This paper addresses the challenges associated with nesting and production scheduling in additive manufacturing (AM). The problem studied consists of grouping a set of parts into batches, which are then assigned to and sequenced across the available machines, guaranteeing the production of all parts. This work stands out by proposing exact methods for the AM nesting and scheduling problem considering irregular-shaped parts with specific release dates, processing times, and due dates, with the aim of minimizing the cumulative tardiness. The proposed approaches include two logic-based Benders decompositions: one combining Mixed Integer Programming (MIP) and Constraint Programming (CP), and the other relying solely on CP. To deal with the sub-problems, a strategic procedure was developed to reduce the solution space while maintaining low resolution times per iteration. Problem-specific cuts are also generated to improve the efficiency of these approaches. Computational experiments show that both decompositions significantly outperform a prior monolithic CP model, with the decomposition based solely on CP yielding the best results. Moreover, the results show that this approach has the potential to achieve similar computational performance of non-exact approaches that are currently considered state-of-the-art. A set of instances is provided to serve as a benchmark for future studies.

中文翻译：

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解决增材制造系统大型嵌套和调度问题的最优分解方法

本文解决了增材制造 (AM) 中与排料和生产调度相关的挑战。研究的问题包括将一组零件分组，然后将其分配给可用机器并在可用机器上排序，以保证所有零件的生产。这项工作的突出之处在于，考虑到具有特定发布日期、加工时间和截止日期的不规则形状零件，提出了针对增材制造嵌套和调度问题的精确方法，旨在最大限度地减少累积延误。所提出的方法包括两种基于逻辑的 Benders 分解：一种结合了混合整数规划 (MIP) 和约束规划 (CP)，另一种仅依赖于 CP。为了处理子问题，开发了一种战略程序来减少解决方案空间，同时保持每次迭代的低分辨率时间。还生成针对特定问题的削减以提高这些方法的效率。计算实验表明，两种分解都明显优于先前的整体 CP 模型，其中仅基于 CP 的分解产生了最佳结果。此外，结果表明，这种方法有可能实现与目前被认为最先进的非精确方法类似的计算性能。提供了一组实例作为未来研究的基准。