The problems on parallel machines form one family over the machine model with pieces: its fields are the interruption field and the fields of parallel machines (machine environment, number of machines, number of jobs, processing times, machine sets, release dates, deadlines, precedence constraints with time lags, communication delays, a server, forbidden times and the input encoding), and its objectives are the completion-time objectives. The entry $\mathrm{pmtn}$ of the three-field notation is the value preemption of the interruption field, the entry restarts the value restarts, and no entry the value none. The value preemption without migration has no machine model of its own.

A problem of the non-preemptive, the preemptive, or the restarts machine model determines the problem of this family with the same values in the common fields and the corresponding value of the interruption field.

Theorem. The two problems are special cases of each other, so that the family describes the problems of the three machine models faithfully. In the family, a specification that is field by field a special case of another describes a special case of the other's problem, and a specification that reduces to another, directly or through flow time, describes a problem whose decision version reduces to that of the other.