Optimizing Distributed Flowshop Scheduling with an Artificial Bee Colony Algorithm: Implications for Operations Management

The Distributed Assembly Permutation Flowshop Scheduling Problem (DAPFSP) extends classical flowshop scheduling by integrating distributed production stages with a final centralized assembly stage. This problem is NP-hard and arises in many real-world applications such as automotive, electronics, and aerospace manufacturing, where products are composed of multiple jobs processed across several factories before final assembly. In this paper, we propose an Artificial Bee Colony (ABC) algorithm specifically adapted to the DAPFSP. The algorithm incorporates six neighborhood structures and six local search procedures based on swap and insert moves, applied at the job, product, and assembly levels, to balance exploration and exploitation effectively. Extensive computational experiments on 810 benchmark instances from the literature demonstrate the competitiveness of the proposed approach. The results show that the ABC algorithm is able to improve 481 best-known solutions, achieving average negative deviations with respect to reference methods while maintaining reasonable computational times. Compared with existing algorithms, Furthermore, the ABC algorithm achieves average improvement margins of 9%–48% across various problem scales, decreasing the average deviation by 0.17 on average and by up to 0.73 for large-size instances.