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REVIEW 4 major objections 5 minor 83 references

Solving the Job Shop Scheduling Problem with Graph Neural Networks: A Customizable Reinforcement Learning Environment

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

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Pith's one-line read A modular RL environment for job shop scheduling shows a feature-only dispatcher outscoring several graph-based ones, and a GNN model close to the state of the art on large benchmarks.

desk verdict A genuinely useful modular library for GNN-based JSSP research, wrapped in a thesis whose headline empirical claims outrun the evidence. read the letter →

arxiv 2506.13781 v1 pith:3S55DISM submitted 2025-06-10 cs.LG cs.AIcs.DM

Pablo Ariño Fernández This is my paper
classification cs.LGcs.AIcs.DM MSC 90B3568T0768T2090C27
keywords jobshopschedulinggraphneuralnetworksimitationlearningreinforcementenvironmentdispatchingrulesnodefeaturesbehavioralcloningcombinatorialoptimization
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

The paper introduces JobShopLib, a modular Python library with a reinforcement learning environment for the job shop scheduling problem, where researchers can independently swap the graph representation, node features, definition of available actions, and reward function. To show the environment works, the author trains task-selection models by imitation learning, cloning decisions from a constraint programming solver on small optimal instances. One of these models uses only per-operation features with no message passing and outperforms several published graph-based dispatchers. A full relational graph neural network trained in the same pipeline reaches near state-of-the-art optimality gaps on large Taillard benchmarks. The paper's claim is that these design choices matter enough to need a customizable testbed, and that feature engineering may currently be a larger source of gains than graph architecture.

What carries the argument

The load-bearing object is JobShopLib's environment layer: a Dispatcher engine that builds semi-active schedules, a ready-operations filter that controls the action set (including non-immediate, dominated, and idle-machine filters), FeatureObservers that maintain node feature matrices incrementally, a GraphUpdater that implements residual scheduling and the adding/removing-arc disjunctive and resource-task graph strategies, and RewardObservers for dense makespan and idle-time rewards. These plug into two Gymnasium-compatible environments, SingleJobShopGraphEnv and MultiJobShopGraphEnv. The argument works by composition: because each SMDP component is an observer or filter, changing one component does not change the others, which is what makes the feature-only vs. graph-based comparison possible in a single training pipeline.

What would settle it

A reader could re-train the strongest published baseline (e.g., Lee and Kim (2024)) inside JobShopLib with the same training data, step budget, and evaluation script used for the feature-only model; if that baseline then matches or beats the feature-only model, the paper's claim that features outweigh graph connectivity would be refuted.

Watch

Extended reading notes

Core claim

In the paper's own telling, the central result is empirical: a dispatcher that ignores graph connectivity entirely and scores operations from JobShopLib's built-in per-operation features alone beats several graph neural network dispatchers reported in the literature, while a relational graph attention/iso-morphism network trained with the same imitation-learning recipe comes close to the best known learned schedulers on large instances. The author reads this as evidence that node features strongly influence performance, and that the field's comparisons have been entangled with different feature sets and training setups. The accompanying contribution is JobShopLib itself, which encodes the design space of state, action, and reward choices as interchangeable components so that future work can isolate what actually drives dispatcher quality.

Load-bearing premise

The comparisons assume that differences in optimality gap or accuracy between JobShopLib models and published dispatchers come from node features or architecture design, rather than from differences in training data, training budget, or evaluation protocols; the paper does not retrain the baselines in its own pipeline.

Editorial extensions

If this is right

  • Node feature choice should be reported and treated as a primary experimental axis in learned dispatching; the feature-only result suggests features can dominate architecture choice.
  • A single pipeline can train both message-passing and non-message-passing models, so future comparisons of GNN schedulers can be run under identical data, training budget, and evaluation protocol.
  • Imitation learning from CP-SAT optimal schedules on small instances transfers to large Taillard instances, giving a practical route to learned dispatchers without RL exploration.
  • Ready-operations filters such as non-immediate and dominated-operation filters change PDR performance substantially, so action-space definitions must be matched, not assumed, when comparing dispatchers.
  • With the library, new graph representations (e.g., resource-task graphs with job or global nodes) can be tested without reimplementing the environment.

Reading between the lines

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

  • If the feature-only advantage survives an apples-to-apples re-training of the published baselines, it would suggest that much of the recent progress credited to GNN architectures for scheduling is actually attributable to feature design and training protocols; the paper does not run that control.
  • A natural next experiment, which JobShopLib makes possible, is a factorial ablation crossing graph representation (none, disjunctive, resource-task), feature set, and action filter within one pipeline; the marginal value of message passing is the difference the paper does not isolate.
  • The library's reward and feature observers could extend to dynamic JSSP variants with due dates or machine breakdowns without changing the core environment, since those objectives enter through pluggable observers.
  • The results hint that reservation-based action spaces may be less valuable for learned dispatchers than for PDRs, because a trained model can learn to wait implicitly; testing this requires training the same model under different ready-operations filters.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. This paper introduces JobShopLib, a modular Python library for the job shop scheduling problem (JSSP) that provides Gymnasium-compatible reinforcement learning environments with customizable graph representations, node features, ready-operation filters, and reward functions. The library includes data structures, benchmark loading, random instance generation, dispatching-rule solvers, CP-SAT integration, and observer-based abstractions for features, graphs, and rewards. To demonstrate the environment, the author trains three dispatchers by behavioral cloning on optimal schedules produced by CP-SAT for small instances and evaluates them on Taillard benchmarks: a non-message-passing MLP baseline, a relational GIN, and a relational GATv2. The abstract claims that the feature-only model outperforms various graph-based dispatchers and that the GNN model is close to state-of-the-art on large instances. The library itself is a substantial and potentially useful contribution, but the comparative empirical claims are not fully supported by the evidence presented, and the paper explicitly acknowledges the absence of ablation studies in Section 9.2.1.

