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ORThought: Benchmarking and Automating Logistics Optimization Modeling

Beinuo Yang, Qishen Zhou, Junyi Li, Chenxing Su, Panagiotis Angeloudis, Simon Hu

arXiv:2508.14410v3cs.AI

TL;DR

Manual optimization modeling in logistics depends on human expertise and can be slow to adapt to changing conditions. This paper introduces an annotated logistics benchmark and ORThought, a structured dual-agent framework. Across four datasets, ORThought reports substantial gains over strong baselines while maintaining high token efficiency.

  • Problem

    Optimization modeling translates operational realities into mathematical programs, but remains a human-expertise bottleneck amid manual reformulation latency and coordination overhead.

    Source: §1 · p. 2

  • Method

    The paper constructs LogiOR with rigorous annotations and proposes ORThought, a dual-agent framework that embeds expert modeling principles in structured reasoning.

    Source: §1 · pp. 3–4

  • Results

    9–17 percentage points: ORThought gains over strong baselines across four datasets while maintaining high token efficiency.

    Source: §7 · p. 18

  • Takeaways & Limitations

    The study reports that structured dual-agent automated modeling is effective across diverse logistics operation tasks, while its analysis identifies limitations for future work.

    Source: §6 · p. 17

    ORThought generates formulations in a single pass, so an incorrect but executable model can yield a plausible objective that the evaluation pipeline does not detect.

    Source: §6 · p. 17

Abstract

from arXiv · show

Optimization modeling stands as the engine of scientific decision-making in logistics and transportation, yet its adoption is hindered by a steep expertise threshold and the latency of manual workflows. Automating this process via Large Language Models (LLMs) offers a potential solution, but current approaches face critical bottlenecks: (i) a lack of high-quality, complex benchmarks; (ii) methodological inefficiencies in autonomous multi-agent frameworks, which often exhibit instability and redundant computation; and (iii) evaluations that lack diagnostic depth. In this work, we address these challenges from the following three aspects. First, we introduce LogiOR, a diverse logistics benchmark with rigorous annotations, and enrich existing datasets with the same annotation standard to support community utilization. Second, we propose ORThought, a structured dual-agent framework. By incorporating expert-level modeling principles via chain-of-thought reasoning, ORThought eliminates the redundancy of uncontrolled autonomous agents. Third, extensive empirical evaluations demonstrate that ORThought consistently outperforms state-of-the-art baselines by 9-17 percentage points, exhibiting distinct advantages in handling complex constraints while maintaining high token efficiency. Building on these results, we further conduct a multidimensional error analysis, which identifies key failure modes and success factors, providing actionable insights for future research. The dataset and code are available at https://huggingface.co/datasets/LabMem012/LogiOR and https://github.com/ZJU-TSELab/ORThought, respectively.

1. Introduction

Optimization modeling remains a human-expertise bottleneck in logistics, while manual workflows struggle with dynamic conditions and coordination demands. The paper introduces an annotated logistics benchmark and a structured dual-agent framework, reporting higher modeling success than existing approaches.

1. Introduction

  • Prior LLM-based automated modeling has expanded from canonical constrained optimization to longer descriptions, implicit constraints, vehicle routing, and dynamic fleet management.The authors cite early evidence of LLMs outperforming task-specific fine-tuned models in the 2023 NL4Opt competition.Source: §1 · p. 3
  • Existing work lacks complex, well-annotated logistics benchmarks, evidence that autonomous multi-agent systems outperform simpler methods, and diagnostic evaluation across problem characteristics.The introduction also identifies computational overhead and instability as concerns for uncontrolled multi-agent interactions.Source: §1 · p. 3
  • LogiOR provides a diverse, complex logistics benchmark with mathematical formulations, executable Gurobi code, solver-verified objectives, and problem characteristics.The same annotation standard is applied to three existing benchmarks to support community use and verification.Source: §1 · pp. 3–4
  • ORThought uses a resource-efficient dual-agent architecture and structured chain-of-thought reasoning to embed expert modeling principles.The authors report state-of-the-art modeling success with reduced computational costs and communication overhead.Source: §1 · p. 4
  • 9–17 percentage points: ORThought consistently outperforms existing approaches, including autonomous frameworks and fine-tuned models, with advantages on complex, larger problems.The paper also reports ablations and error analyses identifying failure modes for future research.Source: §1 · p. 4

2. Literature Review

The review organizes LLM-based automated optimization modeling around benchmarks, training-based adaptation, and inference-time reasoning and agent frameworks. It describes limitations in benchmark coverage and annotation, training transferability, and the cost and stability trade-offs of increasingly complex agent systems.

