A scheduling kernel fixes what a schedule is. It consists of a type of instances, each with a number of jobs, a type of schedules for every instance, and the feasibility predicate that belongs to the machine model itself (for instance, that a machine processes one job at a time). Every job has a release date; problems without release dates are those in which all release dates are $0$.

Every kernel reports, for each schedule and each job, a start time and a completion time. Times are nonnegative rational numbers, since a preempted job may be interrupted at any moment. Constraints and objectives are written against these two accessors only, so that one definition of, say, release dates applies to every kernel.