Decision Information Meets Large Language Models: The Future of Explainable Operations Research

Chen Ma; Hailei Gong; Qingcan Kang; Tao Zhong; Wing Yin Yu; Xiaojin Fu; Xiongwei Han; Yansen Zhang

REVIEW 4 major objections 5 minor 1 cited by

Decision Information Meets Large Language Models: The Future of Explainable Operations Research

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read This paper claims that what-if questions in operations research can receive both correct model updates and quantified explanations, because the structural change a query imposes on the optimization model can be measured and fed to a large…

desk verdict A useful framework-and-benchmark paper whose headline accuracy numbers look defensible, but the signature Decision Information/GED component is never actually tested, and the explanation-quality evaluation has a missing control. read the letter →

arxiv 2502.09994 v1 pith:RFQZG7TB submitted 2025-02-14 cs.AI

Yansen Zhang , Qingcan Kang , Wing Yin Yu , Hailei Gong , Xiaojin Fu , Xiongwei Han , Tao Zhong , Chen Ma This is my paper

classification cs.AI

keywords explainableoperationsresearchlargelanguagemodelsDecisionInformationbipartitegrapheditdistancewhat-ifanalysisLLMagentsoptimizationmodelingindustrialbenchmark

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper argues that explainable operations research can be built by measuring how much a user's what-if query changes the underlying optimization model, then having a large language model translate that measured change into a narrative justification. The authors define this measured change as Decision Information and compute it by converting original and updated optimization programs into linear programs, representing those LPs as bipartite graphs of constraint and variable nodes, and taking the normalized graph edit distance between them. On a new industrial benchmark of 30 problems with 10 expert-authored queries each, the proposed EOR framework with three LLM agents updates Gurobi code and reaches higher modeling accuracy than the Standard and OptiGuide baselines, and its explanations score near 9.3 to 9.5 on a 0-10 scale versus 5 to 7 for baselines under their automated evaluation. The intended payoff is that OR users can ask "what if" questions and receive not just a new solution but a quantified, human-readable account of why the answer changed.

What carries the argument

Decision Information, defined as the parameters and constraints in a user query that reconfigure the OR problem, is the central object. It is quantified by parsing original and updated Python/Gurobi code into a standard LP form, converting each LP into a bipartite graph whose two node sets are constraints and decision variables with attributes for bounds and objective coefficients, and computing the normalized graph edit distance between the graphs, where each attribute substitution, insertion, or deletion costs 1. This numerical measure is fed to the LLM interpreter prompt so the generated explanation cites concrete numeric impact rather than merely describing outcomes. The workflow is organized around three agents, Commander, Writer, and Safeguard, where Writer proposes constraint and data edits in JSON, Safeguard verifies safety, and Writer then acts as interpreter to generate the two explanation parts.

What would settle it

Have an independent human expert panel score blinded explanations from EOR, Standard, and OptiGuide on the same benchmark queries without seeing the numerical impact measure; if the panel does not rank EOR's explanations substantially above the baselines, or if the automated judge's scores diverge from the panel when quantitative phrasing is removed from the rubric, the explanation-quality claim fails.

Watch

Extended reading notes

Core claim

The authors' central claim is that the impact of a what-if query on an OR model can be made explicit by measuring the structural difference between the original and the updated optimization program, and that an LLM can use this measurement to produce explanations that justify both code changes and result changes. In EOR, the query edits are first encoded as LP changes, then as bipartite graphs over constraint and variable nodes; the normalized graph edit distance between the original and updated graph is the quantitative Decision Information that anchors the explanation. Empirically, the paper reports that this anchoring lets GPT-4-Turbo one-shot reach 95.33% modeling accuracy on its benchmark, and that the resulting explanations receive consistent near-expert quality scores on both explanation of correctness and explanation of results.

Load-bearing premise

The explanation-quality claim rests on the assumption that the automated LLM judge, which is told to reward quantitative reasoning, judges explanations the way human experts would for every system compared; the paper reports human expert scores only for the EOR system.

