The crude protein purification automated workstation has recently resolved the bottlenecks induced by manual operations, paving the way for high-throughput protein biomanufacturing. However, its three interacted constraints consisting of batch processing machines, limited buffer, and transportation present challenges for systematic scheduling. Here, we develop a triply-constrained flow shop model, enabling optimization in scheduling the crude protein purification automated workstation. A batching genetic algorithm is designed, where the flexible decoding resolves contradictions between the triple constraints, and the hybrid population initialization enhances performance by incorporating flow-shop heuristic and batching branch-and-bound. Computational experiments are conducted on 27 instances of varying problem scales ranging from small to large, demonstrating a notable 9.18 % reduction in makespan and enhanced stability when compared to three advanced meta-heuristics. Furthermore, the mechanism of how batching settings, including capacities and layouts, impact the makespan is revealed, offering managerial insights. This marks the first demonstration of modeling and scheduling crude protein purification automated workstations, signifying a significant advancement in biomanufacturing systems.