SCHEDBench: A Benchmark for Evaluating LLM Constraint Faithfulness in Natural-Language Combinatorial Scheduling

Avi Sharma; Shrenil Shaun Sharma

REVIEW 2 major objections 8 minor 43 references

SCHEDBench: A Benchmark for Evaluating LLM Constraint Faithfulness in Natural-Language Combinatorial Scheduling

T0 review · 2 major / 8 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read LLMs are not invariant to how the same scheduling problem is worded; reordering constraints shifts violation rates beyond a noise floor for several models, even though the formal constraints, objective, and feasible region are unchanged.

desk verdict A careful, honest benchmark with a credible main finding; the thin fidelity audit and missing code/data link are the two things to fix before I'd trust it fully. read the letter →

arxiv 2608.00991 v1 pith:EHWSHNFH submitted 2026-08-02 cs.AI cs.CL

Shrenil Shaun Sharma , Avi Sharma This is my paper

classification cs.AIcs.CL

keywords LLMevaluationcombinatorialschedulingconstraintfaithfulnesssurface-formvariationjob-shopresource-constrainedprojectnurserosteringtimetabling

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

SCHEDBench tests whether large language models treat two wordings of the same combinatorial scheduling problem as the same problem. It builds 1,132 natural-language instances from six canonical scheduling families and renders each underlying instance in several ways: reordered constraints, re-themed entities, and paraphrased templates. Thirteen LLMs were asked to produce schedules directly, and outputs were checked by solver-based verifiers. The central finding is that no tested model is fully invariant to these semantically equivalent renderings: feasibility drops under full variation, and per-instance hard-constraint violation rates shift beyond a rendering-seed noise floor for a subset of models. Constraint reordering is the only tested axis whose effect consistently clears that floor.

What carries the argument

A template-based verbalization pipeline converts canonical instances into natural-language prompts with three independently seeded variation axes (constraint order, thematic domain, lexical-syntactic template). Each instance is paired across renderings so the formal problem is held fixed. The comparison machinery is a matched-instance ablation set (470 instances) plus a seed-sensitivity noise floor: for each condition, three independently seeded renderings define a per-model band, and a v1-to-variant effect counts as 'beyond noise' only when the bootstrap 95% CI on the median absolute per-instance violation-rate change minus the seed band lies above zero.

What would settle it

Take one of the models flagged as beyond noise on constraint reordering (e.g., Llama 4 Maverick), fix a set of source instances, and generate a large number of random constraint permutations through an independent verbalizer not written by this paper's authors; if the distribution of per-instance violation-rate changes across those permutations matches the seed band obtained by re-rendering with the same order, the reported above-noise ordering effect would be an artifact of the specific template bank rather than a property of the model.

Watch

Extended reading notes

Core claim

On matched formal instances, re-rendering the same scheduling problem shifts per-instance violation rates above the seed-noise floor for a subset of models; signed aggregate changes stay near zero while absolute per-instance changes are substantial. The strongest and most consistent trigger is constraint reordering: changing only the sequence in which constraints appear leaves entity names, numbers, feasible regions, and optimal objectives unchanged, yet moves median absolute violation-rate changes for five of thirteen models beyond the noise band. Feasibility and objective quality are separable: even feasible outputs can have heavy-tailed optimality gaps. The paper concludes that current LL

Load-bearing premise

The entire invariance comparison rests on the assumption that the verbalization pipeline preserves the source instance's constraints, objective, and combinatorial structure exactly across renderings; only 100 of the 1,132 instances were manually audited for semantic fidelity, so an undetected template or entity-substitution slip could change the formal instance and inflate the measured sensitivity.

Editorial extensions

If this is right

If same-input reordering moves violation rates beyond noise, then any single-rendering scheduling benchmark can overstate or understate a model's true constraint-following ability depending on the constraint order it happens to use.
Near-zero signed changes with large absolute per-instance changes mean models are not simply 'stably good' or 'stably bad' across renderings; they improve on some instances while failing on others, so aggregate accuracy hides the instability.
Constraint ordering can act as a latent control variable: a practitioner who wants a model to produce a different schedule could nudge it by reordering constraints without changing any formal content.
Feasibility alone is an incomplete evaluation lens; per-instance violation rates and coverage are needed to expose rendering sensitivity, and objective gap must be reported conditional on feasibility.
The seed-sensitivity band offers a template for other LLM evaluations: without a noise floor from re-rendering the same variant, apparent robustness results are not interpretable.