Editorial extensions

If this is right

On the paper's benchmark, EOR beats the Standard and OptiGuide baselines on modeling accuracy in every LLM and setting tested, with the strongest result being 95.33% for GPT-4-Turbo one-shot.
The benchmark itself gives the field a held-out, expert-authored evaluation set for explainable OR, so future systems can be compared on explanation quality rather than only on solution correctness.
Because Decision Information is computed from LP and graph structure rather than from code text, explanation quality does not depend on which solver or variable naming the code uses.
The normalized graph edit distance provides a numerical severity indicator for a query's impact, which is what lets the LLM produce a quantitative justification instead of a summary.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A natural test the paper does not run is to check how well normalized graph edit distance predicts the actual change in objective value across queries; if it does, Decision Information could serve as a cheap model-agnostic sensitivity score for constraint edits.
The explanation-quality comparison would be more decisive if expert scores were collected for the baselines too; the reported gap currently rests on the automated judge for the baselines, while the paper reports expert scores only for EOR.
The same bipartite-graph difference could be applied to mixed-integer or nonlinear models by first relaxing them to LP form, a direction the paper leaves implicit.
Since the benchmark queries were developed in-house, an independently constructed public query set would show how much of the accuracy gain survives distribution shift.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Here's my read. The paper does three things: proposes a three-agent LLM workflow for editing OR code, introduces a 'Decision Information' measure based on bipartite graph edit distance (GED), and contributes a new benchmark of 30 problems × 10 queries with ground truth. The workflow is described clearly, and the accuracy results in Table 2 are straightforward and reproducible in principle. EOR beats Standard and OptiGuide across the board, and the margin is large. That part looks honest and useful.

The soft spots are concentrated where the paper makes its most distinctive claim. The GED computation is never actually run. The appendix prompt gives the LLM a 'different_model' number, but the paper never shows how that number is computed. In the case study, the explanation says 'the numerical changes in the model, calculated as 100' with no derivation. The '8 out of 10' impact rating is just generated text. So the Decision Information mechanism is not demonstrated—it's described, then handed to the LLM as an input. There is no ablation removing or corrupting that input, so the accuracy gains in Table 2 could come entirely from the agentic scaffolding and the marker-based code edits. The stress-test note is right on this.

The explanation-quality evaluation has a second gap. The automated evaluator is explicitly prompted to reward quantitative reasoning, and the expert scores in Table 3 are only filled in for EOR—Standard and OptiGuide have dashes. That means we cannot check whether the automated evaluator is biased toward EOR's style. It's plausible that the baseline explanations are actually decent but just less numeric. This is a load-bearing problem for the 'near-expert quality' claim.

On the positive side, the benchmark is a real contribution if released. The queries are varied and include constraint deletions and combined changes, which is more than OptiGuide handles. The failure-case table is a good sign of honest reporting.

Overall, this is a solid framework-and-benchmark paper with an unverified central component. It should go to peer review, and the reviewers should push for an actual GED implementation (or a clear statement that it's not implemented), an ablation of the different_model input, and expert evaluations for all methods. The accuracy results are likely to survive; the explanation-quality claim needs more work.

Referee Report

4 major / 5 minor

Summary. The paper proposes EOR, a multi-agent LLM framework for explainable operations research. It introduces the concept of Decision Information, defined as the parameters and constraints in a user query, and proposes to quantify it via normalized graph edit distance (NGED) between bipartite graph representations of the original and updated LPs. The framework uses Commander, Writer, and Safeguard agents to modify solver code and generate justifications. The paper also introduces a benchmark of 30 OR problems with 300 queries and evaluates modeling accuracy and explanation quality against Standard and OptiGuide baselines, reporting large improvements (up to 95.33% accuracy and explanation scores around 9.3–9.5).

Significance. If validated, the framework would be a meaningful step toward transparent LLM-based OR modeling, and the benchmark would be a useful resource. The modeling accuracy results are strong, the detailed prompt templates and code release support reproducibility, and the multi-agent design is clearly described. However, the central quantitative mechanism—NGED-based Decision Information—is never implemented or ablated, and the explanation evaluation is compromised by missing expert baseline scores. These issues prevent the current version from substantiating its headline claims.

major comments (4)

