Integrated Production and Maintenance Scheduling for Energy-Efficient Distributed Flexible Job Shops with Machine Degradation and Limited Maintenance Resources

In distributed flexible job shops, preventive maintenance is required to manage machine degradation, but competition for limited maintenance resources can delay production. This study develops a bi-objective model to minimize makespan and total energy consumption by integrating factory assignment, operation sequencing, machine and processing speed selection, imperfect preventive maintenance, and maintenance resource allocation. To solve this problem, a multi-objective memetic algorithm with constrained maintenance resources (MRC-MOMA) is proposed. The algorithm combines four-layer encoding with a decoder that generates maintenance requests according to machine degradation and schedules them under maintenance resource constraints. Computational experiments show that MRC-MOMA achieves better overall performance than the comparison algorithms in terms of hypervolume (HV) and inverted generational distance (IGD), with sensitivity analysis supporting this advantage within the tested parameter ranges. For the representative instances, increasing maintenance resource capacity substantially reduces maintenance waiting time and shortens makespan, but does not necessarily reduce total energy consumption.