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A number of jobs (trucks, airplanes...) arrive over time at a facility (terminal...). A job cannot be started before its arrival time. Each job has a due date by which its processing must be finished. The facility has a number of docks or machines. Each machine can handle at most one job at a time. For each job and machine combination, there is a value of this assignment, as well as a processing time of the job on the specific machine.
We would like to assign jobs to machines, and a sequence of jobs on the machine so that at most one job is assigned to a specific machine at a specific instance, and there is very little delay, and the value of the assignments is maximized;
Examples are: Assigning airplanes to gates at an airport, assigning trucks to docks at a freight terminal, and assigning manufacturing jobs to machines in a factory.
An extension, not considered here, is to allow a job to finish after its due date (be tardy), at a penalty;