This paper presents a collection of path planning algorithms for real-time movement of multiple robots across a Robotic Mobile Fulfillment System (RMFS). Robots are assigned to move storage units to pickers at working stations instead of requiring pickers to go to the storage area. Path planning algorithms aim to find paths for the robots to fulfill the requests without collisions or deadlocks. The state-of-the-art path planning algorithms, including WHCA*, FAR, BCP, OD&ID and CBS, were adapted to suit path planning in RMFS and integrated within a simulation tool to guide the robots from their starting points to their destinations during the storage and retrieval processes. Ten different layouts with a variety of numbers of robots, floors, pods, stations and the sizes of storage areas were considered in the simulation study. Performance metrics of throughput, path length and search time were monitored. Simulation results demonstrate the best algorithm based on each performance metric.