Scheduling for additive manufacturing with two-dimensional packing and incompatible items
研究了将订单物品分批并安排到3D打印机上的调度问题，目标是最小化完工时间，同时满足物品兼容性、二维不重叠和包含约束。提出了混合整数线性规划模型和启发式算法，实验表明启发式平均缩短12%的完工时间。
Additive manufacturing technology can enable low-cost, efficient production of low-demand, highly-complex customized items with reduced lead time if production is judiciously planned. This paper addresses the assignment of requested items into batches and the scheduling of the batches onto 3D printers. The objective is to minimize the manufacturing makespan while satisfying items’ compatibility, two-dimensional no-overlap and containment packing constraints within a batch, and machine’s capability to manufacture a batch. The problem is modeled as a mixed integer linear program (MIP) that solves instances up to 100 items. For hard and large instances, this paper proposes a matheuristic that fathoms packings using a step-wise check procedure. Computational results reveal that the proposed heuristic improves the makespan of MIP solutions of hard instances by 12% on average, with improvements reaching up to 72% for instances with 150 items. They further show that the proposed heuristic finds the best makespan for 88% of all cases. Finally, we provide useful managerial insights for production flexibility and scheduling policies.