Reading between the lines

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

Beyond the paper: the ordering sensitivity suggests models may not build a representation of the entire constraint set before generating; a testable mechanism is to probe whether moving a single critical constraint to the end of the prompt changes its violation rate more than moving a non-critical one.
The paper leaves solver-code prompting to future work; if the same reordering sensitivity persists when models emit executable solver code, that would indicate the effect lives in the reading or comprehension stage, not merely in output formatting.
The verbalization pipeline could be ported to other hard combinatorial families (e.g., vehicle routing or bin packing) to ask whether constraint-order sensitivity is general or particular to scheduling's precedence-and-resource structure.
If constraint reordering is a genuine control knob, a cheap robustness intervention would be to canonicalize constraint order (for example, always sorting constraints by type or by dependency level) before prompting; the paper does not test this.

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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

Quick take: SCHEDBench is one of the more honest benchmark papers I've seen in the LLM-scheduling niche. It doesn't just throw 1,132 instances at 13 models and report accuracy; it builds in a seed-noise floor, uses paired per-instance changes, reports extraction failures, and separates feasibility from objective quality. The central finding—constraint reordering moves violation rates beyond the reseeding noise for a subset of models—is credible and consistent with the tables. I'd send it to referees, with a request to close one gap: the matched-instance premise needs stronger verification than a 100/1,132 audit.

What's new: this is the first multi-family NL scheduling benchmark covering JSP, RCPSP, timetabling, and nurse rostering, with controlled ablations and solver-verified references. The seed-sensitivity design is the real contribution: instead of just saying "accuracy dropped," they estimate a per-model reseeding noise floor and judge per-instance violation-rate changes against it. Reporting is careful—extraction success rates, median gaps, and a clear limitation that objective-quality claims are conditioned on feasibility. The conclusion that theme and paraphrase effects are largely within noise, while constraint reordering exceeds it for a subset of models, matches the tables.

Soft spots, in order of seriousness. First, verbalization fidelity. The invariance claim is only meaningful if v1/v2/v3 renderings encode identical constraints. The audit in A.6 covers 100 of 1,132 instances and doesn't state whether it checks every rendering variant per instance. That's too thin for a claim where a single systematic template bug could contaminate the result. The templates look deterministic and well-structured, so this is a residual risk rather than a demonstrated error, but it's the point on which the paper stands or falls. A round-trip check—parse the NL back to a formal instance and compare—would settle it. Second, difficulty tiers for ITC and NSPLib are set by BKS-value bins, which is arbitrary; minor, since the main paired comparisons are within-family. Third, C4 says "Code and data are released" but no URL appears in the manuscript. For a benchmark paper, that's a real reproducibility gap. Also minor: A.7 admits some instances retain BKS without a solver feasibility verdict; honest, but worth a footnote.

Overall the central argument holds. The paper doesn't overclaim—"for a subset of models" and "not fully invariant" are the right hedges. Audience: anyone building NL interfaces to scheduling systems or benchmarking LLM robustness on structured constraint problems. It deserves a serious referee. I'd send it to review with a request to expand the fidelity audit, add a round-trip check, and provide a working code/data link.

Referee Report

2 major / 8 minor

Summary. SCHEDBench constructs 1,132 natural-language scheduling instances by templating canonical JSPLib, PSPLib, ITC-2007, INRC-I, and NSPLib instances, with controlled surface-form axes (constraint order, thematic framing, lexical-syntactic paraphrase) and solver-derived reference solutions. The paper evaluates thirteen LLMs zero-shot, measuring feasibility, optimality gap, and per-instance violation-rate changes between renderings. Its central empirical claim (§5.6) is that LLMs are not fully invariant to semantics-preserving surface variation: re-rendering shifts per-instance violation rates above a seed-noise floor for a subset of models, with constraint reordering the most consistent above-noise axis.

