In this paper, a distributed no-wait permutation flowshop scheduling problem with a preventive maintenance operation (PM/DNWPFSP) is investigated. A mixed-integer linear programming model for the PM/DNWPFSP is established. The problem characteristics and preventive maintenance characteristics of the PM/DNWPFSP are analyzed, and an accelerated calculation method of the completion time is proposed. A hybrid artificial bee colony (HABC) algorithm with an iterated local search mechanism for neighborhood search is proposed. To improve the quality of the solution, the shift, the swap and the hybrid operators are conducted in the critical factory. A local search operator based on the shift, the swap and the hybrid operators is proposed to jump out of local optima. A large number of experiments are conducted to evaluate the performance of the proposed HABC. The experimental results show that the proposed HABC algorithm has many promising advantages in solving the PM/DNWPFSP.

The distributed permutation flowshop scheduling is a critical issue in various industries, involving jobs allocation and scheduling among multiple flowshops. This paper extends the research to explore the Distributed Mixed No-Wait Permutation Flowshop Scheduling Problems (DMNWPFSP) with minimizing makespan. The innovation lies in an optimized mathematical model, hybrid heuristic algorithms, an improved iterated greedy algorithm (IIG), and high-quality solutions. Extensive experimental results demonstrate the effectiveness and superiority of the proposed IIG in terms of scheduling quality, computational efficiency, and robustness compared to existing approaches. The outcomes of this work contribute to the field of distributed flowshop scheduling, providing valuable insights for practitioners seeking to enhance production efficiency and competitiveness.