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 problem joining the nesting and scheduling of parts to be printed. 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 a solution is checked in the sub-problem. Current state-of-the-art techniques are extended to solve the orthogonal packing with rotation to speed up the solution of the sub-problem. Extensive computational tests on existing instances and a new benchmark instance set show the algorithm's superior performance compared to an existing integrated mixed-integer programming model.

翻译：近年来，增材制造因其能够生产高度定制化及复杂零件，同时缩短生产周期和降低成本的变革潜力而备受关注。增材制造在传统与新型商业模式中的兴起，迫切需要高效的生产规划流程。其中，增材制造设备（即3D打印机）上待构建零件的分配与排序问题，因融合了零件排样与生产调度而具有高度复杂性。本文针对非关联并行机的集成规划问题，提出了一种新型分支定界算法。该算法基于组合Benders分解：主问题处理调度规划，子问题检验解的可行性。通过扩展当前最先进的旋转正交排样技术来加速子问题的求解。基于现有算例及新基准算例集的大量计算实验表明，与现有集成混合整数规划模型相比，所提算法具有更优性能。