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Ask, Clarify, Optimize: Human-LLM Agent Collaboration for Smarter Inventory Control

Yaqi Duan, Yichun Hu, Jiashuo Jiang

TL;DR

This work investigates improving inventory control for small and medium enterprises by combining a language-model interface with rigorous optimization. It demonstrates that end-to-end LLM solvers incur a 'hallucination tax' due to lack of grounded stochastic reasoning, and introduces a hybrid agentic framework that decouples semantic elicitation from optimization. A scalable Human Imitator testbed enables controlled evaluation against boundedly rational manager inputs, revealing substantial cost savings (around 32%) over end-to-end baselines and clarifying that perfect information alone does not fix computational limits. The study concludes that LLMs are most effective as natural-language interfaces that enable access to solver-based policies, suggesting a practical architectural pattern for prescriptive ERP and decision-support systems. It also offers a reusable evaluation pipeline for interactive AI decision-support across domains.

Abstract

Inventory management remains a challenge for many small and medium-sized businesses that lack the expertise to deploy advanced optimization methods. This paper investigates whether Large Language Models (LLMs) can help bridge this gap. We show that employing LLMs as direct, end-to-end solvers incurs a significant "hallucination tax": a performance gap arising from the model's inability to perform grounded stochastic reasoning. To address this, we propose a hybrid agentic framework that strictly decouples semantic reasoning from mathematical calculation. In this architecture, the LLM functions as an intelligent interface, eliciting parameters from natural language and interpreting results while automatically calling rigorous algorithms to build the optimization engine. To evaluate this interactive system against the ambiguity and inconsistency of real-world managerial dialogue, we introduce the Human Imitator, a fine-tuned "digital twin" of a boundedly rational manager that enables scalable, reproducible stress-testing. Our empirical analysis reveals that the hybrid agentic framework reduces total inventory costs by 32.1% relative to an interactive baseline using GPT-4o as an end-to-end solver. Moreover, we find that providing perfect ground-truth information alone is insufficient to improve GPT-4o's performance, confirming that the bottleneck is fundamentally computational rather than informational. Our results position LLMs not as replacements for operations research, but as natural-language interfaces that make rigorous, solver-based policies accessible to non-experts.

Ask, Clarify, Optimize: Human-LLM Agent Collaboration for Smarter Inventory Control

TL;DR

This work investigates improving inventory control for small and medium enterprises by combining a language-model interface with rigorous optimization. It demonstrates that end-to-end LLM solvers incur a 'hallucination tax' due to lack of grounded stochastic reasoning, and introduces a hybrid agentic framework that decouples semantic elicitation from optimization. A scalable Human Imitator testbed enables controlled evaluation against boundedly rational manager inputs, revealing substantial cost savings (around 32%) over end-to-end baselines and clarifying that perfect information alone does not fix computational limits. The study concludes that LLMs are most effective as natural-language interfaces that enable access to solver-based policies, suggesting a practical architectural pattern for prescriptive ERP and decision-support systems. It also offers a reusable evaluation pipeline for interactive AI decision-support across domains.

Abstract

Inventory management remains a challenge for many small and medium-sized businesses that lack the expertise to deploy advanced optimization methods. This paper investigates whether Large Language Models (LLMs) can help bridge this gap. We show that employing LLMs as direct, end-to-end solvers incurs a significant "hallucination tax": a performance gap arising from the model's inability to perform grounded stochastic reasoning. To address this, we propose a hybrid agentic framework that strictly decouples semantic reasoning from mathematical calculation. In this architecture, the LLM functions as an intelligent interface, eliciting parameters from natural language and interpreting results while automatically calling rigorous algorithms to build the optimization engine. To evaluate this interactive system against the ambiguity and inconsistency of real-world managerial dialogue, we introduce the Human Imitator, a fine-tuned "digital twin" of a boundedly rational manager that enables scalable, reproducible stress-testing. Our empirical analysis reveals that the hybrid agentic framework reduces total inventory costs by 32.1% relative to an interactive baseline using GPT-4o as an end-to-end solver. Moreover, we find that providing perfect ground-truth information alone is insufficient to improve GPT-4o's performance, confirming that the bottleneck is fundamentally computational rather than informational. Our results position LLMs not as replacements for operations research, but as natural-language interfaces that make rigorous, solver-based policies accessible to non-experts.
Paper Structure (48 sections, 15 equations, 18 figures, 12 tables)

This paper contains 48 sections, 15 equations, 18 figures, 12 tables.

Table of Contents

  1. Introduction
  2. Our Main Contributions
  3. Related Work
  4. Stochastic Inventory Control and Deep Reinforcement Learning.
  5. LLMs for Optimization and Decision Support.
  6. Generative Agents and User Simulation.
  7. The Hybrid Agentic Framework
  8. Pipeline Architecture
  9. Information Extraction: Turning Dialogue into Parameters
  10. Optimization: From Parameters to Policies
  11. Policy Interpretation: Communicating Policies in Words
  12. The Human Imitator: A Scalable Testbed
  13. Data Collection: Capturing Managerial Dialogue
  14. Supervised Fine-Tuning (SFT)
  15. Empirical Validation: Quantifying Behavioral Alignment
  16. ...and 33 more sections

Figures (18)

  • Figure 1: LLM-Agent Pipeline for Inventory Management
  • Figure 2: Architecture of the Information Extraction Agent
  • Figure 3: Architecture of the Optimization Agent
  • Figure 4: Representative dialogue between the Human User and the Policy Interpretation Agent.
  • Figure 5: SFT Evaluation Trajectory. The curves illustrate the rapid convergence of the Human Imitator. The drop in Perplexity and the simultaneous rise in semantic similarity metrics (BERTScore, ROUGE-L and SBERT) indicate successful domain adaptation.
  • ...and 13 more figures

Theorems & Definitions (2)

  • Remark 1: Comparison with DPLM
  • Remark 2: Extensibility to Novel Algorithms