  Robotic mobile fulfillment systems (RMFSs) are a new type of warehousing
system, which has received more attention recently, due to increasing growth in
the e-commerce sector. Instead of sending pickers to the inventory area to
search for and pick the ordered items, robots carry shelves (called "pods")
including ordered items from the inventory area to picking stations. In the
picking stations, human pickers put ordered items into totes; then these items
are transported by a conveyor to the packing stations. This type of warehousing
system relieves the human pickers and improves the picking process. In this
paper, we concentrate on decisions about the assignment of pods to stations and
orders to stations to fulfill picking for each incoming customer's order. In
previous research for an RMFS with multiple picking stations, these decisions
are made sequentially. Instead, we present a new integrated model. To improve
the system performance even more, we extend our model by splitting orders. This
means parts of an order are allowed to be picked at different stations. To the
best of the authors' knowledge, this is the first publication on split orders
in an RMFS. We analyze different performance metrics, such as pile-on,
pod-station visits, robot moving distance and order turn-over time. We compare
the results of our models in different instances with the sequential method in
our open-source simulation framework RAWSim-O.
