On a single machine and without release dates, a preemptive schedule can be turned into a non-preemptive one in which no job completes later: process the jobs one after the other from time $0$, in the order of their completion times (ties broken by start times and then by the numbering of the jobs). A job then completes at the total processing time of the jobs before it and itself, and the machine has processed these jobs entirely by the original completion time of the job, so this total is at most that time.

Hence a problem and the same problem with preemption allowed have the same decision versions when there is one operation per job, at most one machine, no release dates, the precedence constraints have zero lags, the objective depends monotonically on the completion times (every objective except the number of jobs not completed just in time), and there are no server, forbidden times, no-idle constraints or batch setups. Deadlines, machine sets, communication delays, no-wait and transportation delays may be present; with one operation per job on one machine the last three impose nothing more on the new schedule.

A specification $s$ reduces to $t$ by dropping preemption if it is of this kind, has no interruption or preemption, and the same specification with the other of the two is field by field a special case of $t$.

Theorem. A specification that reduces to another by dropping preemption describes a problem whose decision version reduces to that of the other.