This paper presents a simulation-based analysis of a service robot operating in a robot-centred FMC, in which the robot is located at the approximate centre of the cell and the machines are arranged in a partial circle around it. The robot's function is to locate and service the parts, which require a series of unloading, moving, and loading operations. The main purpose of the study is to determine the best movement decision for the robot when it becomes free, where multiple products with different but similar operation sequences are processed. The results from the study, based on both statistical and non-statistical analyses, suggest the best policy for the robot movement that holds promise for application to the robot-centred FMC.