Dual-Side Verification for Trustworthy LLM-Based Constrained Resource-Task Assignment Modeling

Constrained resource-task assignment(RTA) is a foundational problem in operations research and engineering decision support. Turning a natural-language assignment description into a correct optimization model and executable solver code requires expertise in both application semantics and mathematical programming. Large language models (LLMs) offer a promising way to automate this process, but they often misread specialized terminology, omit indispensable constraints, and return numerically valid yet semantically infeasible solutions. Existing self-correction methods mainly rely on code-execution errors and therefore fail to detect formulation-level faults when the solver runs successfully. We present RTA-Verifier, a plug-and-play dual-side verification framework for trustworthy LLM-based constrained assignment modeling. A distillation agent first extracts a multi-level modeling structure, including the problem class, assignment variant, low-level constraints, and explicit exclusions. A structure-side verifier then back-translates the generated model and checks whether it faithfully matches the extracted reference, while a solution-side verifier interprets the numerical solution in application-level terms and detects semantic contradictions that are invisible to the solver. The resulting comments guide a focused refinement step. On a published constrained-assignment benchmark with standard and hard splits, RTA-Verifier achieves 80.0% and 67.8% accuracy, improves code executability and numerical-output reliability, and remains effective across different backbone LLMs.