2. Literature Review

  • LLM capabilities such as in-context learning, chain-of-thought, structured reasoning, reflection, and tool use motivate three strands of automated optimization modeling research.The review groups prior work into benchmarks and evaluations, training-based methods, and inference-based methods.Source: §2 · p. 4

2.1. Benchmarks and evaluation

  • Existing benchmarks vary in domain and description style, but often have annotation errors, limited complexity, and insufficient detail for training and fine-grained evaluation.Studies also rarely assess token consumption or modeling-process failures, while aggregate success rates can mask variation across problem types and sizes.Source: §2.1 · pp. 4–5

2.2. Training-based methods

  • Training-based methods adapt model parameters through fine-tuning or reinforcement learning, but require substantial curation and training resources and can be difficult to transfer across architectures.The review describes work targeting smaller models, structured problem representations, solver-based verification, and reinforcement learning.Source: §2.2 · p. 5

2.3. Inference-based methods

  • Inference-based approaches range from single-agent prompting to structured pipelines and autonomous agents, trading flexibility against controllability, coordination cost, and error risk.Structured frameworks use predefined subtasks; autonomous systems can coordinate dynamically but incur communication overhead and cascading-error risk, while systematic comparisons with simpler baselines remain scarce.Source: §2.3 · p. 5

3. Methodology

ORThought separates mathematical formulation from code implementation in a structured dual-agent framework. A Model Agent builds an interpretable formulation and code, while a Solve Agent iteratively detects and repairs execution failures without revising silent formulation errors.

3. Methodology

  • ORThought separates abstract mathematical formulation from concrete code implementation because the two tasks have distinct cognitive demands.The Model Agent and Solve Agent have focused roles, supporting modular optimization and clear error attribution.Source: §3 · p. 6

3.1. Model agent

  • The Model Agent produces structured problem understanding, a formal mathematical model, and executable Gurobi code in a single inference call.Its staged process identifies objectives, variables, and constraints, then formalizes variable domains, the objective, and constraints in sequence.Source: §3.1 · pp. 6–7

3.2. Solve agent

  • The Solve Agent executes code, diagnoses errors, and repairs implementation while conditioning each cycle on the mathematical model.It stops on optimal, infeasible, or unbounded solver outcomes, or at the maximum iteration limit.Source: §3.2 · pp. 7–8
  • Repair is triggered only by execution failures, so successfully running code with an incorrect formulation can produce a silent error the framework does not detect.Formulation-level verification is outside the work's scope.Source: §3.2 · p. 7

4. The LogiOR Benchmark

LogiOR targets the logistics and transportation domain with diverse, relatively complex optimization problems and comprehensive annotations. Its construction combines expert annotation and review, and its instances span multiple categories, formulation types, and problem sizes.

4. The LogiOR Benchmark

  • LogiOR is designed to address the lack of logistics-focused benchmarks, broaden problem diversity and complexity, and provide annotations for fine-grained analysis and verification.It emphasizes medium-scale, mixed-integer, and nonlinear problems that are underrepresented in existing benchmarks.Source: §4 · p. 8

4.1. Dataset construction

  • Over two months, experts selected or adapted problems, independently annotated each with a formulation, executable Gurobi code, verified objective, and characteristics, and reviewed annotations before admission.Problem sources include solver test sets, textbooks, papers, and real-world logistics applications; descriptions were composed or rewritten for clarity and reduced overlap with likely pretraining examples.Source: §4.1 · p. 8

4.2. Dataset analysis

  • LogiOR covers six logistics categories and LP, ILP, MILP, and NLP, with variable, constraint, and nonzero counts spanning multiple orders of magnitude.Compared with existing benchmarks, it has a higher proportion of challenging MILP and NLP problems and a larger share of medium-scale instances.Source: §4.2 · p. 8

5. Experiments and Analysis

The experiments compare ORThought with existing approaches across four benchmarks and examine accuracy, token use, problem characteristics, errors, ablations, and model settings. ORThought outperforms competitive reasoning baselines across datasets, while results also expose challenges on complex problems.

