Distributed Assembly Permutation Flowshop Scheduling with Capacity-Triggered Batch Transportation and Dedicated Closed-Loop Vehicles

This paper investigates a distributed assembly permutation flowshop scheduling problem with first-in-first-out (FIFO) batch transportation triggered by vehicle capacity and heterogeneous dedicated vehicles operating in closed loops. Components are processed at multiple factories and transported in batches to a central assembly station, where a product can be assembled only after all of its required components have arrived. The objective is to minimize the makespan. Factory assignment and sequencing within each factory determine processing completion times and, through the prescribed transportation rules, affect batch departures, vehicle return times, component arrivals, product readiness, and assembly timing. To address these coupled temporal effects, a Timing Propagation Cooperative Population-Based Iterated Greedy algorithm (TPCPIG) is proposed. It combines multisource population construction guided by temporal features, hierarchical joint reinsertion of factory assignment and sequencing, and bilateral cross-factory cooperative reconstruction; all candidate solutions are evaluated by a unified schedule decoder. Computational experiments on 120 test instances show that TPCPIG achieves an overall average relative percentage deviation of 0.906%, compared with 3.006–8.607% for the four comparison algorithms, and obtains the lowest mean makespan for all tested job sizes from n=8 onward. Further ablation experiments and analyses of search behavior clarify the respective roles of the three proposed mechanisms in population construction, evaluation effort, and adjustment across factories.