pith. sign in

arxiv: 2605.22773 · v1 · pith:F6FAJ647new · submitted 2026-05-21 · 💻 cs.AI · math.OC

Deep Reinforcement Learning for Flexible Job Shop Scheduling with Random Job Arrivals

Yu Tang , Muhammad Zakwan , Efe Balta , John Lygeros , Alisa Rupenyan This is my paper

Pith reviewed 2026-05-22 04:59 UTC · model grok-4.3

classification 💻 cs.AI math.OC
keywords flexible job shop schedulingdeep reinforcement learningrandom job arrivalsdispatching rulesproximal policy optimizationtotal completion timescheduling under uncertainty
0
0 comments X

The pith

Deep reinforcement learning selects dispatching rules to minimize total completion time better than any fixed rule in flexible job shops with random arrivals.

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

The paper establishes that an event-based deep reinforcement learning method can address the flexible job shop scheduling problem when jobs arrive at random times. It trains a lightweight neural network agent using Proximal Policy Optimization to choose from known dispatching rules at each event. This avoids solving complex optimization problems repeatedly. A reader would care because standard solvers become too slow for real-time decisions and single rules fail to adapt to different job mixes. If the claim holds, factories could use this to get reliable schedules without heavy computation when arrivals are unpredictable.

Core claim

The central discovery is that the DRL agent, limited to selecting among dispatching rules, achieves lower total completion times than any individual rule on varied datasets and performs well compared to arrival-triggered mixed-integer linear programming, particularly for heterogeneous instances.

What carries the argument

The Proximal Policy Optimization agent trained to select from dispatching rules at scheduling events to minimize total completion time.

If this is right

  • The DRL approach yields better schedules than static dispatching rules across different heterogeneity levels and arrival rates.
  • It delivers performance close to that of a mixed-integer linear programming solver re-optimized at each arrival, especially on heterogeneous data.
  • The method supports online decision making because the trained policy evaluates quickly without full re-solving.
  • Restricting actions to rules keeps the learning problem tractable while still capturing good heuristic behaviors.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same structure might transfer to other dynamic scheduling settings where full optimization is too slow.
  • Performance on homogeneous datasets could improve if the rule set is expanded or if direct assignment actions are added later.
  • Factories with real sensor data on arrivals could test the policy directly to measure gains over current rule-based systems.

Load-bearing premise

Restricting the reinforcement learning agent to selecting from a fixed set of dispatching rules is sufficient to achieve near-optimal performance for random job arrivals instead of permitting direct assignments of jobs to machines.

What would settle it

A test on additional heterogeneous datasets with random arrivals where the DRL method produces higher total completion times than the strongest single dispatching rule or the arrival-triggered MILP solution would disprove the reported superiority.

Figures

Figures reproduced from arXiv: 2605.22773 by Alisa Rupenyan, Efe Balta, John Lygeros, Muhammad Zakwan, Yu Tang.

Figure 1
Figure 1. Figure 1: The framework of our DRL for FJSPs with random [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Mean episode cumulative reward as a function of the [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Schedules of three methods on one heterogeneous [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
read the original abstract

The Flexible Job Shop Scheduling Problem (FJSP) is the optimal allocation of a set of jobs to machines. Two primary challenges persist in FJSP: the unpredictable arrival of future jobs and the combinatorial complexity of the problem, rendering it intractable for conventional mixed-integer linear programming solvers. This paper proposes an event-based \gls{DRL} approach to solve FJSP with random job arrivals. Specifically, we employ the Proximal Policy Optimization algorithm and use lightweight Multi-Layer Perceptrons to train the \gls{DRL} agent for minimizing the total completion time of all jobs. We design the state representation to be directly accessible from the environment, and limit the learning agent to selecting from among a set of well-established dispatching rules. Simulations show that our \gls{DRL} approach outperforms any of the individual dispatching rules on datasets with varying heterogeneity and job arrival rates. We benchmark our \gls{DRL} against an arrival-triggered mixed-integer linear programming solution and show that our method achieves good performance especially when the datasets are heterogeneous.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. This paper introduces an event-based deep reinforcement learning (DRL) approach using Proximal Policy Optimization (PPO) with Multi-Layer Perceptrons (MLPs) for the Flexible Job Shop Scheduling Problem (FJSP) involving random job arrivals. The agent selects from a predefined set of dispatching rules to minimize total job completion time. Simulations indicate that this DRL method outperforms individual dispatching rules across varying levels of dataset heterogeneity and job arrival rates. It is also compared to an arrival-triggered mixed-integer linear programming (MILP) solution, with claims of particularly good performance on heterogeneous datasets.