[§3.2.2, §4.5.1, Table 2] The GED-based Decision Information metric is never implemented or ablated. In the workflow (§3.2.1), the Writer and Safeguard agents do not receive the {different_model} value; it is injected only into the Interpreter prompt (Appendix A.2.1). Consequently, the modeling accuracy gains in Table 2 cannot be attributed to the Decision Information component, and the explanation-quality gains in Table 3 could stem entirely from the prompt's explicit demand for quantitative reasoning. An ablation that removes or corrupts the GED value is required to support the central contribution.
[§4.5.2, Table 3, Appendix A.5] In Table 3, the Expert columns are blank for Standard and OptiGuide, so the claimed alignment between automated and expert evaluation is checked only for EOR. Moreover, the automated evaluator prompt in Appendix A.5 instructs the LLM to focus on quantitative reasoning behind changes, which systematically disadvantages baselines that do not report numeric impact. Without expert scores for all methods, the superiority claim for EOR's explanation quality is unsupported.
[§3.2.2, Figure 3] The vertex cost matrix in §3.2.2 contains index errors: the cell for matching xp'_i to ϵ is labeled #attr(sp'_i) and the cell for matching ϵ to xp_i' is labeled #attr(sp_i'); these should reference the attribute counts of the respective variable nodes. This makes the formal GED definition ambiguous. Additionally, the case study in Figure 3 asserts that "The numerical changes in the model, calculated as 100" without showing the computation, and the quoted 1–10 impact rating appears to be LLM-generated text rather than a value derived from the NGED metric.
[§4.1] The benchmark is described as "the first industrial benchmark" for explainable OR, but the paper provides no statistics on query difficulty, diversity of modification types, or inter-annotator agreement on ground-truth labels. Since the benchmark is a contribution, these details are needed to establish its validity.

minor comments (5)

[§3.2.2] There is a typo: "thEORetical" should be "theoretical."
[Appendix A.3] In the problem description, "trgtgof" appears to be an accidental typo; it should likely be "cost of."
[§4.5.2, Table 3] The "Overall" score is not a simple average of EC and ER; please clarify how the overall score is computed.
[Appendix A.6] Figure 5 repeats the EOR explanation already shown in Figure 3; consider referencing the earlier figure to avoid duplication.
[§4.2] The text says "we propose two methods" for evaluation, but the previous paragraph mentions an automated method and a blind review; clarify which methods are actually used in Table 3.

Circularity Check

1 steps flagged · score 2.0 of 10

No equation-level circularity; explanation-quality comparison is partially self-referential because the auto-evaluator is prompted to reward EOR's own mandated output style.

other [Appendix A.5, prompt template EXPLANATIONS_EVALUATION, Score 2 criterion (used for Table 3)]
"How well does the explanation clarify why and how the results changed due to the query? Focus on the depth of the explanation, particularly the quantitative reasoning behind the changes, not just a description of the result."

This evaluation criterion is applied in Table 3 to all three systems, but only EOR's Interpreter prompt (Appendix A.2.1) mandates a quantitative 1-10 impact rating and supplies a precomputed 'different_model' change measure. The baseline prompts contain no such requirement. The auto-evaluator is therefore instructed to reward exactly the structural feature EOR is engineered to emit, so the gap in ER/Overall scores is partly guaranteed by the evaluator prompt rather than by an independent human standard; this is confirmed by the blank Expert columns for Standard and OptiGuide, which prevent cross-checking the Auto scores against human judgments for the baselines.

full rationale

The paper's headline accuracy results (Table 2) are not circular: EOR's updated programs are run through Gurobi and compared with ground-truth optimal values, and the GED 'Decision Information' score is a defined metric rather than a fitted parameter recycled as a prediction. The explanation-quality comparison, however, contains a mild self-referential loop: the automated judge is explicitly told to reward quantitative reasoning, which is precisely what EOR's Interpreter prompt forces the model to produce while baselines are not asked to do so. This makes the explanation-quality advantage partly definitional under the Auto metric. The Expert columns in Table 3 are blank for both baselines, so the claimed alignment between Auto and Expert cannot be verified for non-EOR systems. Separately, the Decision Information/GED component is never ablated, so the source of the modeling-accuracy gains is unidentified; this is an omitted-control/correctness risk, not a circular reduction. The only notable self-citation is the adoption of the unit-cost GED rule from Xing et al. (2024), which shares authors with this paper, but GED is a standard external concept and the citation is not a load-bearing uniqueness argument. Overall, no equation-level circularity is present; the score reflects the self-referential evaluation loop rather than a fitted-input prediction.

