<p>Distributed manufacturing is gaining popularity. Considering different processing capabilities of factories, this paper studies the distributed heterogeneous hybrid flow shop scheduling problem (DHHFSP), which contains the factory assignment problem and HFSPs within factories. Existing studies have treated them as a coupled problem and solved them synchronously with an integrated method, which leads to mutual interference in solving these sub-problems and limits the solving efficiency. This paper seeks a breakthrough from the factory assignment problem, firstly realizes the decoupling of DHHFSP and presents a decoupling-based improved genetic algorithm (D-IGA). For the factory assignment problem, a rapid factory assignment heuristic is proposed to obtain high-quality factory assignment schemes. A separate encoding and modified genetic operations (involving crossover and mutation) are proposed to efficiently explore the encoding space for HFSPs within factories. To achieve efficient neighborhood exploitation in DHHFSP solution space, a two-level variable neighborhood local search based on critical paths is presented. There are 480 randomly generated instances (problem scale covers small, medium and large) in experiments. The effectiveness of the innovative designs in D-IGA is verified by extensive comparative experiments. D-IGA is compared with other state-of-the-art algorithms. The results show that D-IGA is efficient and effective in addressing DHHFSP. Finally, the proposed method effectively addresses a sensor manufacturing case, achieving a 19.3% reduction in makespan.</p>