5.1. Datasets

  • ORThought is evaluated on four benchmarks—LogiOR and three enhanced, well-known existing datasets; by default, experiments use GPT-4.1-nano (OpenAI, 2024) at temperature 0 and are repeated three times.A trial is successful if the LLM-generated solution achieves the ground-truth optimal objective value verified by OR experts.Source: §5.1 · p. 9, §5.2 · p. 10

5.3.1. Success rate

  • ORThought beats the strongest reasoning baselines, CoT and Reflexion, by 9–17 percentage points across datasets, while success is 46.01% on LogiOR.The reported success rate is 89.02% on NLP4LP and 57.83% on IndustryOR.Source: §5.3.1 · p. 10, Table 2 · p. 11

5.3.2. Token cost

  • ORThought uses slightly more prompt tokens than CoT but fewer than Reflexion, and its completion-token use is below SC and Reflexion while accuracy ranks second-best.Autonomous multi-agent methods are excluded from the token-consumption figure because of their higher token use.Source: §5.3.2 · p. 11, Figure 4 · p. 11

5.4. Performance analysis by problem characteristics (RQ2)

  • ORThought leads on ILP, MILP, and NLP, including gains of 14.66 pp on ILP and 25.00 pp on NLP; it also leads across toy, small, and medium sizes.Its advantage is strongest in Packing at 22.22 pp; success rates decline as problem size increases for all methods.Source: §5.4 · pp. 12–13, Table 3 · p. 12, Table 4 · p. 12

5.5. Error analysis (RQ3)

  • The error analysis finds constraints most error-prone across methods, with incorrect formulations more common than missing or spurious elements.ORThought has fewer variable, objective-function, and code errors than the compared baselines; the analysis counts multiple errors in a single failed problem.Source: §5.5 · pp. 13–14, Figure 5 · p. 13

5.6. Ablation study (RQ4)

  • Removing the understanding module degrades performance across problem types except LP; repair corrected execution errors in 25 of 31 problems, with 11 yielding the optimal solution.Expert knowledge helps most in understanding, and also benefits NLP problems and medium-size instances during modeling.Source: §5.6 · p. 14, Figure 6 · p. 14

5.7.1. LLM choice

  • Across three representative LLMs, ORThought beats the second-best baseline by 4–10 pp; complex problems show a performance leap at 8–14B model sizes.The scaling analysis finds that improvements vary by problem type and size, suggesting model choice should match problem complexity.Source: §5.7.1 · p. 15, §5.7.2 · p. 15, Figure 7 · p. 16

5.7.3. Temperature

  • Temperature 0 performs best for most categories; ORThought gains 15.90 pp on GPT-4.1-nano but only approximately 3 pp on DeepSeek-R1.It also improves GPT-4.1 by 3.64 pp and DeepSeek-V3 by 12.26 pp; its structured guidance is largely redundant with reasoning models’ built-in reasoning.Source: §5.7.3 · p. 15, Figure 8 · p. 16, §5.8 · p. 16

6. Discussion

The discussion identifies limits in ORThought’s one-pass formulation process and in current evaluation practice, alongside trade-offs in model size and the role of human expertise. It points to iterative verification, broader efficiency measures, adaptive model selection, and human-AI collaboration as research directions.

6. Discussion

  • Single-pass generation leaves incorrect but executable formulations vulnerable to silent failure because the evaluation pipeline may not detect their plausible yet wrong objective values.The proposed future directions are offline learning from verified modeling insights and online verification using solver signals and LLM self-checks.Source: §6 · p. 17
  • Current evaluation emphasizes solution correctness but omits computational tractability, although equivalent optimal values can arise from formulations with very different solving times.The discussion recommends measuring runtime, memory, and scaling with problem size.Source: §6 · p. 17
  • Smaller LLMs can achieve competitive success rates on simpler instances, suggesting that adaptive model selection could balance capability against computational cost.Reliable difficulty estimation and mapping difficulty to model size remain challenges; suggested indicators include convexity, constraint density, and objective linearity.Source: §6 · pp. 17–18
  • For high-stakes logistics decisions involving unstated context, changing preferences, or soft constraints, the discussion favors human-AI collaboration over fully automated black-box modeling.The proposed copilot drafts formulations and suggestions while human experts retain verification and final decisions.Source: §6 · p. 18

7. Conclusion

The paper presents ORThought as an LLM framework for automating optimization modeling, alongside LogiOR, a more complex and diverse logistics benchmark. Experiments report gains over strong baselines, and the conclusion identifies future research directions.