Significance. If the library is as modular and documented as described, it is a useful contribution to JSSP and RL research: it packages many design choices that prior systems hard-code, ships with benchmark instances and standard interfaces, and supports both RL and imitation learning workflows. The empirical finding that a feature-only MLP can outperform graph-based dispatchers would be significant if established, because it would separately quantify the contribution of node features relative to message passing. However, the comparisons in the current manuscript are not controlled, the result tables and error bars are missing, and the paper itself acknowledges the lack of ablation studies. As written, the experimental section does not establish the abstract's stronger claims, although those claims are plausibly fixable with additional experiments or appropriately weakened wording.

major comments (4)
  1. [Abstract and Section 8.4] The claim that a feature-only model "outperformed various graph-based dispatchers" is not supported by the evidence in Section 8.4. The non-message-passing baseline is compared against numbers reported in other papers rather than against those models retrained inside JobShopLib under the same protocol. Because training distributions, action-space filters, residual-scheduling conventions, and evaluation code all differ, the comparison does not isolate node features from graph connectivity. A same-pipeline ablation (same training data, same ready-operation filter, same evaluation) is needed to support the abstract's claim; this omission is acknowledged in Section 9.2.1.
  2. [Section 8.4 and Appendix A] The results section contains no quantitative comparison table with per-instance or per-benchmark optimality gaps, no error bars or standard deviations, and no statement of the number of seeds. Figures 8.5 and 8.6 plot averages grouped by size, but the text never defines "near state-of-the-art" numerically or lists which reported baseline values are used. The paper's central quantitative claims are therefore not checkable from the manuscript; Appendix A is listed in the contents but its content is not provided in the visible text. Please add full result tables, seeds, and variance estimates.
  3. [Sections 5.2 and 6.4.1] The action-space filter is a confound in the cross-paper comparison. Published baselines use different ready-operation definitions: non-delay filters in Zhang et al. (2020) and Park et al. (2021b) versus dominated-operation filtering with reservation in Park et al. (2021a) and Lee and Kim (2022, 2024). As the paper itself explains in Section 5.2, this changes the set of reachable schedules and can affect makespan independently of node features. The feature-only model's advantage could therefore be attributable to a different action-space filter rather than to feature expressiveness. Any comparison must match or explicitly control this filter.
  4. [Section 8.1] Details of dataset generation are insufficient for reproducibility and for interpreting generalization. The manuscript does not report the instance-size distribution, the number of training instances, the CP-SAT time limits, or the demonstration sampling procedure. Since the models are trained only on small optimally solved instances, the reader cannot assess whether the Taillard evaluation reflects generalization or protocol differences.
minor comments (5)
  1. [Section 3.2.2] The simplification of the GAT attention score is algebraically incorrect: a^T [Wh_j, Wh_i] is a scalar sum a_1^T W h_j + a_2^T W h_i, not the concatenation [W_1 h_j, W_2 h_i]; the subsequent discussion of expressivity should be corrected accordingly.
  2. [Section 3.3.1] The subsection heading "Relational Message Passsing" contains a typo and should read "Relational Message Passing."
  3. [Sections 5.1.3 and 5.2] The cross-references to the two-job example are inconsistent: the text refers to "Table 1" and "Table 5.2" in different places, while the table is numbered Table 5.1. These references should be unified.
  4. [Section 7.4.1] The action space is described as gymnasium.spaces.MultiDiscrete([num_jobs, num_machines]) with a special value m = -1 for single-machine operations; please clarify how invalid (job, machine) pairs are masked or handled in the Gymnasium API.
  5. [Section 8.4] Figure 8.7 reports GitHub stars; this is not scientific evidence of the library's quality and should be moved to a repository description or omitted from the results section.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the trained dispatchers are evaluated on independent benchmarks and the main limitation is uncontrolled comparison, not derivation-by-construction.

full rationale

The paper's central derivation chain is self-contained: JobShopLib provides modular components, the dispatchers are trained by behavioral cloning on CP-SAT optimal schedules for small instances, and the resulting models are evaluated on the independent Taillard benchmark suite. No fitted parameter or training signal is later renamed as a prediction; the optimality-gap results are computed by running the learned policies on held-out instances, not by recovering an input quantity. The claim that a feature-only model outperforms published graph-based dispatchers rests on cross-paper comparisons that are not controlled for training data, action-space filter, or evaluation protocol, and the author explicitly notes in Section 9.2.1 that ablation studies are absent. That is an experimental-comparison weakness and a correctness risk, not evidence that a claimed prediction reduces by construction to its own inputs. There is no self-citation chain invoked to forbid alternatives, no uniqueness theorem imported from the authors' prior work, and no ansatz smuggled in via citation. The resource-task graph variants are offered as library options with their effectiveness explicitly unproven, so no derivation is forced by definition. Accordingly, no circular step is present and the appropriate score is 0.

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

The central evaluation relies on the assumption that behavioral cloning on small random instances transfers to Taillard benchmarks, and that comparisons to published numbers from different training pipelines are valid. Model hyperparameters and training data parameters are not fully reported, so the experimental results carry hidden degrees of freedom.

free parameters (3)
  • model hyperparameters = not reported
    The central claim of near-SOTA performance depends on the trained models; without these values the exact configurations are not reproducible.
  • best model selection criterion = best validation accuracy or optimality gap
    The paper reports the best model among those trained; selection over validation could inflate results. Section 8.3-8.4.
  • training instance generator parameters = not fully specified
    Random instance sizes and duration ranges define the training distribution, which determines generalization to Taillard benchmarks.
assumptions (3)
  • domain assumption Behavioral cloning on optimal schedules from small instances transfers to larger instances
    The whole experimental strategy (Section 1.1.2) assumes the GNN learns patterns that generalize from CP-solvable small problems to large Taillard instances.
  • domain assumption Comparison to prior published GNN dispatchers is fair despite different training distributions, architectures, and evaluation protocols
    Section 8.4 compares against reported results from other works; this assumes the differences are due to features or architecture rather than experimental setup.
  • domain assumption Taillard benchmark instances are representative for measuring JSSP dispatcher quality
    Standard practice, but the claim of near state-of-the-art on large-scale problems is scoped to this benchmark family.

