During the last decade, several retailers have started to combine traditional store deliveries with the fulfillment of online sales to consumers from omni-channel warehouses, which are increasingly being automated. A popular option is to use autonomous mobile robots (AMRs) in collaboration with human pickers. In this approach, the pickers' unproductive walking time can be reduced even further by zoning the storage system, where the pickers stay within their zone periphery and robots transport order totes between the zones. However, the robotic systems' optimal zoning strategy is unclear: few zones are particularly good for large store orders, while many zones are particularly good for small online orders. We study the effect of no zoning (NZ) and progressive zoning strategies on throughput capacity for balanced zone configurations with both fixed and dynamic order profiles. We first develop queuing network models to estimate pick throughput capacity that correspond to a given number of AMRs and picking with a fixed number of zones. We demonstrate that the throughput capacity is dependent on the chosen zoning strategy. However, the magnitude of the gains achieved is influenced by the size of the orders being processed. We also show that using a dynamic switching strategy has little effect on throughput performance. In contrast, a fixed switching strategy benefiting from changes in the order profile has the potential to increase throughput performance by 17% compared to the NZ strategy, albeit at a higher robot cost.