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Learning to Solve Job Shop Scheduling under Uncertainty

Guillaume Infantes, Stéphanie Roussel, Pierre Pereira, Antoine Jacquet, Emmanuel Benazera

TL;DR

This work addresses the Job-Shop Scheduling Problem under duration uncertainty with the objective of minimizing the average makespan $\mathbb{E}[C_{max}]$. It introduces Wheatley, a Graph Neural Network–driven DRL framework that solves the uncertainty-aware JSSP by modeling it as an MDP, using PPO for policy optimization and a graph rewiring strategy to enable rich information flow. Key contributions include empirical improvements in DRL/JSSP generalization and robustness to duration uncertainty, a scalable GNN architecture with uncertainty handling, and strong performance on Taillard benchmarks, especially in stochastic settings. The method yields a flexible, open-source solution capable of robustly scheduling under uncertainty and generalizing to larger problem sizes, with practical impact for industrial scheduling under real-world variability.

Abstract

Job-Shop Scheduling Problem (JSSP) is a combinatorial optimization problem where tasks need to be scheduled on machines in order to minimize criteria such as makespan or delay. To address more realistic scenarios, we associate a probability distribution with the duration of each task. Our objective is to generate a robust schedule, i.e. that minimizes the average makespan. This paper introduces a new approach that leverages Deep Reinforcement Learning (DRL) techniques to search for robust solutions, emphasizing JSSPs with uncertain durations. Key contributions of this research include: (1) advancements in DRL applications to JSSPs, enhancing generalization and scalability, (2) a novel method for addressing JSSPs with uncertain durations. The Wheatley approach, which integrates Graph Neural Networks (GNNs) and DRL, is made publicly available for further research and applications.

Learning to Solve Job Shop Scheduling under Uncertainty

TL;DR

This work addresses the Job-Shop Scheduling Problem under duration uncertainty with the objective of minimizing the average makespan . It introduces Wheatley, a Graph Neural Network–driven DRL framework that solves the uncertainty-aware JSSP by modeling it as an MDP, using PPO for policy optimization and a graph rewiring strategy to enable rich information flow. Key contributions include empirical improvements in DRL/JSSP generalization and robustness to duration uncertainty, a scalable GNN architecture with uncertainty handling, and strong performance on Taillard benchmarks, especially in stochastic settings. The method yields a flexible, open-source solution capable of robustly scheduling under uncertainty and generalizing to larger problem sizes, with practical impact for industrial scheduling under real-world variability.

Abstract

Job-Shop Scheduling Problem (JSSP) is a combinatorial optimization problem where tasks need to be scheduled on machines in order to minimize criteria such as makespan or delay. To address more realistic scenarios, we associate a probability distribution with the duration of each task. Our objective is to generate a robust schedule, i.e. that minimizes the average makespan. This paper introduces a new approach that leverages Deep Reinforcement Learning (DRL) techniques to search for robust solutions, emphasizing JSSPs with uncertain durations. Key contributions of this research include: (1) advancements in DRL applications to JSSPs, enhancing generalization and scalability, (2) a novel method for addressing JSSPs with uncertain durations. The Wheatley approach, which integrates Graph Neural Networks (GNNs) and DRL, is made publicly available for further research and applications.
Paper Structure (38 sections, 4 figures, 4 tables, 1 algorithm)

This paper contains 38 sections, 4 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related work
  3. JSSP with Uncertainty as a MDP
  4. Background
  5. Representing uncertainty
  6. Sequential Decision Making
  7. State
  8. Actions
  9. Transitions
  10. Reward/Cost
  11. Solving the MDP with Reinforcement Learning
  12. Algorithm
  13. GNN Implementation: Rewiring, Embedding and Addressing Uncertainty
  14. Graph Rewiring and Embedding
  15. Precedences.
  16. ...and 23 more sections

Figures (4)

  • Figure 1: Disjunctive graph representation
  • Figure 2: General Architecture
  • Figure 3: Rewired graph example with precedences, backward precedences and conflicts as cliques. Each type of arc on the right has its own encoding. Operations $\mathit{O}_{11}$, $\mathit{O}_{21}$, $\mathit{O}_{22}$ and $\mathit{O}_{31}$ have here been scheduled in this order.
  • Figure 4: Cumulative makespan of W-10x10 and CP-stoc for 100 duration scenarios.