🤖 AI Summary
This work addresses the challenge of automatically translating complex business requirements into optimization models for multi-warehouse inventory allocation in e-commerce. To this end, the authors propose ORLA, a novel framework that, for the first time, integrates solver feedback into the generative loop of large language models to automatically construct, validate, and select mixed-integer programming formulations from natural language or semi-structured inputs. ORLA supports dynamic constraints, infeasibility recovery, and modular extensibility, while incorporating modeling paradigms such as deviation minimization, soft bandwidth limits, and knapsack-style formulations. Evaluated on 29 real-world production batches from JD.com, ORLA improves allocation accuracy by 4.5 percentage points overall, significantly outperforming existing approaches.
📝 Abstract
Balance-oriented multi-warehouse inventory allocation is a recurring decision problem in large-scale e-commerce supply chains, in which a fixed replenishment quantity is distributed across warehouses to balance post-allocation inventory coverage while accounting for demand forecasts and heterogeneous allocation constraints. In practice, allocation requirements are often scenario-dependent and expressed in semi-structured or natural-language form rather than as ready-to-solve operations research (OR) formulations. We propose an OR-guided Large Language Model (LLM) for Allocation (ORLA) that uses solver feedback to generate, verify, and select OR formulations. ORLA integrates automatic "Problem-Model-Code (PMC)" generation, learning-based formulation selection, and feasibility restoration. We develop three complementary mixed-integer programming formulation families based on deviation minimization, soft band compliance, and knapsack-inspired allocation, together with solver-ready mixed-integer linear programming reformulations, modular constraint extensions, and a penalty-based relaxation mechanism for infeasible cases. The LLM component generates candidate formulations and executable solver code from textual or semi-structured specifications, while the solver provides verification signals for executability, feasibility, and solution quality. To address instance heterogeneity, ORLA estimates the expected quality of candidate formulations, selects promising candidates, and combines their outputs through score-aware aggregation. Experimental results on 29 production evaluation batches from JD.com show that the best single OR formulation improves allocation accuracy by 3.4 percentage points over the incumbent approach, while the full ORLA framework achieves a 4.5 percentage-point overall improvement and improves allocation accuracy in 26 of the 29 evaluation batches.