An instance on parallel machines has $n$ jobs, $m$ machines, and a processing time $p_{ij}$ of job $j$ on machine $i$. A machine model on parallel machines is a kernel whose instances are of this form, together with the relation "at some time of schedule $\sigma$, job $j$ occupies exactly the set $S$ of machines". Non-preemptive and preemptive scheduling are two such models. A job may occupy several machines at once; the time it then needs is its largest processing time on these machines.

The following fields restrict the instances of every machine model.

The machine-environment field:

• identical machines: the processing time of a job is the same on every machine;
• uniform machines: there are a length $q_j$ for every job and a positive speed $s_i$ for every machine with $p_{ij} \cdot s_i = q_j$;
• unrelated machines: no restriction.

Processing times are integral, so uniform machines are represented with the time unit chosen fine enough that every quotient $q_j / s_i$ is an integer.

The processing-time field:

• unit: $p_{ij} = 1$;
• equal: there is a number $p$ with $p_{ij} = p$;
• one or two: $p_{ij} \in \{1, 2\}$;
• arbitrary: no restriction.

In the environment field each value is a special case of the next. Unit processing times are a special case of equal ones and of one or two, and every value of arbitrary ones.

Theorem. Over every machine model, the machine-environment and processing-time fields are sound.