Energy-efficient Distributed Heterogeneous Hybrid Flow-shop Scheduling Using Graph Neural Network and Deep Reinforcement Learning

With growing environmental awareness and increasing energy demands, sustainable manufacturing has become a focal point in the industry. Meanwhile, globalization has propelled distributed manufacturing systems as a dominant trend. This paper tackles the energy-efficient distributed heterogeneous hybrid flow-shop scheduling problem (EDHHFSP), aiming to minimize both makespan and total energy consumption. We first formulate a mixed-integer linear programming (MILP) model to provide a benchmark for small instances. More importantly, we propose a novel end-to-end deep reinforcement learning framework based on a heterogeneous graph neural network, which models the scheduling problem as a distributed decision-making process. A key innovation lies in the design of an action space composed of "job–factory" and "operation–machine" pairs, enabling fine-grained, decentralized scheduling decisions. Our approach starts with a novel heterogeneous graph representation of scheduling states, capturing complex interactions among jobs, factories, and machines. A three-stage embedding mechanism is developed to encode real-time scheduling environments. The agent then learns a parameterized policy using the proximal policy optimization (PPO) algorithm, guided by a reward function that balances makespan and energy efficiency. Experimental results demonstrate that our method generalizes well across different problem scales and significantly outperforms traditional heuristics and learning-based baselines in terms of both scheduling quality and energy savings.