Given are m identical machines, each of which performs the same N operations Oi, 1 ⩽ i ⩽ N, cyclically and indefinitely, i.e. a production run on a machine looks like O1, O2,..., ON, O1, O2,..., ON, O1,.... There are ni ⩽ m tools available to perform operation Oi. The tools are transported between the machines by means of an infinitely fast transport device. Given a particular transport policy we prove the existence of stationary cyclic behaviour, determine the corresponding cycle time, and investigate the long run behaviour of the system starting from a given initial state.