Significance. Should the experimental findings prove robust upon detailed verification, the paper contributes a computationally efficient method for handling dynamic and stochastic FJSP, where traditional solvers struggle with intractability. By restricting the action space to established dispatching rules, the approach combines machine learning with domain expertise, potentially improving upon static heuristics while remaining practical. The benchmarking against MILP is a positive aspect, especially highlighting benefits in heterogeneous settings. This could have implications for real-time scheduling in manufacturing systems.

major comments (1)
  1. [Abstract / DRL agent design] The restriction of the DRL agent's action space to selecting among a fixed set of well-established dispatching rules (as stated in the abstract) is central to the approach. To support the claim that this yields 'good performance especially when the datasets are heterogeneous' relative to the arrival-triggered MILP, the manuscript must demonstrate that the chosen rule set is expressive enough to resolve assignment conflicts that arise under high job heterogeneity and random arrivals. If optimal dynamic policies require machine-job pairings outside this fixed vocabulary, outperformance over individual rules is expected but the MILP comparison claim is undermined.
minor comments (2)
  1. [Abstract] The abstract reports simulation outperformance and MILP comparisons but omits quantitative metrics, dataset sizes, number of runs, error bars, or statistical tests. Adding these details (or references to specific tables/figures) would clarify the strength of the empirical support.
  2. Ensure consistent definition of acronyms (DRL, FJSP, PPO, MLP, MILP) on first use and clarify the exact composition of the dispatching rule set used for the agent's action space.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address the major comment point by point below and commit to revisions that strengthen the presentation of our results.

read point-by-point responses

  1. Referee: The restriction of the DRL agent's action space to selecting among a fixed set of well-established dispatching rules (as stated in the abstract) is central to the approach. To support the claim that this yields 'good performance especially when the datasets are heterogeneous' relative to the arrival-triggered MILP, the manuscript must demonstrate that the chosen rule set is expressive enough to resolve assignment conflicts that arise under high job heterogeneity and random arrivals. If optimal dynamic policies require machine-job pairings outside this fixed vocabulary, outperformance over individual rules is expected but the MILP comparison claim is undermined.

    Authors: We agree that additional evidence is needed to substantiate the expressiveness of the fixed rule set for heterogeneous cases. In the revised manuscript we will add a dedicated analysis subsection that reports the frequency of rule selections by the trained PPO agent across heterogeneity levels, along with examples of state-driven switches that address assignment conflicts (e.g., balancing load versus processing-time priorities). Empirical inspection of the learned policy shows consistent use of multiple rules rather than fixation on a single one, which explains the observed gap over static heuristics and the competitive results versus arrival-triggered MILP on heterogeneous instances. We therefore maintain that the current vocabulary is sufficient for the evaluated problem distributions, while acknowledging that extremely rare conflict patterns might benefit from rule augmentation; this limitation will be noted explicitly. revision: yes

Circularity Check

0 steps flagged

No significant circularity; empirical benchmarks are external

full rationale

The paper trains a PPO agent with MLP policy to select among a fixed set of established dispatching rules for event-based FJSP under random arrivals, then reports simulation results against independent baselines (individual dispatching rules and arrival-triggered MILP). No equations, parameters, or uniqueness claims are shown to reduce by construction to the same fitted quantities or self-citations; the performance claims rest on direct comparison to external solvers and heuristics rather than internal redefinition or renaming.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The approach rests on standard RL assumptions and simulation environments without introducing new physical entities or many fitted parameters beyond typical PPO hyperparameters.

axioms (1)
  • domain assumption State representation is directly accessible from the environment.
    Invoked when designing the observation for the DRL agent.

pith-pipeline@v0.9.0 · 5718 in / 1125 out tokens · 33791 ms · 2026-05-22T04:59:26.145457+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    We employ the Proximal Policy Optimization algorithm and use lightweight Multi-Layer Perceptrons to train the DRL agent for minimizing the total completion time of all jobs. We design the state representation to be directly accessible from the environment, and limit the learning agent to selecting from among a set of well-established dispatching rules.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

27 extracted references · 27 canonical work pages · 2 internal anchors

  1. [1]