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Cite this review

Pith. "Pith review of Solving the Job Shop Scheduling Problem with Graph Neural Networks: A Customizable Reinforcement Learning Environment." pith.science (2026). https://pith.science/paper/3S55DISM

@misc{pith2026250613781,
  author       = {Pith},
  title        = {Pith review of: Solving the Job Shop Scheduling Problem with Graph Neural Networks: A Customizable Reinforcement Learning Environment},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3S55DISM}},
  note         = {Machine review of arXiv:2506.13781}
}
read the original abstract

The job shop scheduling problem is an NP-hard combinatorial optimization problem relevant to manufacturing and timetabling. Traditional approaches use priority dispatching rules based on simple heuristics. Recent work has attempted to replace these with deep learning models, particularly graph neural networks (GNNs), that learn to assign priorities from data. However, training such models requires customizing numerous factors: graph representation, node features, action space, and reward functions. The lack of modular libraries for experimentation makes this research time-consuming. This work introduces JobShopLib, a modular library that allows customizing these factors and creating new components with its reinforcement learning environment. We trained several dispatchers through imitation learning to demonstrate the environment's utility. One model outperformed various graph-based dispatchers using only individual operation features, highlighting the importance of feature customization. Our GNN model achieved near state-of-the-art results on large-scale problems. These results suggest significant room for improvement in developing such models. JobShopLib provides the necessary tools for future experimentation.

Figures

Figures reproduced from arXiv: 2506.13781 by the authors.

Figure 1.1
Figure 1.1. Gantt chart representing a possible solution to Example [PITH_FULL_IMAGE:figures/full_fig_p018_1_1.png] view at source ↗
Figure 1.2
Figure 1.2. Gantt chart representing an optimal solution to Example [PITH_FULL_IMAGE:figures/full_fig_p019_1_2.png] view at source ↗
Figure 2.1
Figure 2.1. Groups of schedules. While semi-active schedules are efficient for a given sequence, it may be possible to improve some of them further by changing the sequence itself (e.g., allowing an operation to “jump ahead” of another on the same machine if it doesn’t delay anything else overall). Schedules where no such sequence-altering improvements (termed global left-shifts) are possible are called active sched￾ules. This … view at source ↗
Figures from the paper (20 more)
Figure 2.2
Figure 2.2. Figure 2.2: Disjunctive graph of Example 1. The label m indicates the identifier of the machine required to process the operation, while d indicates the duration of the operation (pij ) in hours. Regarding colors, disjunctive edges are shown in red, while conjunctive edges are c…
Figure 2.3
Figure 2.3. Figure 2.3: Disjunctive graph of Example 1 representing the optimal solution presented in [PITH_FULL_IMAGE:figures/full_fig_p034_2_3.png]
Figure 4.1
Figure 4.1. Figure 4.1: The reinforcement learning loop 4.2 Reinforcement Learning Reinforcement learning (Sutton and Barto, 2018) is a learning paradigm where an agent learns to make sequential decisions by interacting with an environment modeled as an MDP. The funda￾mental difference betw…
Figure 5.1
Figure 5.1. Figure 5.1: Resource-task graph representations of Example [PITH_FULL_IMAGE:figures/full_fig_p061_5_1.png]
Figure 5.2
Figure 5.2. Figure 5.2: Example of a disjunctive graph (b) representing a partial schedule (a) of the instance [PITH_FULL_IMAGE:figures/full_fig_p063_5_2.png]
Figure 5.3
Figure 5.3. Figure 5.3: Comparison of two possible solutions to the instance defined in Table [PITH_FULL_IMAGE:figures/full_fig_p065_5_3.png]
Figure 6.1
Figure 6.1. Figure 6.1: Main JobShopLib’s data structures. The arguments of JobShopInstance’s from_taillard_file and from_matrices methods have been simplified. They can be seen in JobShopInstance’s documentation. Private methods and attributes of all the classes are also omitted for simpli…
Figure 6.2
Figure 6.2. Figure 6.2: Dispatcher and DispatcherObserver class diagram. Private methods and attributes of all the classes are omitted for simplicity. 6.5 Dispatching Rules Using the Dispatcher class, creating basic dispatching rules is a straightforward task. However, before writing the fi…
Figure 7.1
Figure 7.1. Figure 7.1: High-level overview of JobShopLib’s RL environment’s architecture [PITH_FULL_IMAGE:figures/full_fig_p092_7_1.png]
Figure 7.2
Figure 7.2. Figure 7.2: FeatureObserver and CompositeFeatureObserver class diagram. The classes’ private methods and attributes (except class attributes) are omitted for simplicity. Some type hints were also omitted for size constraints. 7.2 The Graph Representation Before explaining how th…
Figure 7.3
Figure 7.3. Figure 7.3: JobShopGraph and Node class diagram. Private methods and attributes of all the classes are omitted for simplicity. 7.2.1 Defining the Initial Graph The initial graph (V0, E0) needs to be created outside the GraphUpdater class, which only updates the graph. In other w…
Figure 7.4
Figure 7.4. Figure 7.4: Class hierarchy of JobShopLib’s graph updaters. The omitted arguments of ResidualGraphUpdater’s constructor are those present in all GraphUpdater’s subclasses (dispatcher, job_shop_graph, and subscribe). Private methods and attributes of all the classes are also omit…
Figure 7.5
Figure 7.5. Figure 7.5: Class hierarchy of JobShopLib’s reward observers. Private methods and attributes (except class attributes) are omitted for simplicity [PITH_FULL_IMAGE:figures/full_fig_p105_7_5.png]
Figure 8.1
Figure 8.1. Figure 8.1: Diagram showing a message passing block. [PITH_FULL_IMAGE:figures/full_fig_p121_8_1.png]
Figure 8.2
Figure 8.2. Figure 8.2: Accuracy in train and validation sets for the best Non- [PITH_FULL_IMAGE:figures/full_fig_p125_8_2.png]
Figure 8.3
Figure 8.3. Figure 8.3: Accuracy in train and validation sets for the best RGIN model. [PITH_FULL_IMAGE:figures/full_fig_p126_8_3.png]
Figure 8.4
Figure 8.4. Figure 8.4: Average optimality gaps (a) and accuracy (b) obtained in their respective validation [PITH_FULL_IMAGE:figures/full_fig_p127_8_4.png]
Figure 8.5
Figure 8.5. Figure 8.5: Average optimality gap in Taillard benchmark ( [PITH_FULL_IMAGE:figures/full_fig_p128_8_5.png]
Figure 8.6
Figure 8.6. Figure 8.6: Average optimality gap obtained in Taillard benchmark ( [PITH_FULL_IMAGE:figures/full_fig_p129_8_6.png]
Figure 8.7
Figure 8.7. Figure 8.7: Number of GitHub stars obtained in JobShopLib and gnn_scheduler repositories since their creation. 7 In GitHub, a star is a simple way for users to indicate that they like or appreciate a repository and want to keep track of it. It essentially functions as a “like" o…

