Globalization is heaving its impact on many field. For the field of warehousing this development, in combination with the actual shortage of labor, means that many warehouse owners are forced to reduce their warehouse costs in order to stay competitive with warehouses in low-wage countries. On the other side the warehouse owners are pulled by recent technical innovations, which have reduced the drawbacks of automation. One of these recent innovations, is the mobile fulfillment unit-to-unit order picking system, which is presented in this paper. To make this system more affordable and hence to increase the competitiveness of warehouses in western Europe, research is required optimizing each of the system parts. This research focuses on the order processing part of the system, which has changed considerably compared to existing mobile fulfillment order picking systems. In this system units are brought to two sides of a stationary order picker, who then transfers products from one unit to another unit. The order processing problem covers the sequencing of the unit visits at the order picking station, the batching of these units and the determination of the products that should be transferred. Using insights from literature, several approaches are proposed to each of the problem parts. Each of these approaches is then tested and validated. Combining the approaches for each problem part leads to solutions addressing the full problem. All these solutions are tested against each other using a data set of one day of an existing warehouse. The tests are executed for multiple different order picking station configuration and for multiple data set sizes. This leads to an overview of the effectiveness of each of these solutions in terms of computational time and the reduced number of AGV visits. From the results several conclusions can be drawn concerning the optimal solution for a specific warehouse. For an example warehouse in the Netherlands, a significant reduction of 25% can be obtained, regarding the number of visits, compared to the baseline approach. Which means the required number of AGVs can be lower, the investment costs for this system can be reduced and hence the competitiveness for this warehouse can be increased by implementing one of solutions presented in this paper.