Assumptions & free parameters 1 free parameters · 4 assumptions · 1 invented entities

The framework rests on four unproven premises: fixed decision variables, LP-convertibility of all benchmark programs, validity of unit-cost graph edit distance as a measure of decision impact, and validity of LLM-as-judge without full expert calibration. None of these are fitted to data, but the core Decision Information measure is a hand-chosen metric with no external validation.

free parameters (1)

Unit cost of graph edit operations = 1 per attribute mismatch, insertion, deletion
Chosen in Section 3.2.2 following Xing et al. 2024; not fitted to data and not justified by experiments. All normalized graph edit distance values scale linearly with this cost.

assumptions (4)

domain assumption Decision variables remain unchanged under user queries.
Stated in Section 3.1; queries that add or delete variables are out of scope, limiting generality of the framework.
domain assumption Every OR program can be converted to a standard linear program in general form.
Section 3.2.2 assumes LP conversion, but the benchmark includes integer programs (e.g., aircraft counts in Appendix A.3); no parser or relaxation rule is provided.
ad hoc to paper Graph edit distance with unit costs is a valid quantitative measure of Decision Information.
Section 3.2.2 defines the measure but provides no experiments, ablations, or human validation connecting GED values to perceived decision impact.
domain assumption LLM-based evaluator scores approximate expert human judgment of explanation quality.
Section 4.2 and Appendix A.5 rely on GPT-4o as the automated judge; expert scores are only reported for EOR in Table 3, so agreement across methods is not demonstrated.

invented entities (1)

Decision Information
purpose: A named quantity intended to measure the impact of constraint and parameter changes in a user query on the OR solution.
Defined in Section 3.2 (Definition 1) and operationalized only through graph edit distance; no independent empirical handle or external benchmark validates that the metric tracks actual decision impact.

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Cite this review

Pith. "Pith review of Decision Information Meets Large Language Models: The Future of Explainable Operations Research." pith.science (2026). https://pith.science/paper/RFQZG7TB

@misc{pith2026250209994,
  author       = {Pith},
  title        = {Pith review of: Decision Information Meets Large Language Models: The Future of Explainable Operations Research},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RFQZG7TB}},
  note         = {Machine review of arXiv:2502.09994}
}

read the original abstract

Operations Research (OR) is vital for decision-making in many industries. While recent OR methods have seen significant improvements in automation and efficiency through integrating Large Language Models (LLMs), they still struggle to produce meaningful explanations. This lack of clarity raises concerns about transparency and trustworthiness in OR applications. To address these challenges, we propose a comprehensive framework, Explainable Operations Research (EOR), emphasizing actionable and understandable explanations accompanying optimization. The core of EOR is the concept of Decision Information, which emerges from what-if analysis and focuses on evaluating the impact of complex constraints (or parameters) changes on decision-making. Specifically, we utilize bipartite graphs to quantify the changes in the OR model and adopt LLMs to improve the explanation capabilities. Additionally, we introduce the first industrial benchmark to rigorously evaluate the effectiveness of explanations and analyses in OR, establishing a new standard for transparency and clarity in the field.

Figures

Figures reproduced from arXiv: 2502.09994 by the authors.

**Figure 1.** The framework of EOR. Contributions. 1) We formulate the problem of the explainable OR problem within the context of LLMs, laying a foundation for future research in this area. 2) We introduce the concept of “Decision Information” and utilize bipartite graphs in conjunction with LLMs to quantify its importance in response to user queries, enhancing both the modeling capabilities and the explanation of complex what-i… view at source ↗

**Figure 2.** The overall workflow of EOR. 3.2.1 THE WORKFLOW OF EOR As shown in [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** An example illustrating the code and explanations generated by EOR. [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: An example illustrating codes generated by different models. [PITH_FULL_IMAGE:figures/full_fig_p024_4.png]

**Figure 5.** Figure 5: An example illustrating explanations generated by different models. [PITH_FULL_IMAGE:figures/full_fig_p025_5.png]

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Forward citations

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