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Reference graph

Works this paper leans on

83 extracted references · 50 canonical work pages

  1. [1]

    Adams, E

    J. Adams, E. Balas, and D. Zawack. The shifting bottleneck procedure for job shop scheduling. Management Science, 34 0 (3): 0 391--401, 1988

    1988

  2. [2]

    On the bottleneck of graph neural networks and its practical implications

    Uri Alon and Eran Yahav. On the bottleneck of graph neural networks and its practical implications. In International Conference on Learning Representations, 2021. URL https://openreview.net/forum?id=i80OPhOCVH2

    2021

  3. [3]

    Applegate and W

    D. Applegate and W. Cook. A computational study of job-shop scheduling. ORSA Journal on Computer, 3 0 (2): 0 149--156, 1991

    1991

  4. [4]

    A markovian decision process

    Richard Bellman. A markovian decision process. Journal of Mathematics and Mechanics, 6 0 (5): 0 679--684, 1957. URL http://www.jstor.org/stable/24900506

    arXiv 1957

  5. [5]

    Machine learning for combinatorial optimization: A methodological tour d’horizon

    Yoshua Bengio, Andrea Lodi, and Antoine Prouvost. Machine learning for combinatorial optimization: A methodological tour d’horizon. European Journal of Operational Research, 290 0 (2): 0 405--421, 2021. ISSN 0377-2217. doi:https://doi.org/10.1016/j.ejor.2020.07.063. URL https://www.sciencedirect.com/science/article/pii/S0377221720306895

    doi:10.1016/j.ejor.2020.07.063 2021

  6. [6]

    The disjunctive graph machine representation of the job shop scheduling problem

    Jacek B azewicz, Erwin Pesch, and Ma gorzata Sterna. The disjunctive graph machine representation of the job shop scheduling problem. European Journal of Operational Research, 127 0 (2): 0 317--331, 2000

    work page 2000

  7. [7]

    Boussa\" i d, J

    I. Boussa\" i d, J. Lepagnot, and P. Siarry. A survey on optimization metaheuristics. Information Sciences, 237: 0 82--117, 2013

    work page 2013

  8. [8]

    How attentive are graph attention networks? In International Conference on Learning Representations, 2022

    Shaked Brody, Uri Alon, and Eran Yahav. How attentive are graph attention networks? In International Conference on Learning Representations, 2022. URL https://openreview.net/forum?id=F72ximsx7C1

    2022

Show all 83 references
  1. [9]

    Khalil, Andrea Lodi, Christopher Morris, and Petar Veličković

    Quentin Cappart, Didier Chételat, Elias B. Khalil, Andrea Lodi, Christopher Morris, and Petar Veličković. Combinatorial optimization and reasoning with graph neural networks. In Zhi-Hua Zhou, editor, Proceedings of the Thirtieth International Joint Conference on Artificial Int...

    2021

  2. [10]

    The application/json Media Type for JavaScript Object Notation (JSON)

    Douglas Crockford. The application/json Media Type for JavaScript Object Notation (JSON) . Internet-Draft draft-crockford-jsonorg-json-04, Internet Engineering Task Force, March 2006. URL https://datatracker.ietf.org/doc/draft-crockford-jsonorg-json/04/. Work in Progress

    2006

  3. [11]

    G. Cybenko. Approximation by superpositions of a sigmoidal function . Mathematics of Control, Signals, and Systems (MCSS), 2 0 (4): 0 303--314, December 1989. ISSN 0932-4194. doi:10.1007/BF02551274. URL http://dx.doi.org/10.1007/BF02551274

    1989 doi

  4. [12]

    Graph neural networks are dynamic programmers

    Andrew Dudzik and Petar Veli c kovi\' c . Graph neural networks are dynamic programmers. In Proceedings of the 36th International Conference on Neural Information Processing Systems, NIPS '22, Red Hook, NY, USA, 2022. Curran Associates Inc. ISBN 9781713871088

    2022

  5. [13]

