Learning to Solve Grouped 2D Bin Packing Problems in the Manufacturing Industry

The two-dimensional bin packing problem (2DBP) is a critical optimization problem in the furniture production and glass cutting industries, where the objective is to cut smaller-sized items from a minimum number of large standard-sized raw materials. In practice, factories manufacture hundreds of customer orders (sets of items) every day, and to relieve pressure in management, a common practice is to group the orders into batches for production, ensuring that items from one order are in the same batch instead of scattered across the production line. In this work, we formulate this problem as the grouped 2D bin packing problem, a bi-level problem where the upper level partitions orders into groups and the lower level solves 2DBP for items in each group. The main challenges are (1) the coupled optimization of upper and lower levels and (2) the high computational efficiency required for practical application. To tackle these challenges, we propose an iteration-based hierarchical reinforcement learning framework, which can learn to solve the optimization problem in a data-driven way and provide fast online performance after offline training. Extensive experiments demonstrate that our method not only achieves the best performance compared to all baselines but is also robust to changes in dataset distribution and problem constraints. Finally, we deployed our method in the ARROW Home factory in China, resulting in a 4.1% reduction in raw material costs. We have released the source code and datasets to facilitate future research.