On batch scheduled multiple mobile robots cluttering a workspace

The problem of operating multiple mobile robots in a common workspace is studied using, batch scheduling of the robot tasks with a view to answering the question: "Are k+1 robots better then k?". Our model which has a time complexity which is doubly exponential gives an affirmative answer in the absence of economic considerations but with a simple economic model gives optimal finite values for the number of robots that can be profitably operated in the workspace. The approximations used are discussed and the results compared with a simulation. Finally, the batch and list scheduled modes of operation will be compared.