    Matthias Fey and Jan E. Lenssen. Fast graph representation learning with PyTorch Geometric . In ICLR Workshop on Representation Learning on Graphs and Manifolds, 2019

    2019

  6. [14]

    Design patterns: elements of reusable object-oriented software

    Erich Gamma, Richard Helm, Ralph Johnson, and John Vlissides. Design patterns: elements of reusable object-oriented software. Addison-Wesley Longman Publishing Co., Inc., USA, 1995. ISBN 0201633612

    1995

  7. [15]

    M. R. Garey, D. S. Johnson, and R. Sethi. The complexity of flowshop and jobshop scheduling. Mathematics of Operations Research, 1 0 (2): 0 117--129, 1976

    1976

  8. [16]

    Schoenholz, Patrick F

    Justin Gilmer, Samuel S. Schoenholz, Patrick F. Riley, Oriol Vinyals, and George E. Dahl. Neural message passing for quantum chemistry. In Proceedings of the 34th International Conference on Machine Learning - Volume 70, ICML'17, page 1263–1272. JMLR.org, 2017

    2017

  9. [17]

    On embeddings for numerical features in tabular deep learning

    Yury Gorishniy, Ivan Rubachev, and Artem Babenko. On embeddings for numerical features in tabular deep learning. In Proceedings of the 36th International Conference on Neural Information Processing Systems, NIPS '22, Red Hook, NY, USA, 2022. Curran Associates Inc. ISBN 9781713871088

    2022

  10. [18]

    Gupta and A

    A. Gupta and A. Sivakumar. Job shop scheduling techniques in semiconductor manufacturing. International Journal of Advanced Manufacturing Technology, 27: 0 1163--1169, 2006. doi:10.1007/s00170-004-2296-z. URL https://doi.org/10.1007/s00170-004-2296-z

    2006 doi

  11. [19]

    Harris, K

    Charles R. Harris, K. Jarrod Millman, St \' e fan J. van der Walt, Ralf Gommers, Pauli Virtanen, David Cournapeau, Eric Wieser, Julian Taylor, Sebastian Berg, Nathaniel J. Smith, Robert Kern, Matti Picus, Stephan Hoyer, Marten H. van Kerkwijk, Matthew Brett, Allan Haldane, Jai...

    2020

  12. [20]

    A survey of priority rule-based scheduling

    Reinhard Haupt. A survey of priority rule-based scheduling. Operations Research Spektrum, 11 0 (1): 0 3--16, 1989

    1989

  13. [21]

    Deep Residual Learning for Image Recognition

    Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep Residual Learning for Image Recognition . In Proceedings of 2016 IEEE Conference on Computer Vision and Pattern Recognition, CVPR '16, pages 770--778. IEEE, June 2016. doi:10.1109/CVPR.2016.90. URL http://ieeexplore.i...

    2016

  14. [22]

    Residual scheduling: A new reinforcement learning approach to solving job shop scheduling problem, 2023

    Kuo-Hao Ho, Ruei Yu Jheng, Ji-Han Wu, Fan Chiang, Yen-Chi Chen, Yuan-Yu Wu, and I-Chen Wu. Residual scheduling: A new reinforcement learning approach to solving job shop scheduling problem, 2023. URL https://openreview.net/forum?id=5uIL1E8h1E

    2023

  15. [23]

    Efficient dispatching rules for scheduling in a job shop

    Oliver Holthaus and Chandrasekharan Rajendran. Efficient dispatching rules for scheduling in a job shop. International Journal of Production Economics, 48 0 (1): 0 87--105, 1997. ISSN 0925-5273. doi:https://doi.org/10.1016/S0925-5273(96)00068-0. URL https://www.sciencedirect.c...

    1997 doi

  16. [24]

    Stinchcombe, and Halbert L

    Kurt Hornik, Maxwell B. Stinchcombe, and Halbert L. White. Multilayer feedforward networks are universal approximators. Neural Networks, 2: 0 359--366, 1989. URL https://api.semanticscholar.org/CorpusID:2757547

    1989

  17. [25]

    Imitation learning: a survey of learning methods

    Ahmed Hussein, Mohamed Medhat Gaber, Eyad Elyan, and Chrisina Jayne. Imitation learning: a survey of learning methods. ACM computing surveys, 50, 2017. ISSN 0360-0300. doi:10.1145/3054912. URL http://hdl.handle.net/10059/2298

    2017 doi

  18. [26]

    Learning to solve job shop scheduling under uncertainty

    Guillaume Infantes, St \'e phanie Roussel, Pierre Pereira, Antoine Jacquet, and Emmanuel Benazera. Learning to solve job shop scheduling under uncertainty. In Bistra Dilkina, editor, Integration of Constraint Programming, Artificial Intelligence, and Operations Research, pages...

    2024

  19. [27]

    S. M. Johnson. Optimal two- and three-stage production schedules with setup times included. Naval Research Logistics Quarterly, 1 0 (1): 0 61--68, 1954. doi:https://doi.org/10.1002/nav.3800010110. URL https://onlinelibrary.wiley.com/doi/abs/10.1002/nav.3800010110

    1954 doi

  20. [28]

    Yunus Kathawala and William R. Allen. Expert systems and job shop scheduling. International Journal of Operations & Production Management, 13 0 (2): 0 23--35, 1993. doi:10.1108/01443579310025286

    1993 doi

  21. [29]

    Kingma and Jimmy Ba

    Diederik P. Kingma and Jimmy Ba. Adam: A method for stochastic optimization. In Yoshua Bengio and Yann LeCun, editors, ICLR (Poster), 2015. URL http://dblp.uni-trier.de/db/conf/iclr/iclr2015.html#KingmaB14

    2015

  22. [30]

