Online order picking has become one of the key issues for ensuring the service level of modern retail e-commerce. This paper studies the online order batching and batch assignment problem (OOBBAP) with multiple pickers of picker-to-parts warehouses. First, we establish a biobjective optimization model that minimises the total picking time and order response time. Then, an online order batching algorithm embedded with the sequencing algorithm and optimal path algorithm is designed to solve the model. Finally, we use retail e-commerce from China with data on 87,277 orders of an online shopping festival to examine the optimization results of the model. The optimization results of the key indicators are satisfactory. The optimization rates of the maximum order response time, average order response time, total picking time, average picking time of picking posts, picker total walking distance and average walking distance are between 7.45% and 30.20%. The model demonstrates an excellent ability to solve the OOBBAP in multiple picker warehouses, which can provide a reference solution for similar picking problems in picker-to-parts retail e-commerce warehouses.