Significance. The benchmark fills a real gap: existing scheduling benchmarks use a single formulation per instance, so they cannot separate search failure from surface-form sensitivity. The seed-sensitivity design is a strong guard against rendering-seed artifacts, and the reporting of full |ΔVR| distributions with a v1 violation-rate anchor is careful. The 1,132-instance corpus across six scheduling families with solver-based verification is a useful resource. If the verbalization-fidelity premise holds, the finding that constraint ordering acts as a latent control variable is practically important for NL interfaces to optimization. The main risk is that the fidelity premise is currently supported by a small manual audit, so the empirical claim is conditional on additional verification.

major comments (2)

[§3.2, Appendix A.6, §5.6] The load-bearing premise of the central invariance claim is that every v1/v2/v3A/v3B prompt generated from a source instance encodes exactly the same constraints, objective, and domains. The only direct evidence is the hand audit in Appendix A.6: 100 of 1,132 instances, zero errors. That sample is too small to certify a template pipeline with interacting axes, and A.6 does not state whether the audited prompts covered all rendering variants or only one rendering per source instance, nor does it report inter-annotator agreement. A single un-audited template bug—e.g., an RCPSP-MM mode clause dropping a resource, or an NSPLib coverage target changing from 'exactly' to 'at least'—would alter the formal instance, so an observed |ΔVR| shift could be caused by a constraint change rather than surface-form sensitivity. The seed-noise analysis cannot detect this semantic drift. This is a residual
[§4.3, Tables 4/13/14] The seed-noise floor is estimated on a fixed 150-instance subset, but the v1→axis effects are measured on the 470-instance ablation set. For a 'beyond noise' verdict, the noise distribution on the 150 subset must calibrate the effect distribution on the 470 set. The paper does not demonstrate this: the 150 set is domain-stratified, but no comparison of seed-band medians by family or difficulty between the two sets is given, and no rationale is provided for choosing 150. If the 150 set is unrepresentative (e.g., has lower baseline violation rates), the floor could be mis-estimated and verdicts could flip. Please add a calibration check, compute the seed band on the full 470 set, or report sensitivity of the 'Beyond noise?' verdicts to the subset choice.

minor comments (8)

[Abstract] Missing space in 'introducesSCHEDBench'.
[Appendix A.2, Tables 3, 9–11] For ITC and NSPLib, Easy/Medium/Hard are defined by equal-sized BKS-value bins; this is not a hardness measure. Please rename the tiers (e.g., 'BKS tier') or justify them with solver runtime or optimality-gap data.
[Appendix A.7] The abstract and contributions state 'solver-derived feasibility and optimality,' but instances that time out retain OBKS without a feasibility verdict. Please state the fraction of instances for which CP-SAT confirmed feasibility/optimality versus those that inherit library BKS values.
[Appendix C4] 'Code and data are released' appears without a URL or repository identifier, which blocks independent verification of the verbalization pipeline and the seed-sensitivity analysis.
[Table 12] Asterisks on Qwen model names are unexplained; add a footnote.
[Table 3] The column labeled 'Diff.n d' is ambiguous; separate the difficulty column from the instance-count column and align counts with Table 2.
[§5.1, Table 3] The statement that GPT-5.5 is 'near-perfect across difficulty levels' for JSP is not supported by the per-difficulty cells in Table 3; clarify whether the claim refers to the v1 subset (Table 9) or the v4 full set, and reconcile the apparent conflict.
[§6] The conclusion that 'no model is fully invariant' is stronger than the subset-level evidence in §5.6, where only a subset of models shows above-noise violation-rate shifts (e.g., GPT-5.5 has zero violation-rate change under v2/v3A/v3B). Please align the summary with the precise claim.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the central claim is a measured empirical result with an independent seed-noise control.

full rationale

The paper's central claim — that LLM scheduling behavior is not fully stable under semantics-preserving rendering variation — is an empirical observation, not a derivation. The evaluation compares per-instance violation-rate changes between matched v1 and ablation renderings against a seed band B_{m,c} computed from independently seeded renderings of the same condition; this seed band is an independent noise estimate, not a fitted parameter that forces the outcome. No parameter is fitted to a subset and then renamed a prediction: the |ΔVR| effect is directly measured by paired model outputs, and the seed band only serves as a statistical floor. The verbalization pipeline's fidelity is an assumption audited on 100 of 1,132 instances, so a template bug would be a validity risk, but it is not a circular step because the benchmark metrics and conclusions are not defined in terms of that assumption. The paper contains no load-bearing self-citations; all cited prior benchmarks and libraries are external to the authors. The absence of a code/data URL is a reproducibility limitation, not circularity. Under the hard rules, the derivation is self-contained against external benchmarks, and the honest non-finding is a circularity score of 0.