    Deep reinforcement learning for job shop scheduling problems: A comprehensive literature review,

    L. Lv, C. Zhang, J. Fan, and W. Shen, “Deep reinforcement learning for job shop scheduling problems: A comprehensive literature review,” Knowledge-Based Systems, p. 113633, 2025

    work page 2025

  2. [2]

    On the job-shop scheduling problem,

    A. S. Manne, “On the job-shop scheduling problem,”Operations research, vol. 8, no. 2, pp. 219–223, 1960

    work page 1960

  3. [3]

    Baptiste, C

    P. Baptiste, C. Le Pape, and W. Nuijten,Constraint-based scheduling: applying constraint programming to scheduling problems. Springer Science & Business Media, 2001, vol. 39

    work page 2001

  4. [4]

    Gurobi Optimization,Gurobi Optimizer Reference Manual, 2024, available at https://www.gurobi.com

    L. Gurobi Optimization,Gurobi Optimizer Reference Manual, 2024, available at https://www.gurobi.com

    work page 2024

  5. [5]

    The CP-SAT solver: A new state-of-the-art constraint programming solver,

    L. Perron and P. Schaus, “The CP-SAT solver: A new state-of-the-art constraint programming solver,” Google Research, Tech. Rep., 2020, technical Report

    work page 2020

  6. [6]

    Adaptive scheduling for assembly job shop with uncertain assembly times based on dual q-learning,

    H. Wang, B. R. Sarker, J. Li, and J. Li, “Adaptive scheduling for assembly job shop with uncertain assembly times based on dual q-learning,”International Journal of Production Research, vol. 59, no. 19, pp. 5867–5883, 2021

    work page 2021

  7. [7]

    M. L. Puterman,Markov decision processes: discrete stochastic dy- namic programming. John Wiley & Sons, 2014

    work page 2014

  8. [8]

    Proximal Policy Optimization Algorithms

    J. Schulman, F. Wolski, P. Dhariwal, A. Radford, and O. Klimov, “Proximal policy optimization algorithms,”arXiv preprint arXiv:1707.06347, 2017

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  9. [9]

    Rapid modeling and discovery of priority dispatching rules: An autonomous learning approach,

    C. D. Geiger, R. Uzsoy, and H. Aytu ˘g, “Rapid modeling and discovery of priority dispatching rules: An autonomous learning approach,” Journal of Scheduling, vol. 9, no. 1, pp. 7–34, 2006

    work page 2006

  10. [10]

    Towards energy efficient scheduling and rescheduling for dynamic flexible job shop problem,

    M. Nouiri, A. Bekrar, and D. Trentesaux, “Towards energy efficient scheduling and rescheduling for dynamic flexible job shop problem,” Ifac-PapersOnline, vol. 51, no. 11, pp. 1275–1280, 2018

    work page 2018

  11. [11]

    Digital twin enhanced dynamic job- shop scheduling,

    M. Zhang, F. Tao, and A. Nee, “Digital twin enhanced dynamic job- shop scheduling,”Journal of Manufacturing Systems, vol. 58, pp. 146– 156, 2021

    work page 2021

  12. [12]

    Predictive-reactive strategy for identical parallel machine rescheduling,

    A. Tighazoui, C. Sauvey, and N. Sauer, “Predictive-reactive strategy for identical parallel machine rescheduling,”Computers & Operations Research, vol. 134, p. 105372, 2021

    work page 2021

  13. [13]

    Adaptive production rescheduling system for managing unforeseen disruptions,

    A. J. Figueroa, R. Poler, and B. Andres, “Adaptive production rescheduling system for managing unforeseen disruptions,”Mathemat- ics, vol. 12, no. 22, p. 3478, 2024

    work page 2024

  14. [14]

    Digital twin-based smart manufac- turing: Dynamic line reconfiguration for disturbance handling,

    B. Fu, M. Bi, S. Umeda, T. Nakano, Y . Nonaka, Q. Zhou, T. Matsui, D. M. Tilbury, and K. Barton, “Digital twin-based smart manufac- turing: Dynamic line reconfiguration for disturbance handling,”IEEE Transactions on Automation Science and Engineering, 2025

    work page 2025

  15. [15]

    A neural reinforcement learning approach to learn local dispatching policies in production scheduling,

    S. Riedmiller and M. Riedmiller, “A neural reinforcement learning approach to learn local dispatching policies in production scheduling,” inIJCAI, vol. 2, 1999, pp. 764–771

    work page 1999

  16. [16]

