ORLoopBench: Solver-in-the-Loop Benchmarks for Self-Correction and Behavioral Rationality in Operations Research

Operations Research practitioners debug infeasible models through an iterative process: inspecting Irreducible Infeasible Subsystems (\textbf{IIS}), identifying constraint conflicts, and repairing formulations until feasibility is restored. Existing LLM benchmarks mostly treat OR as one-shot translation from problem descriptions to solver code, omitting this diagnostic loop. We formalize infeasible-model repair as a solver-in-the-loop Markov Decision Process in which each action triggers solver re-execution and \textbf{IIS} recomputation, yielding deterministic, verifiable feedback. We introduce \textbf{ORLoopBench}, a benchmark suite with two components: \textbf{ORDebug} releases 5,362 LP/MILP repair instances, while \textbf{ORBias} evaluates closed-form operational decision rationality across inventory settings. Solver-verified RLVR training enables an 8B model to surpass frontier APIs on LP repair (95.3\% vs 92.4\% RR@5), improves diagnostic behavior, and transfers to MILP repair. The same evaluation exposes semantic drift in whole-model code regeneration: feasible regenerated MILPs can solve the wrong problem. Process-level evaluation with solver oracles enables targeted training for reliable OR self-correction.

Many organizations use optimization software to make decisions such as how much inventory to keep, how to schedule resources, or how to route products through a supply chain. These models often fail because of small mistakes in the written constraints, but the error messages from solvers can be hard for non-experts to interpret. This paper studies whether AI assistants can use solver feedback to find and fix such mistakes. We introduce ORLoopBench, a test suite for evaluating AI systems on two practical tasks: repairing broken optimization models through repeated feedback, and checking whether language models make biased decisions in operations-style settings. We also train an AI repair agent that learns from solver-verified feedback. Across our experiments, this agent fixes more modeling errors and needs fewer repair attempts than general-purpose language models. The results suggest that AI systems can become more useful assistants for optimization modeling when they are connected to reliable feedback from domain tools, while also showing the need to test their behavior carefully before using them in decision workflows.