Energy-Efficient Distributed Flexible Job Shop Scheduling with Machine Degradation and State-Driven Imperfect Preventive Maintenance

This study addresses a distributed flexible job shop scheduling problem with machine degradation and state-driven imperfect preventive maintenance, denoted as MD-SDIPM-DFJSP. A bi-objective model is developed to minimize makespan and total energy consumption by jointly optimizing job assignment, operation sequencing, machine selection, and processing speed. The model links processing speed with processing time, power consumption, and degradation increment, and uses a unified degradation bound to represent both degradation and reliability constraints. Preventive maintenance is treated as an imperfect recovery action and is generated according to machine states and idle-window conditions. To solve the problem, a degradation-aware multi-objective memetic algorithm (DMA) is proposed, incorporating four-layer encoding, state-driven decoding, hybrid initialization, knowledge-guided neighborhood search, and a speed-based adjustment operator. Numerical experiments show that Gurobi solved the small instance to optimality with a 0% optimality gap, and the resulting schedule satisfied the modeled production, maintenance, degradation, reliability, and energy accounting requirements. Across 84 combinations of instances and factory sizes, DMA achieved the highest HV in 72 cases and the lowest IGD in 62 cases. The Wilcoxon tests further confirmed its overall advantages over the three comparison algorithms in terms of both HV and IGD.