Two-machine Scheduling under Arbitrary Precedence Constraints

Suppose jobs, in the Johnson's two-machine n-job flow-shop scheduling problem, are grouped into disjoint subsets within which a job order that may not be preempted is specified. Furthermore, suppose that a precedence relation between these subsets is given such that the processing of a subset must be completed, on each machine, before the processing of another subset begins on the machine. This paper considers a problem to fmd a sequence in which jobs are to be processed on the machines in order to minimize the total elapsed time, under such general precedence constraints, from the start of the first job on machine I until the end of the last job on machine 11. An efficient algorithm to obtain an optimal sequence is given and a simpl(, example is shown.