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In the e-commerce era, efficient order fulfillment processes in distribution centers have become a key success factor. One novel technology to streamline these processes is robot-assisted order picking. In these systems, human order pickers are supported by autonomous mobile robots (AMRs), which carry bins for collecting picking orders, autonomously move through the warehouse, and wait in front of a shelf containing a requested stock keeping unit (SKU). Once a picker has approached a waiting AMR and placed the requested SKU into the respective bin, AMR and picker may separate and move toward other picking positions. In this way, pickers continuously move between different waiting AMRs without having to return to the depot. This paper treats the coordination of multiple AMRs and multiple pickers to minimize the makespan. We present a heuristic method for the deterministic case that can handle the requirements of large e-commerce fulfillment centers and successfully solves instances with more than one thousand picking positions. Based on the obtained solutions, the performance of our picking system is compared with the traditional warehouse setup without AMR support and to another work policy using fixed pairings of picker and AMR per order. We find that largely improved makespans can be expected. In addition, we analyze the effects of stochastic picking times, speed differences between AMRs and pickers, and a zoning strategy. The ripple effect caused by stochastic picking times, in which a single delay may cascade through a tightly synchronized schedule and deteriorate picking performance, can be effectively mitigated by separating the workforce into smaller subgroups. Another important finding is that pickers and AMR should have approximately the same travel speed because slower AMRs deteriorate system performance. Finally, zoning slightly decreases the flexibility of the system and should be used if dictated by organizational reasons. History: This paper has been accepted for the Transportation Science Special Issue on Emerging Topics in Transportation Science and Logistics. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2023.1207. [ABSTRACT FROM AUTHOR]