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Open Access

ARTICLE

An Intelligent Algorithm for Dynamic Scheduling of Parallel Machines Considering Multi-Task Collaboration in Order Processing

Pei Xie1, Xiaoying Yang1,*, Bo Li1, Zhijie Pei1, Fenghai Yang2
1 School of Mechatronics Engineering, Henan University of Science and Technology, Luoyang, 471003, China
2 Luoyang Bearing Research Institute Co., Ltd., Luoyang, China
* Corresponding Author: Xiaoying Yang. Email: email

Computers, Materials & Continua https://doi.org/10.32604/cmc.2026.083100

Received 29 March 2026; Accepted 28 May 2026; Published online 16 June 2026

Abstract

To address the critical requirements for collaborative delivery of multiple tasks within each order in personalized mass customization, this paper develops a dynamic parallel machine scheduling model that accounts for stochastic machine failures and order priorities, thereby more accurately reflecting the uncertainties and complexities of real-world production environments. A dual-objective optimization framework is adopted to minimize both the makespan (maximum task completion time) and the variance of task completion times, aiming to improve the coordination and reliability of intra-order task delivery. An adaptive weighted reward function is designed to balance overall scheduling efficiency with consistency among tasks during reinforcement learning training. To tackle the challenges posed by partially observable Markov decision processes (POMDP) induced by unexpected machine breakdowns, a Gated Recurrent Unit (GRU)-embedded Proximal Policy Optimization (PPO) intelligent scheduling algorithm is proposed. The algorithm incorporates an Action Masking mechanism to prevent invalid scheduling actions, while the GRU module captures historical state sequences to enhance perception of dynamic production environments. Extensive validation on benchmark datasets, along with comparisons against traditional heuristic algorithms, metaheuristic algorithms, and other deep reinforcement learning methods, demonstrates that the proposed approach achieves robust convergence, high resilience, and strong generalization across both static and dynamic scenarios, significantly improving coordinated delivery performance of order tasks. Overall, the proposed method not only provides an efficient and scalable real-time decision-making solution for Parallel Machine Scheduling Problems (PMSP) but also offers new theoretical and practical insights for optimizing complex production scheduling in intelligent manufacturing systems.

Keywords

Parallel machine scheduling problems; dynamic scheduling; gated recurrent unit; proximal policy optimization; coordinated delivery

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