This paper deals with the assignment of operators to machines on partially automated systems in which operators conduct several tasks such as loading, unloading, transportation and control. We assume that an operator can be assigned simultaneously to several machines and that the productivity of each machine depends on the operators' assignment. Consequently, the system's performance depends upon operators' assignment. We present in this paper the modelling of operators' assignment to machines. We formalize the problem and introduce a graph representing the problem. We calculate the number of all possible assignments of K operators on M machines (when K is smaller than M ) as well as the number of possible transitions. We consider three cases. In the first case, each operator can operate simultaneously on any group of X machines. In the second case, an operator can operate only on two successive machines. In the third case, we assume that an operator can operate simultaneously on any group of X consecutive machines.