Anni Zhang | Searcharxiv

arXiv2026

Solver-Verified Formulation Generation and Selection for Multi-Warehouse Inventory Allocation Using Large Language Models

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.

math.OC↗

arXiv2025

Open, Small, Rigmarole -- Evaluating Llama 3.2 3B's Feedback for Programming Exercises

Large Language Models (LLMs) have been subject to extensive research in the past few years. This is particularly true for the potential of LLMs to generate formative programming feedback for novice learners at university. In contrast to Generative AI (GenAI) tools based on LLMs, such as GPT, smaller and open models have received much less attention. Yet, they offer several benefits, as educators can let them run on a virtual machine or personal computer. This can help circumvent some major concerns applicable to other GenAI tools and LLMs (e. g., data protection, lack of control over changes, privacy). Therefore, this study explores the feedback characteristics of the open, lightweight LLM Llama 3.2 (3B). In particular, we investigate the models' responses to authentic student solutions to introductory programming exercises written in Java. The generated output is qualitatively analyzed to help evaluate the feedback's quality, content, structure, and other features. The results provide a comprehensive overview of the feedback capabilities and serious shortcomings of this open, small LLM. We further discuss the findings in the context of previous research on LLMs and contribute to benchmarking recently available GenAI tools and their feedback for novice learners of programming. Thereby, this work has implications for educators, learners, and tool developers attempting to utilize all variants of LLMs (including open, and small models) to generate formative feedback and support learning.

cs.CY↗