Solving a real-world large-scale cutting stock problem: A clustering-assignment-based model
针对家具厂切割拼接生产中的大规模下料问题，提出基于聚类分配的模型，通过迭代启发式算法在一分钟内获得高质量解，相比工厂方法降低成本20.90%、减少切割废料4.97%。
This study stems from a furniture factory producing products by cutting and splicing operations. We formulate the problem into an assignment-based model, which reflects the problem accurately, but is intractable, due to a large number of binary variables and severe symmetry in the solution space. To overcome these drawbacks, we reformulate the problem into a clustering-assignment-based model (and its variation), which provides lower (upper) bounds of the assignment-based model. According to the classification of the board types, we categorize the instances into three cases: Narrow Board, Wide Board, and Mixed Board. We prove that the clustering-assignment-based model can obtain the optimal schedule for the original problem in the Narrow Board case. Based on the lower and upper bounds, we develop an iterative heuristic to solve instances in the other two cases. We use industrial data to evaluate the performance of the iterative heuristic. On average, our algorithm can generate high-quality solutions within a minute. Compared with the greedy rounding heuristic, our algorithm has obvious advantages in terms of computational efficiency and stability. From the perspective of the total costs and practical metrics, our method reduces costs by 20.90% and cutting waste by 4.97%, compared with a factory’s method.