LLM Framework for Multi-Warehouse Inventory Formulation Selection

A recent preprint on arXiv (2607.25956) introduces a framework utilizing solver-guided large language models (LLMs) to select formulations for operations research (OR) in multi-warehouse inventory allocation. Traditionally, this issue is approached through mixed-integer programming (MIP), yet no single formulation is effective across diverse instances due to elements like demand concentration and inventory discrepancies. This framework matches each allocation scenario with a solver-compatible formulation from a library of OR experts, each representing a unique MIP formulation with specific allocation priorities. The training process involves balanced expert-conditioned supervised fine-tuning (SFT) for schema learning, followed by MIP solver assessments on past instances to transform allocation-quality improvements into training signals, ultimately aiming to enhance allocation efficiency through optimal MIP formulation selection.