    Dynamic job-shop scheduling using reinforcement learning agents,

    M. E. Aydin and E. ¨Oztemel, “Dynamic job-shop scheduling using reinforcement learning agents,”Robotics and Autonomous Systems, vol. 33, no. 2-3, pp. 169–178, 2000

    work page 2000

  17. [17]

    A distributed approach solving partially flexible job-shop scheduling problem with a q- learning effect,

    W. Bouazza, Y . Sallez, and B. Beldjilali, “A distributed approach solving partially flexible job-shop scheduling problem with a q- learning effect,”IF AC-PapersOnLine, vol. 50, no. 1, pp. 15 890– 15 895, 2017

    work page 2017

  18. [18]

    Optimization of global production scheduling with deep reinforcement learning,

    B. Waschneck, A. Reichstaller, L. Belzner, T. Altenm ¨uller, T. Bauern- hansl, A. Knapp, and A. Kyek, “Optimization of global production scheduling with deep reinforcement learning,”Procedia Cirp, vol. 72, pp. 1264–1269, 2018

    work page 2018

  19. [19]

    Deep reinforcement learning for dynamic flexible job shop scheduling prob- lem considering variable processing times,

    L. Zhang, Y . Feng, Q. Xiao, Y . Xu, D. Li, D. Yang, and Z. Yang, “Deep reinforcement learning for dynamic flexible job shop scheduling prob- lem considering variable processing times,”Journal of Manufacturing systems, vol. 71, pp. 257–273, 2023

    work page 2023

  20. [20]

    Dynamic multi-objective scheduling for flexible job shop by deep reinforcement learning,

    S. Luo, L. Zhang, and Y . Fan, “Dynamic multi-objective scheduling for flexible job shop by deep reinforcement learning,”Computers & Industrial Engineering, vol. 159, p. 107489, 2021

    work page 2021

  21. [21]

    Deep reinforcement learning for dynamic scheduling of a flexible job shop,

    R. Liu, R. Piplani, and C. Toro, “Deep reinforcement learning for dynamic scheduling of a flexible job shop,”International Journal of Production Research, vol. 60, no. 13, pp. 4049–4069, 2022

    work page 2022

  22. [22]

    A drl-based reactive scheduling policy for flexible job shops with random job arrivals,

    L. Zhao, J. Fan, C. Zhang, W. Shen, and J. Zhuang, “A drl-based reactive scheduling policy for flexible job shops with random job arrivals,”IEEE Transactions on Automation Science and Engineering, vol. 21, no. 3, pp. 2912–2923, 2023

    work page 2023

  23. [23]

    Dynamic scheduling for flexible job shop with insufficient transportation resources via graph neural network and deep reinforcement learning,

    M. Zhang, L. Wang, F. Qiu, and X. Liu, “Dynamic scheduling for flexible job shop with insufficient transportation resources via graph neural network and deep reinforcement learning,”Computers & Industrial Engineering, vol. 186, p. 109718, 2023

    work page 2023

  24. [24]

    Dynamic scheduling for flexible job shop with new job insertions by deep reinforcement learning,

    S. Luo, “Dynamic scheduling for flexible job shop with new job insertions by deep reinforcement learning,”Applied Soft Computing, vol. 91, p. 106208, 2020

    work page 2020

  25. [25]

    Preference learning based deep reinforcement learning for flexible job shop scheduling problem,

    X. Liu, L. Han, L. Kang, J. Liu, and H. Miao, “Preference learning based deep reinforcement learning for flexible job shop scheduling problem,”Complex & Intelligent Systems, vol. 11, no. 2, p. 144, 2025

    work page 2025

  26. [26]

    High-Dimensional Continuous Control Using Generalized Advantage Estimation

    J. Schulman, P. Moritz, S. Levine, M. Jordan, and P. Abbeel, “High- dimensional continuous control using generalized advantage estima- tion,”arXiv preprint arXiv:1506.02438, 2015

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  27. [27]

    Stable-baselines3: Reliable reinforcement learning im- plementations,

    A. Raffin, A. Hill, A. Gleave, A. Kanervisto, M. Ernestus, and N. Dormann, “Stable-baselines3: Reliable reinforcement learning im- plementations,”Journal of machine learning research, vol. 22, no. 268, pp. 1–8, 2021

    work page 2021