warehouse logistics teams

Abstract: Online 3D bin packing with a bounded buffer requires irreversible item-selection and placement decisions under limited knowledge of future arrivals. Feasibility alone is insufficient, as feasible actions can produce different residual-space structures and subsequent packing opportunities. A central architectural question is how to allocate spatial reasoning between item selection and placement evaluation. We propose Spatial Affordance Retrieval (SAR), a novel learning-based framework that coordinates global item-space matching with geometry-aware placement ranking. A voxel-token spatial encoder represents 3D container occupancy, enabling a picker to match buffered items to the residual space without requiring item-specific placement proposals as inputs. After item selection, a loader ranks feasible rotation-position candidates using candidate geometry, local geometric features (LGF), and inter-candidate comparison, without directly accessing global spatial tokens. The feasible candidate set connects the two stages, which are jointly optimized under a shared long-horizon packing return. On the Random, JD, and SF datasets, the best SAR variants improve utilization over the strongest evaluated online baselines by 0.96-4.20 percentage points under the no-buffer setting (K=1). With a buffer (K=5), the best utilization rates across SAR variants reach 93.55%, 91.04%, and 90.41%, respectively. Ablations support the complementary roles of global item-space matching and geometry-aware placement evaluation, counterfactual analysis suggests that learned item selection favors greater future packing potential, and experiments demonstrate compatibility with multiple candidate generators.

Abstract: This paper presents significant upper-bound improvements for dynamic 2D square bin packing, where square items arrive and depart over time and the objective is to minimize the peak number of concurrent active unit bins. In our model, repacking is permitted only within a destination bin upon item arrival; migration between active bins is strictly forbidden. By introducing a streamlined two-list algorithm and proving a tight $5/16$ occupied-area bound for Next-Fit Decreasing Height, we reduce the upper bound on the asymptotic competitive ratio for arbitrary squares from 4.2154 down to 3.918, breaking a longstanding theoretical ceiling. For restricted variants, we establish asymptotic competitive ratios of at most 3.356 for unit-fraction side lengths and 2.211 for power-fraction side lengths.