Heuristics for the two-dimensional cutting stock problem with usable leftover

Abstract

Utilization of residue is a challenge in engineering practice, because unreasonable cutting causes excess materials wasted and increases the production cost. This work considers the residual two-dimensional cutting stock problem with usable leftover in which unused parts of cutting patterns can be used for future orders. We propose an algorithm that combines the iterative sequential value correction heuristic with the beam search heuristic, considering both the accumulation and the reusability of leftovers to reduce the material consumption. Cutting plans are constructed iteratively and the best one are chosen as the solution. Cutting patterns in the cutting plan are generated sequentially by recursive techniques, and potentially usable leftover are accumulated by beam search heuristic. Item values are corrected after each pattern to diversify cutting plans. Three sets of simulations under different number of periods, over medium and large instances from the literature, are used to demonstrate the effectiveness of the heuristics. Computational results show that the algorithm provides better solutions, which can save a considerable amount of plate in a long-term production period. The utilization of wastages can save a considerable amount of stock plate and contract the production cost of enterprises in the long-term production period.