An End-to-End Framework for Energy-Efficient Cascaded Dual-Shop Collaborative Scheduling With Mating Operations

Due to the complexity of modern production processes and environments, most products must pass through multiple workshops from raw materials to finished goods. This article investigates a collaborative scheduling problem in a cascaded dual-shop production setting. Unlike single-shop scheduling or distributed multiworkshop scheduling, this problem emphasizes collaborative optimization between two interdependent workshops. In addition, real-world production often involves a mode where main and suborders must be integrated through mating operations. This study formulates an energy-efficient cascaded dual-shop collaborative scheduling problem with the mating operation (ECDCSP-M). The focus is on developing a mixed-integer linear programming (MILP) model for the ECDCSP-M and designing an end-to-end graph-based deep reinforcement learning (GDRL) approach. A dual-shop heterogeneous graph is constructed to capture the real-time state of the entire system, in which "job-factory" and "operation-machine" pairs are defined as agent actions. A heterogeneous graph neural network (HGNN) is then proposed, employing a three-stage embedding mechanism to model complex relationships, including mating operations. Experimental results show that the proposed method achieves strong generalization across varying problem complexities and provides robust solutions to challenging scheduling scenarios.