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OptiRepair: Closed-Loop Diagnosis and Repair of Supply Chain Optimization Models with LLM Agents

Ruicheng Ao, David Simchi-Levi, Xinshang Wang

TL;DR

OptiRepair splits this task into a domain-agnostic feasibility phase (iterative IIS-guided repair of any LP) and a domain-specific validation phase (five rationality checks grounded in inventory theory) and trains two 8B-parameter models using self-taught reasoning with solver-verified rewards.

Abstract

Problem Definition. Supply chain optimization models frequently become infeasible because of modeling errors. Diagnosis and repair require scarce OR expertise: analysts must interpret solver diagnostics, trace root causes across echelons, and fix formulations without sacrificing operational soundness. Whether AI agents can perform this task remains untested. Methodology/Results. OptiRepair splits this task into a domain-agnostic feasibility phase (iterative IIS-guided repair of any LP) and a domain-specific validation phase (five rationality checks grounded in inventory theory). We test 22 API models from 7 families on 976 multi-echelon supply chain problems and train two 8B-parameter models using self-taught reasoning with solver-verified rewards. The trained models reach 81.7% Rational Recovery Rate (RRR) -- the fraction of problems resolved to both feasibility and operational rationality -- versus 42.2% for the best API model and 21.3% on average. The gap concentrates in Phase 1 repair: API models average 27.6% recovery rate versus 97.2% for trained models. Managerial Implications. Two gaps separate current AI from reliable model repair: solver interaction (API models restore only 27.6% of infeasible formulations) and operational rationale (roughly one in four feasible repairs violate supply chain theory). Each requires a different intervention: solver interaction responds to targeted training; operational rationale requires explicit specification as solver-verifiable checks. For organizations adopting AI in operational planning, formalizing what "rational" means in their context is the higher-return investment.

OptiRepair: Closed-Loop Diagnosis and Repair of Supply Chain Optimization Models with LLM Agents

TL;DR

OptiRepair splits this task into a domain-agnostic feasibility phase (iterative IIS-guided repair of any LP) and a domain-specific validation phase (five rationality checks grounded in inventory theory) and trains two 8B-parameter models using self-taught reasoning with solver-verified rewards.

Abstract

Problem Definition. Supply chain optimization models frequently become infeasible because of modeling errors. Diagnosis and repair require scarce OR expertise: analysts must interpret solver diagnostics, trace root causes across echelons, and fix formulations without sacrificing operational soundness. Whether AI agents can perform this task remains untested. Methodology/Results. OptiRepair splits this task into a domain-agnostic feasibility phase (iterative IIS-guided repair of any LP) and a domain-specific validation phase (five rationality checks grounded in inventory theory). We test 22 API models from 7 families on 976 multi-echelon supply chain problems and train two 8B-parameter models using self-taught reasoning with solver-verified rewards. The trained models reach 81.7% Rational Recovery Rate (RRR) -- the fraction of problems resolved to both feasibility and operational rationality -- versus 42.2% for the best API model and 21.3% on average. The gap concentrates in Phase 1 repair: API models average 27.6% recovery rate versus 97.2% for trained models. Managerial Implications. Two gaps separate current AI from reliable model repair: solver interaction (API models restore only 27.6% of infeasible formulations) and operational rationale (roughly one in four feasible repairs violate supply chain theory). Each requires a different intervention: solver interaction responds to targeted training; operational rationale requires explicit specification as solver-verifiable checks. For organizations adopting AI in operational planning, formalizing what "rational" means in their context is the higher-return investment.
Paper Structure (86 sections, 16 equations, 8 figures, 12 tables)

This paper contains 86 sections, 16 equations, 8 figures, 12 tables.

Table of Contents

  1. Introduction
  2. A closed-loop framework linking optimization feasibility to operational decisions.
  3. A domain-specialized training pipeline that outperforms frontier API models.
  4. Empirical evidence that domain specialization, not model scale, drives operational value.
  5. Related Work
  6. AI and LLMs in Operations Management
  7. LLM-Assisted Optimization
  8. Supply Chain Theory and Training Methods
  9. Closed-Loop Diagnosis and Repair Framework
  10. Multi-Echelon LP Formulation
  11. Error Classification
  12. Two-Phase Closed-Loop MDP
  13. Phase I: Diagnose and Repair.
  14. State space.
  15. Action space.
  16. ...and 71 more sections

Figures (8)

  • Figure 1: Two-phase closed-loop architecture of OptiRepair. Phase I (domain-agnostic) iteratively diagnoses and repairs an infeasible LP via solver IIS feedback. Upon reaching Optimal, Phase II (domain-specific) validates operational correctness through a replaceable domain oracle---implemented here with five supply chain rationality checks.
  • Figure 2: Phase I repair interaction. The agent receives an infeasible supply chain LP (Gurobi), uses GET_IIS to diagnose conflicting constraints, and repairs the capacity bound. When the solver returns Optimal, the episode transitions to Phase II. Full system prompt and transcript appear in Appendix \ref{['sec:app_prompts']}.
  • Figure 3: Phase II rationality repair interaction. The rationality oracle detects that the Phase I repair created a cost-consistency violation: the high-cost retailer holds more inventory than the cheaper warehouse. The agent corrects the objective coefficient; the solver re-optimizes and the oracle confirms all five checks pass.
  • Figure 4: OptiRepair-SC construction pipeline. ① A multi-echelon supply chain generator produces valid LPs with 2--5 echelons and 12--24 periods. ② A saboteur injects one of ten error types, grouped into five categories (demand/timing, balance/capacity, cost/structure, coefficient/sign, constraint/index). ③ Gurobi confirms the sabotaged model is infeasible (or Optimal-but-irrational for ME-5). ④ The ground-truth fix is verified against five rationality checks. ⑤ Validated instances form OptiRepair-SC (976 problems, disjoint train/test splits).
  • Figure 5: OptiSTaR training pipeline. Top: Phase I iterates through beam search exploration ($K\!=\!32$ candidates), STaR distillation, and GRPO refinement; three iterations raise $\text{RR@}{5}$ from 44.4% to 75.7%. Gurobi provides IIS feedback for beam search and outcome rewards for GRPO. Middle right: Phase II trains independently on oracle-generated data (SFT) refined by solver-based GRPO. Bottom: The two independently trained 8B models combine into the final pipeline ($\text{RRR} = 81.7\%$).
  • ...and 3 more figures