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In the customised manufacturing of complex structural components, such as precision instruments and ships, jobs often have different priorities and involve a mix of online and offline operations. To address these challenges, this paper studies the dual-resource flexible job shop scheduling problem with special workers and job priority constraints (DRFJSP-OJP). Correspondingly, a mixed-integer linear programming (MILP) model is developed, and a multi-critical-path co-driven evolutionary algorithm (MCPEA) is proposed, which includes three key innovations. Firstly, a priority-driven three-layer segmented encoding and priority-based multi-segment active decoding scheme is designed. Secondly, a migration operator based on exemplar selection is introduced to accelerate the convergence. Finally, the global critical-path of the problem and local critical-paths with priorities are defined, then a problem-specific neighbourhood structure is designed. The experimental results indicate that the constructed MILP model can successfully solve small-scale problems. Meanwhile, MCPEA demonstrates superior overall performance than other methods, not only improving production efficiency but also ensuring the timely processing of high-priority jobs. Finally, MCPEA is applied to a real-world case from a complex structural component manufacturing enterprise. The optimised scheduling scheme shortens makespan by 49.60%, and decreases delay rate by 33.33%.
Zhang et al. (Wed,) studied this question.