基于求解器验证的多仓库库存分配公式生成与选择——利用大语言模型
Solver-Verified Formulation Generation and Selection for Multi-Warehouse Inventory Allocation Using Large Language Models
AI总结：
提出ORLA框架，利用大语言模型从自然语言需求自动生成运筹学公式，通过求解器反馈验证并选择最优公式，在京东29个生产批次上实现分配准确率提升4.5个百分点。
摘要：
面向平衡的多仓库库存分配是大型电商供应链中反复出现的决策问题，其中固定补货量根据需求预测和异构分配约束在各仓库间分配，以平衡分配后的库存覆盖率。实践中，分配需求通常依赖于场景，并以半结构化或自然语言形式表达，而非现成的运筹学公式。我们提出了一种运筹学引导的大语言模型分配框架（ORLA），该框架利用求解器反馈来生成、验证和选择运筹学公式。ORLA集成了自动的“问题-模型-代码”生成、基于学习的公式选择以及可行性恢复。我们基于偏差最小化、软带约束和背包启发式分配开发了三种互补的混合整数规划公式族，以及求解器就绪的混合整数线性规划重构、模块化约束扩展和针对不可行情况的基于惩罚的松弛机制。大语言模型组件从文本或半结构化规范生成候选公式和可执行的求解器代码，而求解器提供可执行性、可行性和解质量的验证信号。为应对实例异构性，ORLA估计候选公式的预期质量，选择有前景的候选，并通过分数感知聚合组合其输出。在京东29个生产评估批次上的实验结果表明，最佳单一运筹学公式相比现有方法将分配准确率提高了3.4个百分点，而完整的ORLA框架实现了4.5个百分点的整体提升，并在29个评估批次中的26个中提高了分配准确率。
英文摘要：
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.
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