Automated material handling systems are usually characterised by robotic cells that result in the improvement of the production rate. The main purpose of this research is to study the scheduling of a rotationally arranged robotic cell with the multi-function robot (MFR). This special class of industrial robot is able not only to transfer the part between two adjacent processing stages but also to perform a special operation in transit. Considering MFR for material handling and operation, the objective function of the research here is the maximisation of production rate, or equivalently the minimization of the steady-state cycle time for identical part production. This problem is modelled as a travelling salesman problem to give computational benefits with respect to the existing solution methods. Then, the lower bound for the cycle time is deduced in order to measure the productivity gain of two practical production permutations, namely uphill and downhill permutations. As a design problem, a preliminary analysis initially identifies the regions where the productivity gain of a regular multi-function robotic cell is more than that of the corresponding single-function robotic cell for both small- and large-scale cells. The conclusion shows the suggested topics for future research.