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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-insp","title":"Solver-Verified Formulation Generation and Selection for Multi-Warehouse Inventory Allocation Using Large Language Models","url":"https://arxiv.org/abs/2606.29366","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.29366v1 Announce Type: cross \nAbstract: 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. 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