Abstract
In a general two-machine n-job scheduling problem, it is assumed that every possible sequence of jobs can be executed, so that whichever best served a given measure can be selected. This paper considers two more restricted cases in which certain orderings are prohibited, either by technological constraints or by externally imposed policy. In the first case, some of the decisions of a schedule have already been made and the schedule must be completed without altering what has been decided. In the second case, jobs are grouped into disjoint subsets within which a job order is specified, but which May be preempted between jobs. For each of these two cases, a rule is given for determining the sequence in which jobs are to be processed on the machines in order to minimize the total elapsed time.
