Placement strategy for trim minimization in one-dimensional cutting stock

The cutting stock problem(CSP) is one of the famous problems of operational research. In the past few decades a number of techniques are proposed to solve the problem. Almost in all technique, the bottleneck is the column generation phase due to the enumerative nature. In this paper, we propose a technique, for column generation that reduces the total number of cutting pattern to be generated. The approach emphasizes the fact that the total number of pattern to be generated would be at most the number of stock requirement. In this approach we have used placement strategy i.e. taking each stock requirement at a time and checking relative position of other required stock. The results obtained are better than already existing delayed column generation, the trim loss have reduced for dataset varying from .001-.05%.