Assumptions & free parameters 3 free parameters · 3 assumptions · 0 invented entities

The benchmark introduces no new physical or formal entities. The listed free parameters are methodological sample sizes, not fitted model parameters. The axioms are the standard assumptions of any template-based, solver-verified benchmark; the weakest is the fidelity of the un-audited verbalizations.

free parameters (3)

ablation subset size = 470
Number of instances in the matched ablation set; chosen as a tractable stratified sample, not fitted to data.
seed-band subset size = 150
Subset used for estimating the seed-noise floor; chosen for computational budget, not fitted.
number of reseeding runs k = 3
Three independently seeded renderings used to define the noise band; arbitrary but adequate for bootstrap CI estimation.

assumptions (3)

domain assumption Template verbalization preserves each source instance's constraints, objective, and combinatorial structure across all renderings.
Section 3.2 describes the pipeline; Appendix A.6 audits only 100/1132 instances, so this is assumed for the remaining 1032.
domain assumption The OR-Tools CP-SAT verifier correctly decides feasibility and objective bounds.
Appendix A.7; no local solve beat canonical BKS, but solver timeouts leave some instances unverified and they remain in the set.
domain assumption The seed band, estimated on a 150-instance subset with k=3 reseeds, is a valid noise floor for per-instance violation-rate shifts.
Section 4.3; relies on the assumption that reseeding captures rendering noise and that 3 seeds are sufficient for the bootstrap CI.

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Cite this review

Pith. "Pith review of SCHEDBench: A Benchmark for Evaluating LLM Constraint Faithfulness in Natural-Language Combinatorial Scheduling." pith.science (2026). https://pith.science/paper/EHWSHNFH

@misc{pith2026260800991,
  author       = {Pith},
  title        = {Pith review of: SCHEDBench: A Benchmark for Evaluating LLM Constraint Faithfulness in Natural-Language Combinatorial Scheduling},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EHWSHNFH}},
  note         = {Machine review of arXiv:2608.00991}
}

read the original abstract

This paper introduces SCHEDBench, a natural-language benchmark for evaluating combinatorial scheduling constraint faithfulness under surface-form variation. Grounded in canonical scheduling instances and solver-derived feasibility and optimality, SCHEDBench assesses whether large language models (LLMs) generate schedules with the same constraint-feasible behavior across varied natural-language (NL) surface forms. SCHEDBench spans 1,132 instances across job-shop scheduling problems (JSP), single and multi-mode resource-constrained project scheduling problems (RCPSP), nurse rostering/scheduling, and curriculum timetabling problems of varying difficulty. Instances are templated into natural language problems using domain-specific templates, themed entities, lexical-syntactic template rephrasing, and constraint-level surface-form variation, with reference solutions verified for feasibility and objective optimality. Across thirteen frontier and open-weight LLMs, we find that models are not reliably invariant to semantically equivalent renderings of the same scheduling problem. Surface-form variation reduces feasibility and induces above-noise shifts in per-instance hard-constraint violations on matched instances. Among the tested isolated axes, constraint reordering yields the clearest above-noise sensitivity.

Figures

Figures reproduced from arXiv: 2608.00991 by the authors.

**Figure 1.** Overview of the SCHEDBench generation pipeline. and a broader range of horizon lengths. 3.2 Data to Text Verbalization We verbalize each source instance through a controlled slot-filling pipeline rather than LLM-based generation. Each instance is parsed into structured constraint entries covering operations, resource capacities, precedence relations, coverage requirements, and penalty terms; verbalized with famil… view at source ↗

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

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Fisher, H. and Thompson, G. L. , title =. Industrial Scheduling , editor =

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