The scheduling problems of distributed production have received increasing attention in recent years. To coordinate the scheduling of production and transportation, we propose a novel distributed assembly permutation flowshop scheduling problem with flexible assembly and batch delivery (DAPFSP-FABD). The objective is to minimise the total cost of delivery and tardiness. Given that the problem involves six successive decisions, several batch allocation strategies for both production and distribution are proposed, and four neighbourhood structures are designed to search for the best batch sequence, batch allocation, product sequence, and job sequence. Seven algorithms, including four heuristics, a variable neighbourhood descent (VND) algorithm, and two iterated greedy (IG) algorithms, are proposed. In the IG, two types of destruction and construction operations are present to facilitate escape from local optima, thereby resulting in two IG algorithms: IG_desP and IG_desJ. Finally, extensive computational and statistical experiments are carried out. The results show that the proposed batch allocation strategies can improve the solution significantly. Additionally, the heuristics can obtain reasonable solutions in a short time, while IG_desJ performs the best regarding the quality of solutions. This study can help cross-regional companies coordinate the scheduling of production and transportation and enhance the performance of supply chains.