    Kipf and Max Welling

    Thomas N. Kipf and Max Welling. Semi-supervised classification with graph convolutional networks. In International Conference on Learning Representations, 2017. URL https://openreview.net/forum?id=SJU4ayYgl

    2017

  23. [31]

    Korte and J

    B. Korte and J. Vygen. Combinatorial Optimization: Theory and Algorithms. Springer, 5th edition, 2012

    2012

  24. [32]

    Cp-sat primer - under the hood, 2024

    Dominik Krupke. Cp-sat primer - under the hood, 2024. URL https://d-krupke.github.io/cpsat-primer/07_under_the_hood.html#how-does-it-work. Accessed: 2024-10-20

    2024

  25. [33]

    Lawrence

    S. Lawrence. Resource constrained project scheduling: An experimental investigation of heuristic scheduling techniques (supplement). Technical report, Carnegie-Mellon University, Graduate School of Industrial Administration, Pittsburgh, Pennsylvania, 1984

    1984

  26. [34]

    Deep learning

    Yann LeCun, Yoshua Bengio, and Geoffrey Hinton. Deep learning. nature, 521 0 (7553): 0 436, 2015

    2015

  27. [35]

    Imitation learning for real-time job shop scheduling using graph-based representation

    Je-Hun Lee and Hyun-Jung Kim. Imitation learning for real-time job shop scheduling using graph-based representation. In 2022 Winter Simulation Conference (WSC), pages 3285--3296, 2022. doi:10.1109/WSC57314.2022.10015445

    2022

  28. [36]

    Graph-based imitation learning for real-time job shop dispatcher

    Je-Hun Lee and Hyun-Jung Kim. Graph-based imitation learning for real-time job shop dispatcher. IEEE Transactions on Automation Science and Engineering, pages 1--14, 2024. doi:10.1109/TASE.2024.3486919

    2024

  29. [37]

    Real-time scheduling simulation optimisation of job shop in a production-logistics collaborative environment

    Yun Luo Lei Cai, Wenfeng Li and Lijun He. Real-time scheduling simulation optimisation of job shop in a production-logistics collaborative environment. International Journal of Production Research, 61 0 (5): 0 1373--1393, 2023. doi:10.1080/00207543.2021.2023777. URL https://do...

    2023

  30. [38]

    Pep 585 -- type hinting generics in standard collections

    Ivan Levkivskyi, Guido van Rossum, and Jukka Lee. Pep 585 -- type hinting generics in standard collections. https://www.python.org/dev/peps/pep-0585/, 2020. Accessed: 2025-05-17

    2020

  31. [39]

    Liao and C

    J. Liao and C. Lin. Optimization and simulation of job-shop supply chain scheduling in manufacturing enterprises based on particle swarm optimization. International Journal of Simulation Modelling, 18: 0 187--196, 03 2019. doi:10.2507/IJSIMM18(1)CO5

    2019 doi

  32. [40]

    Robert C. Martin. Clean Code: A Handbook of Agile Software Craftsmanship. Prentice Hall PTR, USA, 1 edition, 2008. ISBN 0132350882

    2008

  33. [41]

    Asynchronous methods for deep reinforcement learning

    Volodymyr Mnih, Adria Puigdomenech Badia, Mehdi Mirza, Alex Graves, Timothy Lillicrap, Tim Harley, David Silver, and Koray Kavukcuoglu. Asynchronous methods for deep reinforcement learning. In International Conference on Machine Learning, pages 1928--1937, 2016. URL https://ar...

    1928 arXiv

  34. [42]

    Muth and G.L

    J.F. Muth and G.L. Thompson. Industrial scheduling. Prentice-Hall, Englewood Cliffs, NJ, 1963

    1963

  35. [43]

    Vinod Nair and Geoffrey E. Hinton. Rectified linear units improve restricted boltzmann machines. In Proceedings of the 27th International Conference on International Conference on Machine Learning, ICML'10, page 807–814, Madison, WI, USA, 2010. Omnipress. ISBN 9781605589077

    2010

  36. [44]

    Ng, Daishi Harada, and Stuart J

    Andrew Y. Ng, Daishi Harada, and Stuart J. Russell. Policy invariance under reward transformations: Theory and application to reward shaping. In Proceedings of the Sixteenth International Conference on Machine Learning, ICML '99, page 278–287, San Francisco, CA, USA, 1999. Mor...

    1999

  37. [45]

    Schedulenet: Learn to solve multi-agent scheduling problems with reinforcement learning

    Junyoung Park, Sanjar Bakhtiyar, and Jinkyoo Park. Schedulenet: Learn to solve multi-agent scheduling problems with reinforcement learning. ArXiv, abs/2106.03051, 2021 a . URL https://api.semanticscholar.org/CorpusID:235358953

    2021 arXiv

  38. [46]

    Learning to schedule job-shop problems: representation and policy learning using graph neural network and reinforcement learning

    Junyoung Park, Jaehyeong Chun, Sang - Hun Kim, Youngkook Kim, and Jinkyoo Park. Learning to schedule job-shop problems: representation and policy learning using graph neural network and reinforcement learning. International Journal of Production Research, 59 0 (11): 0 3360--33...

    2021

  39. [47]

    Cp-sat, 2024

    Laurent Perron and Frédéric Didier. Cp-sat, 2024. URL https://developers.google.com/optimization/cp/cp_solver/. Accessed: 2024-05-07

    2024

  40. [48]

    Surgical case scheduling as a generalized job shop scheduling problem

    Dinh-Nguyen Pham and Andreas Klinkert. Surgical case scheduling as a generalized job shop scheduling problem. European Journal of Operational Research, 185 0 (3): 0 1011--1025, 2008. ISSN 0377-2217. doi:https://doi.org/10.1016/j.ejor.2006.03.059. URL https://www.sciencedirect....

