Considering problems like product blockage and machine faults in the batch scheduling of product assembly lines, this paper proposes a multi-objective flow shop batch scheduling model taking these problems into account, and by comparing with the traditional flow shop scheduling model, it verifies the feasibility and superiority of this model. The results show that, regarding the product blockage problem, this paper improves the MWH heuristic algorithm, leading to better quality of the initial population produced; and that it also proposes a new ISBOX crossover operator algorithm, which is used in combination with the nondominated solution information to calculate the new solution for offsprings, improving the local search capability of the algorithm. In order to address machine faults, this paper obtains new solutions by optimizing the maximum completion time and the early completion time, takes the new solutions as the initial population, and uses the proposed model to optimize the robustness and stability of the existing algorithm. By comparing the proposed model and the traditional scheduling model in terms of product blockage and machine fault, this paper finds that the proposed algorithm has high local and global convergence, and generates high-quality nondominated solutions. According to the re-scheduling strategy, this algorithm can effectively reduce the effects of product blockage and machine faults on the objective function.