7. Conclusion

  • The work introduces an LLM-based framework to automate optimization modeling, addressing the expertise threshold and latency of manual workflows.Source: §7 · p. 18
  • Across four datasets, ORThought gains 9–17 percentage points over strong baselines while maintaining high token efficiency.The conclusion says these advantages persist across problem types, sizes, and base LLMs.Source: §7 · p. 18
  • LogiOR is a dedicated logistics benchmark with greater problem complexity and diversity than existing datasets.The conclusion also identifies iterative formulation verification, adaptive model selection, and human-AI collaboration as future research directions.Source: §7 · p. 18

CRediT authorship contribution statement

The authorship statement assigns contributions spanning conceptualization, methodology, software, investigation, formal analysis, resources, supervision, and writing.

CRediT authorship contribution statement

A. LogiOR

LogiOR pairs a logistics problem description with rich annotations intended to support evaluation, peer review, and reasoning-model training. ORThought’s two-agent prompts structure modeling and code production, including debugging against the mathematical model.

A. LogiOR

  • The LogiOR example includes rich annotations that support model evaluation, peer review for dataset errors, and potential training of reasoning models.The example describes shipping 1,000 tons across three routes, with linear transport costs and congestion fees based on total traffic flow.Source: A. LogiOR · p. 20

B. Design of ORThought

  • ORThought’s two-agent prompts guide problem analysis and mathematical model construction, then request executable Gurobi code and debugging that preserves model adherence.The prompts ask for decision variables, objectives, and constraints; the debugging prompt supplies the problem, model, code, and error message.Source: B. Design of ORThought · pp. 23–25

C. Setting of Ablation Study

The ablation variants are specified through prompt modifications.

C. Setting of Ablation Study

  • The four ablation variants are implemented by modifying prompts.The passage introduces four variants but does not describe their individual settings.Source: C. Setting of Ablation Study · p. 26

C.1. w/o repair

This ablation removes the Solve Agent’s retrieval of error information and its repair step.

C.1. w/o repair

  • The variant removes the Solve Agent’s retrieval of sandbox error information and its repair step.The passage does not specify other changes to the framework.Source: §C.1 · p. 26

C.2. w/o understanding

The ablations alter the problem-understanding and formulation prompts, while the illustrated transportation model defines shipment quantities, minimizes cost, and enforces supply and demand requirements.

C.2. w/o understanding

  • The C.2 variant removes the “Understanding the Problem” part while keeping the other parts unchanged.This isolates the effect of omitting that stage in the prompt.Source: §C.2 · p. 26

C.3. w/o expert knowledge in understanding

  • The C.3 variant replaces the understanding prompt with a general question about the optimization problem, rather than the original expert-oriented prompt.The replacement begins, “From an optimization perspective, what is your understanding.”Source: §C.3 · p. 26

C.4. w/o expert knowledge in formulation

  • The C.4 variant replaces the step-by-step modeling prompt with a general request to define and present all model components.The replacement also asks that the full model be enclosed in model tags.Source: §C.4 · p. 26

D.1. A correctly solved instance

  • The solved-instance example models shipments from three industries to five shops, with continuous quantities and industry capacity and shop-demand requirements.The example’s problem statement supplies the costs, capacities, and demands used in the instance.Source: §D.1 · p. 26, C. Main Constraints · p. 27

C. Main Constraints:

  • The model minimizes total transportation cost, using cost c_ij for shipping from industry i to shop j.Its constraints cap each industry’s total shipments by capacity and require each shop’s demand to be met exactly.Source: C. Main Constraints · p. 27

D.2. Part of incorrectly solved instances

The examples illustrate errors in variables, objectives, and constraints, including missing constraints in a parcel-packing formulation.

D.2. Part of incorrectly solved instances

  • The incorrect production variables treat joint production of Basic and Advanced products as a choice between them.The problem description specifies that processing raw material yields both products simultaneously.Source: §D.2 · p. 30
  • A constraint using “less than or equal to” is incorrect where the relationship should be equality.The example identifies the relation as an incorrect constraint.Source: §D.2 · p. 30
  • The incorrect objective uses wrong variables and therefore fails to represent the stated profit logic for direct and further-processed products.The example’s intended profit objective includes revenues and processing costs.Source: §D.2 · pp. 30–31
  • The examples also identify a spurious constraint that is absent from the problem.The passage classifies it as an added constraint that does not exist in the problem.Source: §D.2 · p. 31
  • In parcel packing, the understanding stage identified two-direction non-overlap, but the formulation omitted the reverse-direction variables and constraints.The instance asks to place parcels without overlap in a fixed-width container while minimizing used height.Source: §D.2 · p. 32

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