    2008 doi

  41. [49]

    Pomerleau

    Dean A. Pomerleau. Alvinn: An autonomous land vehicle in a neural network. In D. Touretzky, editor, Advances in Neural Information Processing Systems, volume 1. Morgan-Kaufmann, 1988. URL https://proceedings.neurips.cc/paper_files/paper/1988/file/812b4ba287f5ee0bc9d43bbf5bbe87...

    1988

  42. [50]

    Stable-baselines3: Reliable reinforcement learning implementations

    Antonin Raffin, Ashley Hill, Adam Gleave, Anssi Kanervisto, Maximilian Ernestus, and Noah Dormann. Stable-baselines3: Reliable reinforcement learning implementations. Journal of Machine Learning Research, 22 0 (268): 0 1--8, 2021. URL http://jmlr.org/papers/v22/20-1364.html

    2021

  43. [51]

    S.M. Ross. Applied Probability Models with Optimization Applications. Dover Books on Advanced Mathematics. Dover Publications, 1992. ISBN 9780486673141. URL https://books.google.es/books?id=ciU87-2kO1wC

    1992

  44. [52]

    Chapter 1 - introduction

    Francesca Rossi, Peter van Beek , and Toby Walsh. Chapter 1 - introduction. In Francesca Rossi, Peter van Beek , and Toby Walsh, editors, Handbook of Constraint Programming, volume 2 of Foundations of Artificial Intelligence, pages 3--12. Elsevier, 2006. doi:https://doi.org/10...

    2006 doi

  45. [53]

    Rumelhart, G.E

    D.E. Rumelhart, G.E. Hinton, and R.J. Williams. Learning representations by back-propagating errors. Nature, 323 0 (6088): 0 533--536, 1986. doi:10.1038/323533a0

    1986 doi

  46. [54]

    Konstantin Rusch, Michael M

    T. Konstantin Rusch, Michael M. Bronstein, and Siddhartha Mishra. A survey on oversmoothing in graph neural networks. ArXiv, abs/2303.10993, 2023. URL https://api.semanticscholar.org/CorpusID:257632346

    2023 arXiv

  47. [55]

    Sarfaraj, Md

    N. Sarfaraj, Md. L. Lingkon, and N. Zahan. Applying flexible job shop scheduling in patients management to optimize processing time in hospitals. International Journal of Research in Industrial Engineering, 10 0 (1): 0 46--55, 2021. ISSN 2783-1337. doi:10.22105/riej.2021.26014...

    2021

  48. [56]

    The graph neural network model

    Franco Scarselli, Marco Gori, Ah Chung Tsoi, Markus Hagenbuchner, and Gabriele Monfardini. The graph neural network model. IEEE Transactions on Neural Networks, 20 0 (1): 0 61--80, 2009. doi:10.1109/TNN.2008.2005605

    2009

  49. [57]

    Kipf, Peter Bloem, Rianne van den Berg, Ivan Titov, and Max Welling

    Michael Schlichtkrull, Thomas N. Kipf, Peter Bloem, Rianne van den Berg, Ivan Titov, and Max Welling. Modeling relational data with graph convolutional networks. In Aldo Gangemi, Roberto Navigli, Maria-Esther Vidal, Pascal Hitzler, Rapha \"e l Troncy, Laura Hollink, Anna Torda...

    2018

  50. [58]

    Jordan, and P

    John Schulman, Philipp Moritz, Sergey Levine, Michael I. Jordan, and P. Abbeel. High-dimensional continuous control using generalized advantage estimation. CoRR, abs/1506.02438, 2015. URL https://api.semanticscholar.org/CorpusID:3075448

    2015 arXiv

  51. [59]

    Proximal policy optimization algorithms

    John Schulman, Filip Wolski, Prafulla Dhariwal, Alec Radford, and Oleg Klimov. Proximal policy optimization algorithms. ArXiv, abs/1707.06347, 2017. URL https://api.semanticscholar.org/CorpusID:28695052

    2017 arXiv

  52. [60]

    Smit, Jianan Zhou, Robbert Reijnen, Yaoxin Wu, Jian Chen, Cong Zhang, Zaharah Bukhsh, Yingqian Zhang, and Wim Nuijten

    Igor G. Smit, Jianan Zhou, Robbert Reijnen, Yaoxin Wu, Jian Chen, Cong Zhang, Zaharah Bukhsh, Yingqian Zhang, and Wim Nuijten. Graph neural networks for job shop scheduling problems: A survey. Computers & Operations Research, 176: 0 106914, 2025. ISSN 0305-0548. doi:https://do...

    2025

  53. [61]

    Flexible job shop scheduling via graph neural network and deep reinforcement learning

    Wen Song, Xinyang Chen, Qiqiang Li, and Zhiguang Cao. Flexible job shop scheduling via graph neural network and deep reinforcement learning. IEEE Transactions on Industrial Informatics, 19 0 (2): 0 1600--1610, 2023. doi:10.1109/TII.2022.3189725

    2023

  54. [62]

    Storer, S.D

    R.H. Storer, S.D. Wu, and R. Vaccari. New search spaces for sequencing problems with applications to job-shop scheduling. Management Science, 38 0 (10): 0 1495--1509, 1992

    1992

  55. [63]

    Sutton and Andrew G

    Richard S. Sutton and Andrew G. Barto. Reinforcement Learning: An Introduction. The MIT Press, second edition, 2018. URL http://incompleteideas.net/book/the-book-2nd.html

    2018

  56. [64]

    Policy gradient methods for reinforcement learning with function approximation

    Richard S Sutton, David McAllester, Satinder Singh, and Yishay Mansour. Policy gradient methods for reinforcement learning with function approximation. In S. Solla, T. Leen, and K. M\" u ller, editors, Advances in Neural Information Processing Systems, volume 12. MIT Press, 19...

