Abstract: Flexible robotic cells combine the capabilities of robotic flow shops with those of flexible manufacturing systems. In an m-machine flexible cell, each part visits each machine in the same order. However, the m operations can be performed in any order, and each machine can be configured to perform any operation. We derive the maximum percentage increase in throughput that can be achieved by changing the assignment of operations to machines and then keeping that assignment remains constant throughout a lot's processing. We find that no increase can be gained in two-machine cells, and that the gain in three- and four-machine cells each is at most 14-2/7%.