Discrete Multi-Objective Grey Wolf Algorithm Applied to Dynamic Distributed Flexible Job Shop Scheduling Problem with Variable Processing Times

Uncertainty in processing times is a key issue in distributed production; it severely affects scheduling accuracy. In this study, we investigate a dynamic distributed flexible job shop scheduling problem with variable processing times (DDFJSP-VPT), in which the processing time follows a normal distribution. First, the mathematical model is established by simultaneously considering the makespan, tardiness, and total factory load. Second, a chance-constrained approach is employed to predict uncertain processing times to generate a robust initial schedule. Then, a heuristic scheduling method which involves a left-shift strategy, an insertion-based local adjustment strategy, and a DMOGWO-based global rescheduling strategy is developed to dynamically adjust the scheduling plan in response to the context of uncertainty. Moreover, a hybrid initialization scheme, discrete crossover, and mutation operations are designed to generate a high-quality initial population and update the wolf pack, enabling GWO to effectively solve the distributed flexible job shop scheduling problem. Based on the parameter sensitivity study and a comparison with four algorithms, the algorithm's stability and effectiveness in both static and dynamic environments are demonstrated. Finally, the experimental results show that our method can achieve much better performance than other rules-based reactive scheduling methods and the hybrid-shift strategy. The utility of the prediction strategy is also validated.