Nowadays, improving the management of complex supply chains is a key to become competitive in the twenty-first century global market. Supply chains are composed of multi-plant facilities that must be coordinated and synchronised to cut waste and lead times. This paper proposes a Distributed Assembly Permutation Flowshop Scheduling Problem (DAPFSP) with two stages to model and study complex supply chains. This problem is a generalisation of the Distributed Permutation Flowshop Scheduling Problem (DPFSP). The first stage of the DAPFSP is composed of f identical production factories. Each one is a flowshop that produces jobs to be assembled into final products in a second assembly stage. The objective is to minimise the makespan. We present first a Mixed Integer Linear Programming model (MILP). Three constructive algorithms are proposed. Finally, a Variable Neighbourhood Descent (VND) algorithm has been designed and tested by a comprehensive ANOVA statistical analysis. The results show that the VND algorithm offers good performance to solve this scheduling problem.