stage divide the sheet into several segments. For the k-stage pattern on the sheet to be optimal, the pattern on each segment must be an optimal (k - 1)-stage pattern. Assume that the optimal (k - 2)-stage patterns are known (k 3); the exact algorithm solves one knapsack problem for each segment to obtain the optimal (k - 1)-stage pattern on the segment and determines the optimal k-stage pattern on the sheet by solving one additional knapsack problem. The exact algorithm uses general strips, which consists of blanks of different sizes, whereas the heuristic algorithm uses uniform strips, each one of which contains only blanks of the same size. The computational results indicate that the algorithms are more efficient than other algorithms tested.