    1999

  57. [65]

    Taillard

    E. Taillard. Benchmarks for basic scheduling problems. European Journal of Operational Research, 64 0 (2): 0 278--285, 1993

    1993

  58. [66]

    A reinforcement learning environment for job-shop scheduling, 2021

    Pierre Tassel, Martin Gebser, and Konstantin Schekotihin. A reinforcement learning environment for job-shop scheduling, 2021

    2021

  59. [67]

    Gymnasium: A standard interface for reinforcement learning environments

    Mark Towers, Ariel Kwiatkowski, Jordan Terry, John U Balis, Gianluca De Cola, Tristan Deleu, Manuel Goul \ a o, Andreas Kallinteris, Markus Krimmel, Arjun KG, et al. Gymnasium: A standard interface for reinforcement learning environments. arXiv preprint arXiv:2407.17032, 2024

    2024 arXiv

  60. [68]

    Attention is all you need

    Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, ukasz Kaiser, and Illia Polosukhin. Attention is all you need. In I. Guyon, U. Von Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett, editors, Advances in Neural In...

    2017

  61. [69]

    V. V. Vazirani. Approximation Algorithms. Springer, 2010

    2010

  62. [70]

    Graph attention networks, 2018

    Petar Veličković, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Liò, and Yoshua Bengio. Graph attention networks, 2018

    2018

  63. [71]

    Dynamic job-shop scheduling in smart manufacturing using deep reinforcement learning

    Libing Wang, Xin Hu, Yin Wang, Sujie Xu, Shijun Ma, Kexin Yang, Zhijun Liu, and Weidong Wang. Dynamic job-shop scheduling in smart manufacturing using deep reinforcement learning. Computer Networks, 190: 0 107969, 2021. ISSN 1389-1286. doi:https://doi.org/10.1016/j.comnet.2021...

    2021

  64. [72]

    JSSP instances and results

    Thomas Weise. JSSP instances and results. https://github.com/thomasWeise/jsspInstancesAndResults, Accessed: 2025-04-18. GitHub repository

    2025

  65. [73]

    R. J. Williams. Simple statistical gradient-following algorithms for connectionist reinforcement learning. Machine Learning, 8: 0 229--256, 1992

    1992

  66. [74]

    The future of jobs report 2023

    World Economic Forum . The future of jobs report 2023. Technical report, World Economic Forum, Geneva, 2023. URL https://www.weforum.org/publications/the-future-of-jobs-report-2023/

    2023

  67. [75]

    A survey of job shop scheduling problem: The types and models

    Hegen Xiong, Shuangyuan Shi, Danni Ren, and Jinjin Hu. A survey of job shop scheduling problem: The types and models. Computers & Operations Research, 142: 0 105731, 2022

    2022

  68. [76]

    How powerful are graph neural networks? In International Conference on Learning Representations, 2019

    Keyulu Xu, Weihua Hu, Jure Leskovec, and Stefanie Jegelka. How powerful are graph neural networks? In International Conference on Learning Representations, 2019. URL https://openreview.net/forum?id=ryGs6iA5Km

    2019

  69. [77]

    Yamada and R

    T. Yamada and R. Nakano. A genetic algorithm applicable to large-scale job-shop problems. In Proceedings of the Second International Workshop on Parallel Problem Solving from Nature (PPSN'2), pages 281--290, Brussels, Belgium, 1992

    1992

  70. [78]

    Y. Yu, J. Wang, Y. Liu, et al. Revisit the environmental impact of artificial intelligence: the overlooked carbon emission source? Frontiers of Environmental Science & Engineering, 18: 0 158, 2024. doi:10.1007/s11783-024-1918-y. URL https://doi.org/10.1007/s11783-024-1918-y

    2024 doi

  71. [79]

    Solving job shop scheduling problems via deep reinforcement learning

    Erdong Yuan, Shuli Cheng, Liejun Wang, Shiji Song, and Fang Wu. Solving job shop scheduling problems via deep reinforcement learning. Applied Soft Computing, 143: 0 110436, 2023. ISSN 1568-4946. doi:https://doi.org/10.1016/j.asoc.2023.110436. URL https://www.sciencedirect.com/...

    2023

  72. [80]

    Learning to dispatch for job shop scheduling via deep reinforcement learning

    Cong Zhang, Wen Song, Zhiguang Cao, Jie Zhang, Puay Siew Tan, and Xu Chi. Learning to dispatch for job shop scheduling via deep reinforcement learning. In H. Larochelle, M. Ranzato, R. Hadsell, M. F. Balcan, and H. Lin, editors, Advances in Neural Information Processing System...

    2020

  73. [81]

    A review on learning to solve combinatorial optimisation problems in manufacturing

    Cong Zhang, Yaoxin Wu, Yining Ma, Wen Song, Zhang Le, Zhiguang Cao, and Jie Zhang. A review on learning to solve combinatorial optimisation problems in manufacturing. IET Collaborative Intelligent Manufacturing, 5 0 (1), March 2023. ISSN 2516-8398. doi:10.1049/cim2.12072

    2023 doi

  74. [82]

    A constraint program for solving the job-shop problem

    Jianyang Zhou. A constraint program for solving the job-shop problem. In Eugene C. Freuder, editor, Principles and Practice of Constraint Programming --- CP96, pages 510--524, Berlin, Heidelberg, 1996. Springer Berlin Heidelberg. ISBN 978-3-540-70620-5

    1996

  75. [83]

    Pep 604 -- allow writing union types as x | y

    Mark Zhu, Ivan Levkivskyi, and Jukka Lehtosalo. Pep 604 -- allow writing union types as x | y. https://www.python.org/dev/peps/pep-0604/, 2020. Accessed: 2025-05-17

    2020

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.