In recent years, there has been considerable interest in the transformative potential of additive manufacturing (AM) since it allows for producing highly customizable and complex components while reducing lead times and costs. The rise of AM for traditional and new business models enforces the need for efficient planning procedures for AM facilities. In this area, the assignment and sequencing of components to be built by an AM machine, also called a 3D printer, is a complex challenge combining two combinatorial problems: The first decision involves the grouping of parts into production batches, akin to the well-known bin packing problem. Subsequently, the second problem pertains to the scheduling of these batches onto the available machines, which corresponds to a parallel machine scheduling problem. For minimizing makespan, this paper proposes a new branch-and-cut algorithm for integrated planning for unrelated parallel machines. The algorithm is based on combinatorial Benders decomposition: The scheduling problem is considered in the master problem, while the feasibility of an obtained solution with respect to the packing problem is checked in the sub-problem. Current state-of-the-art techniques are extended to solve the orthogonal packing with rotation and used to speed up the solution of the sub-problem. Extensive computational tests on existing and new benchmark instances show the algorithm’s superior performance, improving the makespan by 18.7% on average, with improvements reaching up to 97.6% for large problems compared to an existing integrated mixed-integer programming model.

中文翻译：

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增材制造中集成规划的新分支和切割方法


近年来，人们对增材制造 （AM） 的变革潜力产生了浓厚的兴趣，因为它可以生产高度可定制的复杂组件，同时缩短交货时间和降低成本。增材制造在传统和新商业模式中的兴起迫使需要对增材制造设施进行高效的规划程序。在这一领域，由增材制造机器（也称为 3D 打印机）构建的组件的分配和排序是一项复杂的挑战，结合了两个组合问题：第一个决定涉及将零件分组到生产批次中，类似于众所周知的料箱包装问题。随后，第二个问题与将这些批次调度到可用机器上有关，这对应于并行机器调度问题。为了最小化 makespan，本文提出了一种新的 branch-and-cut 算法，用于不相关的并行机器的集成规划。该算法基于组合 Benders 分解：在主问题中考虑调度问题，而在子问题中检查所得解与打包问题相关的可行性。当前最先进的技术被扩展为解决旋转的正交保压，并用于加快子问题的求解。对现有和新基准测试实例的广泛计算测试表明，该算法具有卓越的性能，与现有的集成混合整数规划模型相比，平均将 makespan 提高了 18.7%，对于大型问题，改进高达 97.6%。