Large language models (LLMs) can translate business descriptions into optimization models, but the generated executable code may misstate constraints or objectives, causing solvers to return optimal solutions to the wrong problem. Even when a solution obeys the stated rules, a better plan might exist. For organizations that repeatedly perform optimization modeling, we propose a low‑cost, locally deployable LLM framework that automatically verifies and improves model formulations.
We introduce OSCAR (Optimization modeling by Simulator, Coder, And Reviewer). The offline Simulator is certified against labeled feasible/infeasible decision examples and is used to compare candidate formulations and keep searching beyond mere feasibility. The Coder invokes various LLMs to produce model code, while the Reviewer checks the output against the Simulator’s labels.
Each improvement attempt requires two decisions: which LLM to call (different price‑performance trade‑offs) and when to stop searching. We model this as sequential decisions under unknown difficulty. With known priors we prove that a cost‑ordered escalation is optimal; for arbitrary menus we derive a prior‑free competitive guarantee.
Experiments on five benchmark problems use two small open‑weight LLMs that run on a single GPU. OSCAR achieves 95%–100% accuracy under the reported settings, while single‑attempt accuracies of the two models are 29% and 48%. Across five runs per problem, Codex and Claude Code incur average token costs 3.1× and 5.8× those of OSCAR, respectively.
OSCAR can operate with locally hosted models or switch to the cloud depending on budget and confidentiality needs. Firms should keep labeled decision examples of feasible and infeasible actions to clarify plain‑language operating rules. When an LLM’s interpretation conflicts with these labels, OSCAR follows the labels. As LLM capabilities and prices evolve, OSCAR’s simple operating rules and tunable settings let firms adapt model choices and continue to benefit.
Review