A Novel Global Sequence-based Mathematical Formulation for Energy-efficient Flexible Job Shop Scheduling Problem

With increasing emphasis on energy efficiency, more researchers are focusing on energy-efficient flexible job shop scheduling problems. Mathematical programming is a commonly used optimization method for such scheduling challenges, offering the advantages of achieving global optima and serving as a foundation for other approaches. However, current mathematical programming formulations face several challenges, including insufficient consideration of various forms of energy consumption and low efficiency, particularly in handling large-scale instances, which struggle to converge. In this study, we propose a novel global sequence-based approach with high computational efficiency. In this model, immediate precedence relationships are identified using constraints, enabling the precise determination of idle durations within any idle slots. The proposed formulation achieves a significant reduction in energy consumption by up to 20% relative to other formulations. Furthermore, it successfully reaches feasible solutions in challenging cases.